Light-absorbing organic atmospheric particles, termed
brown carbon, undergo chemical and photochemical aging processes during
their lifetime in the atmosphere. The role these particles play in the
global radiative balance and in the climate system is still uncertain. To
better quantify their radiative forcing due to aerosol–radiation
interactions, we need to improve process-level understanding of aging
processes, which lead to either “browning” or “bleaching” of organic
aerosols. Currently available laboratory techniques aim to simulate
atmospheric aerosol aging and measure the evolving light absorption, but
they suffer from low sensitivity and precision. This study describes the use of
electrodynamic balance photophoretic spectroscopy (EDB-PPS) for high-sensitivity and high-precision measurements of light absorption by a single
particle. We demonstrate the retrieval of the time-evolving imaginary part of
the refractive index for a single levitated particle in the range of
10-4 to 10-5 with uncertainties of less than 25 % and 60 %,
respectively. The experimental system is housed within an environmental
chamber, in which aging processes can be simulated in realistic atmospheric
conditions and lifetimes of days to weeks. This high level of sensitivity
enables future studies to explore the major processes responsible for
formation and degradation of brown carbon aerosols.
Introduction
Most radiative transfer schemes in climate models treat organic aerosol, a
major subset of atmospheric aerosols that comprise 20 %–90 % of the total
particulate mass (Kanakidou et
al., 2005; Zhang et al., 2007), as non-absorbing in the UV–vis wavelength
range, attributing them with a negative (cooling) radiative effect. However,
light-absorbing organic aerosol, termed brown carbon (BrC), with wavelength-dependent light absorption (λ-2-λ-6) in the UV–vis
wavelength range
(Chen
and Bond, 2010; Hoffer et al., 2004; Kaskaoutis et al., 2007; Kirchstetter
et al., 2004; Lack et al., 2012b; Moosmuller et al., 2011; Sun et al.,
2007), may be the dominant light absorber downwind of urban and
industrialized areas and in biomass burning plumes
(Feng
et al., 2013). Recently, it has been shown that including BrC absorption
properties in radiative transfer models leads to a stronger wavelength
dependency of light absorption by aerosols and to significant changes in the
overall effective radiative forcing from aerosol–radiation interactions
(ERFari)
(Feng
et al., 2013; Lack and Cappa, 2010). Atmospheric aging processes of organic
aerosol can lead, through complex mechanisms, to formation of light-absorbing compounds (“browning”) or to their degradation (“bleaching”). The
accurate characterization of these processes is one of the main open
questions in atmospheric chemistry research and has been the focus of many
recent studies (see Laskin et al., 2015, for a review).
Although significant advances have been made, the contribution of BrC to
anthropogenic radiative forcing still poses significant uncertainty. The
estimated ERFari attributed to BrC is 0.1 to 0.25 W m-2, offsetting 10 %
to 25 % of the global mean aerosol cooling effect (-1.1-1.95-0.1 W m-2)
(Bond
et al., 2013; Brown et al., 2018; Feng et al., 2013; Myhre et al., 2013). On
a regional scale surrounding megacities and industrial areas, this value
may be up to an order of magnitude higher
(Feng
et al., 2013), which nearly doubles the local warming effect caused by the
increase in the CO2 concentration. For this reason, it is imperative to
(i) better understand the formation and degradation of BrC aerosols
resulting from chemical and photochemical aging processes
(Dasari
et al., 2019; Drozd and McNeill, 2014; Hems and Abbatt, 2018; Lambe et al.,
2013; Lee et al., 2013, 2014; Marrero-Ortiz et al., 2019; Powelson et al.,
2014; Romonosky et al., 2015; Saleh et al., 2014; Schnitzler and Abbatt,
2018; Zhao et al., 2015; Zheng et al., 2013), (ii) quantify the BrC
wavelength-dependent light absorption, and (iii) identify the main molecular
species responsible for this absorption.
Laboratory studies simulating BrC formation and degradation mechanisms
generally take one of two approaches to quantify wavelength-dependent light
absorption in the UV–vis wavelength range, which is described using the
imaginary part (κ) of the complex refractive index (CRI; m=n+iκ). The first approach uses bulk liquid phase or gas–liquid multiphase
experiments to simulate atmospheric chemical processes. This is then
followed by UV–vis spectroscopy absorption measurements
(Nguyen
et al., 2012; Nozière et al., 2010; Nozière and Córdova, 2008;
Updyke et al., 2012). The advantages are high sample volume available for
analysis and the extremely high sensitivity of UV–vis absorption
spectroscopy. The disadvantage is that supersaturated conditions often
encountered in atmospheric aerosol particles are impossible to generate in a
bulk volume. This is an important disadvantage of the bulk approach as
chemical activity, viscosity, and diffusivity under supersaturated conditions
may alter the chemical aging significantly.
The second approach uses an environmental chamber, reactor, or flow tube to
reproduce atmospheric processes. In this context, particles are generated by
aerosolization into the experimental volume or by gas-phase chemistry
leading to reduced volatility of precursor compounds with subsequent
gas-to-particle conversion. These aerosols are then subjected to chemical or
physical aging processes using radiation, relative humidity, and reactive
gaseous components. The aged material may then be collected on filter
substrates, extracted with a liquid solvent, and analyzed by UV–vis
spectroscopy. Alternatively, aerosols may be measured with a suite of
particle-ensemble, flow-through optical methods, such as cavity-enhanced and
photoacoustic spectroscopy, for both direct and indirect measurements of
light absorption
(Flores
et al., 2014a, b; He et al., 2018; Nakayama et al., 2013). To maintain
particle size and concentration high enough for analysis using these
techniques and to simulate atmospheric exposure of up to several days,
precursor concentrations often far exceed those of the ambient atmosphere.
This difference in environment between the reactor and the real atmosphere
may affect the final distribution of products after multi-generation
chemical aging, which may lead to misleading interpretations of the
experimental results. An advantage of the optical instruments compared with
the filter extraction techniques is the independence from solubility,
extraction efficiency, and solvent matrix effects. Additionally, particles
are measured in situ and with higher time resolution. Disadvantages are the
relatively low sensitivity to absorption and, for some instruments, the
frequent need for calibration (Lack et al.,
2012a). As a result, κ for BrC aerosols is often reported with
values near the limit of quantification of the retrieval technique or
actually conflicts with results from analyses of similar chemical systems
(Liu
et al., 2013, 2012; Nakayama et al., 2013; Ofner et al., 2011) and with
uncertainties that can exceed 100 %
(Bluvshtein
et al., 2016; Flores et al., 2014a, b; He et al., 2018; Lack et al.,
2012b; Lavi et al., 2013; Nakayama et al., 2010, 2013; Trainic et al., 2011;
Washenfelder et al., 2013).
To make significant progress, reduce uncertainties, and resolve
contradictions, this study aims to extend the approach of electrodynamic
balance photophoretic spectroscopy (EDB-PPS) for high-sensitivity and high-precision measurements of UV–vis light absorption by a single particle, in
an environmental chamber, exposed to realistic atmospheric aging processes.
Photophoresis describes the optical forces acting on an illuminated
particle. Direct photophoresis (or “radiation pressure” force,
Frp), always in the direction of light propagation (away from the light
source), and indirect photophoresis (Fph), a less recognized force,
central to this work, that strongly depends on the absorption of light.
Unlike radiation pressure, indirect photophoresis is a result of an uneven
temperature distribution on the surface of the particle resulting from
absorption. It acts through momentum transfer with the surrounding gas
molecules, and thereby it is temperature and pressure dependent. To resolve
the direction (away from or towards the light source) and the magnitude of
the indirect photophoresis force, one needs to determine the internal
electric field distribution (Bohren,
1983; Mackowski, 1989). Pope et al. (1979)
and Arnold et al. (1980) conceived the idea of
PPS on a single levitated particle and described the spectrally dependent
ratio of the measured photophoretic force to the gravitational force on the
particle. Building upon their seminal work with the following developments in
the mathematical description of indirect photophoresis
(Beresnev
et al., 1992; Mackowski, 1989; Rohatschek, 1995), computational advances in
Mie theory, and internal field calculation
(Mackowski and Mishchenko, 2011), we extend the use of
PPS. Here we describe how PPS can be used for high-sensitivity retrieval of
the imaginary part of the refractive index of organic aerosol proxy
particles levitated in an environmental chamber EDB and subject to aging
processes. The EDB is a well-established tool in atmospheric science, used
for the study of thermodynamic and chemical properties of single levitated
particles
(Krieger
et al., 2000; Steimer et al., 2015; Tang and Munkelwitz, 1994; Zardini et
al., 2008). Its high sensitivity to changes in the net vertical force acting
on the particle makes it ideal for measurements of photophoresis, i.e., the
miniscule optical forces acting on the levitated particle as a result of its
interaction with light. With this approach we gain from combining the
advantage of light absorption sensitivity nearing that of bulk UV–vis
measurements with the advantage of studying chemical processes in the
particle phase (accessible supersaturated conditions) in an environmental
chamber able to simulate a wide range of atmospheric conditions. This could
contribute to the study of light absorption evolution during atmospheric
aging of BrC aerosols.
Schematic diagram of the experimental setup. (a) Measurement of
high-resolution elastic light scattering at 90∘ by illuminating the particle
with a 765–781 nm TDL. (b) Continuous illumination of the particle with a
red light-emitting diode (LED) used for the active feedback adjustment of
the DC voltage and alternating illumination with the 473 nm laser used to
impose vertical optical forces on the particle.
ExperimentalElectrodynamic balance
Over 100 years ago Robert Millikan and Harvey Fletcher, in their famous oil
drop experiment, showed that tuning the electric potential between two
capacitor plates, required to levitate a charged particle, can be used as a
balance with a sensitivity of about 10-13 g. Today, the electrodynamic
balance (EDB) is an established tool used to derive thermodynamic and
physical information of a single, levitated particle. The EDB used in this
study (Fig. 1) is based on the double-ring design characterized by Davis
et al. (1990) and described in
previous publications
(Colberg et al., 2004;
Steimer et al., 2015). Only a brief description follows. The EDB is hosted
within a 180 cm3 environmental chamber, which allows temperature and
pressure regulation with precision of ±0.02 K and ±2 hPa. Mass
flow controllers are used to regulate gas flow rate and composition to 5 cm3 min-1
of dry N2. A single-droplet generator (Hewlett-Packard 51633A ink jet
cartridge) is used to inject an electrically charged diluted aqueous
solution of the sample material to the center of the trap. After complete
loss of water, the resulting particle (typically 7–13 µm in radius)
is balanced by a DC voltage that is regulated with a 25 Hz automated video
feedback loop. The DC voltage (U) that is applied between the EDB endcap
electrodes, to hold the particle in the center of the trap, is proportional
to the net vertical force acting on the particle. A sensitivity on the
applied DC voltage as low as 0.01 % is equivalent to changes in mass in
the range of 10-13 to 10-12 g depending on the particle's size and
density. This is commonly used to measure small changes in particle mass due
to loss or uptake of gaseous components by the particle
(Steimer
et al., 2015; Tang and Munkelwitz, 1994; Zardini et al., 2008). In this
study, we alternately illuminate a suspended particle with a 473 nm, 33 mW mm-2 (±15%) diode laser (Laser Quantum, gem 473) at 25 %
duty 40 s cycles (Fig. 1b). Variations in the DC voltage from “laser
off” to “laser on” (Fig. 2, ΔU/U0) in each cycle were used to
measure changes in the net vertical force induced by illumination of the
particle:
ΔUU0=Uon-UoffUoff=Fph+FrpFg+Fs.
Here, Fph and Frp are the indirect photophoretic and radiation
pressure forces. The subscripts “on” and “off” relate to the light source.
Gravity (Fg) and Stokes drag (Fs) caused by the gas flow are
constant at the timescale of the measurement, and are given by
2Fg=43πa3ρpg,3Fs=6πaηqvCcS,
where a and ρp are radius and mass density of the levitated
particle, g is the standard acceleration due to gravity, η is the gas
dynamic viscosity, qv is volumetric flow rate, S is a characteristic flow
cross section, and Cc is the Cunningham slip correction factor
(Kim et al., 2005). This
formulation enables the direct measurement of the sum of the optical forces
(Fph+Frp), which are related to the particle size and CRI.
After determining the particle size and the real part of the refractive
index n (Sect. 2.2.), the sum Fph+Frp is iteratively
calculated by varying κ to minimize the difference between the
measured and calculated ΔU/U0.
Change in the applied DC voltage in response to alternately
illuminating a trapped light-absorbing particle. Here, a particle with 12.72 µm radius and κ≈1.36×10-4 was levitated in 400 mbar of dry nitrogen. For
more details on how the particle size and imaginary part of the CRI were
determined, refer to Sects. 2.2 and 3.
The following section describes how the particle size and real refractive
index are determined from high-resolution light-scattering measurements, and
Sect. 2.3 describes how Fph+Frp is finally calculated and used
to retrieve the imaginary part of the CRI.
Determination of size and real refractive index
Mie resonance spectroscopy is used to simultaneously retrieve the particle's
radius (a) and real part (n) of the CRI defined as
a=λx2π,
and
nλ=nD+m11λ2-1λD2.
Here, n(λ) is the wavelength-dependent real refractive index,
nD is the refractive index at the sodium D line, m1 is a dispersion
coefficient, and x is the size parameter. Polynomial regression parameters
between the refractive index and size parameter of transverse electric (TE)
and transverse magnetic (TM) mode resonances were calculated
(Lam et al., 1992;
Preston and Reid, 2013, 2015) and a look-up table of these parameters was
generated for all possible TE and TM resonances with order numbers of 3 to 8
and mode numbers of 26 to 180. We obtained high-resolution spectra by
illuminating the levitated particle with a tunable diode laser at both
parallel and perpendicular linear polarizations (tunable diode laser – TDL, New Focus, model
Velocity 6312) in the range λ=765–781 nm and recording the
elastic light scattering at a π/2 angle (Steimer et
al., 2015) (Figs. 1a, 4). Then, a, nD, and m1 are retrieved by
minimizing the sum of absolute values of the differences between measured
and calculated wavelengths of the Mie resonances over the three-dimensional
parameter space.
Photophoretic spectroscopy
Direct photophoresis or radiation pressure is readily calculated from
Frp=Qext-Qbsπa2Ic,
where I is the radiant flux density (W m-2) and c is the speed of
light. Qext and Qbs are Mie extinction and backscattering
efficiencies (unitless). We use the Mie MATLAB functions developed by
Mätzler (2002) to calculate the efficiencies.
Indirect photophoresis (Fph) is directed away from the light source for
a highly absorbing particle (positive photophoresis) but towards the light
source for low absorptivity (negative photophoresis). This is a result of
the structure of the internal electric field within a spherical particle
interacting with radiation. Multiple refractions and internal reflections
lead to size-dependent, nano-focusing of the incident beam within the
particle volume. For particles larger than the wavelength of the incident
light, the energy is “focused” closer to the non-illuminated side of the
particle. In highly absorbing particles, however, most of the energy is
absorbed by the illuminated hemisphere of the particle, heating it more than
the “dark” hemisphere. Therefore, a key parameter determining the
direction and amplitude of Fph is the temperature asymmetry parameter
(J), resulting from the uneven internal electric field and, consequently,
uneven temperature distribution (Yalamov et al., 1976).
To calculate J, one can use an integration of the source function over the
particle volume:
Jx,m=3nκx∫01∫-11Bt,μt3μdμdt.
Here B(t,μ) is the dimensionless electric field distribution inside the particle, and
t (fraction of a) and μ=cosθ are the spherical
coordinates. Simply put, J indirectly describes the temperature gradient
between the illuminated and the dark side of the particle surface.
Unlike radiation pressure, Fph acts through the presence of gas
molecules around the illuminated particle. Impaction and reflection of the
surrounding gas molecules, and consequent momentum transfer with the
particle's surface, are temperature dependent and thus lead to a net force
directed from the warmer to the colder particle hemisphere. Indirect
photophoresis is also strongly pressure (p) dependent. It reaches its maximum
value at pressures where the Knudsen number (Kn=L/a) is around unity,
i.e., where the gas mean free path (L) is comparable to the radius of the
particle (a). In the free molecular regime, i.e., Kn≫1, Fph is proportional to p, whereas in the continuum regime, i.e., Kn≪1, Fph is inversely proportional to p. Rohatschek (1995) provided a pressure-dependent model of Fph interpolating previous
formulations at the two pressure regime limits. His approach provides a
convenient estimate of Fph between the free molecular and continuum
limits:
Fph=2Fmaxp/pmax+pmax/p,
with
9Fmax=Da2JIkpαT2,10pmax=D3Tπa2αT,
where αT is the thermal accommodation coefficient, kp is the
particle thermal conductivity, and T is the gas temperature away from the
particle surface. Further, D relates to gas phase parameters as follows:
D=πc^η2TπCs3,
where Cs is the thermal slip coefficient and c^ is the mean
thermal velocity of the gas molecules
c^=8RTπM,
in which R is the gas constant and M is the gas molar mass.
Our experimental setup (particle radius of 7–13 µm and pressure
range of 400–800 hPa) is limited to Kn=0.0075–0.03. We are therefore
constrained to a transition flow regime referred to as the slip-flow regime
(typically 10-2 < Kn < 10-1), where Fph
deviates significantly from Rohatschek's interpolation. Mackowski (1989) presented an analytical solution of
the spherical geometry heat conduction equation in three dimensions for
calculating Fph in the slip-flow regime by adding a tangential velocity
slip boundary condition (also referred to as thermal stress slip flow) to
the continuum regime solution of Yalamov et al. (1976):
Fph=-4πCsη2IaJρgkpT1+3CmKn1+2CtKn+2kgkp-1.
The momentum exchange coefficient is taken as Cm=1.175±0.175
(Reed, 1977), while the thermal slip (Cs)
(Ivchenko et al., 1993) and temperature jump
(Ct) (Loyalka, 1968) coefficients
14Cs=320.4375+0.2084αT0.856+0.1092αT,15Ct=5182-αTαT1+0.1621αT,
are functions of the thermal accommodation coefficient αT. Here
we used a value of αT=0.85±0.15 to accommodate a range of
values published for a variety of materials
(Ganta
et al., 2011; Li et al., 2001; Shaw and Lamb, 1999; Trott et al., 2007). It
was shown that with increased absorption (i.e., steep interface temperature
jump) or decreasing particle size, Eq. (14) deviates from experimental
measurements (Mackowski, 1989;
Soong et al., 2010). A solution to this problem was presented by Soong et
al. (2010), who adopted a modified slip boundary condition
from Lockerby et al. (2004). The authors
developed the following correction to Mackowski's solution:
Fph_corr=Fph1+2CmKnCs.
From Eq. (16) it is clear that at Kn≪1 the correction
factor approaches unity. For the purpose of this study, i.e., low
absorptivity particles and Kn=0.0075–0.03, the correction is small, but
we nevertheless apply it in our evaluation and term the corrected
photophoretic force hereafter Fph.
Indirect photophoretic force calculated with the Rohatschek (1995)
approximation at the full pressure range (gray line), Mackowski (1989)
analytical solution (dashed line), and Soong et al. (2010) correction (solid
line) for a slightly absorbing particle with radius of 10 µm, T=20∘C,
m=1.466+i10-4,
λ=473 nm, I=35 mW mm-2
and full thermal accommodation. The black rectangle and the insert plot show
the pressure range that is possible with our experimental system.
As mentioned above, J is the key parameter linking the particle's CRI to
Fph. Mackowski (1989) also presented an
expression for J by analytical integration of Eq. (7):
J=-6nκm2x3Im∑N=1∞NN+2mcN+1cN∗RNCN+dN+1dN∗RN+1CN∗-NN+2N+1cN+1cN∗CN+dNdN+1∗CN∗+2N+1NN+1dNcN∗SN,
where the coefficients CN, RN, SN, cN, and dN are
18CN=N+1mx-ψN′mxψNmx,19RN=ImmCNImm2,20SN=i2Imm2xm+m∗CN2-m+2N+1Rem2mRN+2N+1m∗CN2RN+1,21cN=ψNmxc̃N,22dN=ψNmxd̃N.
Here, c̃N and d̃N are the Mie coefficients for the
internal field, computed using the MATLAB Mie routines by Mätzler (2002), and ΨN is the Ricatti–Bessel function of the order of
N. For clarity, the prime denotes the differentiation with respect to the
argument in brackets and the superscript * denotes the complex conjugate.
Figure 3 shows Fph calculated with the above three models over a wide
pressure range extending from the free molecular to the continuum flow
regimes. From Eq. (13) and Fig. 3, one can show that Mackowski's
formulation equals Rohatschek's solution at the continuum limit (i.e.,
Kn≪1) only for particles that are good heat conductors
compared with the surrounding gas (i.e., kg/kp≪1).
For applications involving slightly absorbing (κ≤10-3)
micron-sized, organic particles, the indirect photophoretic force is
generally 1–2 orders of magnitude larger than radiation pressure but about
2–3 orders of magnitude lower than gravity. High sensitivity and stability
of the EDB is therefore imperative for high-sensitivity retrieval of
κ from EDB-PPS measurement.
Results and discussion
To test the methodology a slightly absorbing organic particle with known CRI
and thermal properties is required. For this purpose, we selected PEG400
(polyethylene glycol with mean molecular weight of ≈400 g mol-1) as a proxy. PEG400 has the advantage of being an organic,
non-volatile liquid, miscible with water (needed for injection of a droplet
into the EDB). Additionally, PEG400 has well-characterized optical and
thermodynamic properties
(Francesconi
et al., 2007; Han et al., 2008; Marcos et al., 2018; Reyes et al., 2000),
which we assume to be unchanged by addition of 0.23 wt % (0.19 % mole)
of carminic acid (CA, Sigma-Aldrich). The imaginary part of the refractive
index for this PEG400-CA solution κ=(1.394±0.05)×10-4 was determined with a simple Beer–Lambert setup composed
of the 473 nm laser introduced in Sect. 2.1, a 1 mm cuvette, and a power meter
and using the following relations (Sun et al., 2007):
23A=log10I0I=αL,24α=4πκλ,
where A is the optical attenuation or absorption of a bulk sample with an
optical path length L and attenuation coefficient α at wavelength
λ. Combining Eqs. (23) and (24) leads to
κ=Aln10λ4πL.
High viscosity of the PEG400 (105–130 mPa s at 293 K; Merck) leads to
slight heterogeneity of the liquid in the cuvette. For this reason, we
repeated these spectroscopic measurements with the laser beam (< 1 mm
in diameter) crossing the cuvette at different positions on its surface.
This led to the 3.6 % uncertainty in the value of κ stated above.
Measured Mie scattering spectra at π/2 angle of a levitated
particle. The positions of the TE and TM resonance modes (e.g.,
TMnl; identified by their order (l) and
mode (n) numbers) were used to retrieve the particle's real refractive index
(nD=1.4665, m1=2745) and size (a=9.2906µm). We
note that the lower-order modes in the fitted TE spectrum are too narrow to
be observed in the measured spectrum with the current resolution. Residual
noise in the measured spectrum originates mostly from laser power
oscillations due to frequency scanning operation and from horizontal
oscillation of the particle due to the applied AC field.
A droplet with 3 % wt of the PEG400-CA solution in water was injected into
the EDB under dry N2 flow as described in Sect. 2.1. Following size
stabilization and water evaporation, high-resolution Mie resonance spectra
were measured to determine the particle real part of the CRI (nD=1.4665, m1=2745) and size (a=9.2906µm). Figure 4
shows the measured TE and TM mode spectra and the fitted resonance peaks
along with their identification by order (l) and mode (n) numbers. Figure 5
shows the response of the EDB to changes in the net vertical force due to
illumination of the levitated particle (ΔU/U0) at different
pressure values within the range of our experimental setup. Also shown in
Fig. 5 is the response calculated using the three models described in
Sect. 2.3. It is clear that both the Mackowski and the Soong formulations,
which are barely distinguishable within the resolution of Fig. 5, fit the
measured data very well, whereas the Rohatschek interpolation, which assumes
kg/kp≪1
and does not account for slip-flow conditions, overestimates the response.
The error bars on the measured data represent the standard deviation over
five illumination cycles and the gray shaded area represents the uncertainty
propagated through the Soong model calculation. The major contributor to the
latter is a 15 % uncertainty on the radiant flux, which is measured in our
experiment with a power meter (nova-display, Ophir Optronics LTD) and a beam
profiler (CMOS-1.001-Nano, CINOGY Technologies GmbH).
Measured and simulated EDB response (ΔU/U0) to the
illumination of a slightly absorbing particle due to the photophoretic
effect. The two analytical solutions Mackowski (1989) (dotted line) and Soong
et al. (2010) (solid line) that account for slip-flow conditions agree well
with our measurements (empty circles). Error bars: standard deviation over
five illumination cycles. Gray shaded area: measurement uncertainty
propagated through the Soong model calculation, dominated by the 15 %
uncertainty on the radiant flux measured with a power meter and a beam
profiler.
It is important to note that as expected, for a pure PEG400 particle (i.e.,
no measurable absorption at 473 nm) at similar conditions, but a slightly
less sensitive setup, no signal could be detected.
Thermal conductivity (W m-1 K-1) of organic compounds from Latini et al. (2014) and references therein.
Number ofMeanStandardStandarddata setsvaluedeviationdeviation (%)Alcohols7750.14820.025617.3Alkanes10250.12590.018214.5Alkenes1350.13010.024418.7Aromatics5700.11740.018015.3Carboxylic acids3180.15760.042727.1Cycloalkanes350.12620.013410.6Cycloalkenes100.13030.01048.0Esters2360.12610.017914.2Ethers1110.12680.018114.3Ketones1850.14170.020314.3
To further demonstrate the potential of the EDB-PPS approach in determining
the imaginary RI with high sensitivity and precision, an additional particle
from the same PEG400-CA batch, with a radius of 12.858 µm was levitated
and the response of the EDB to change in the net vertical force was recorded
over about 16 h of illumination cycles. To take advantage of the inverse
pressure dependence of the photophoretic effect, this experiment was
conducted at 400 hPa, which is at the lower limit of our experimental setup. Figure 6 shows the measured ΔU/U0 and the point-by-point
retrieved κ, which decreases from about 1.25×10-4 to
about 0.06×10-4 over the laser on time (i.e., 25 % of
the total experiment time). Both traces demonstrate a decay feature as a
result of slow photolysis of the CA (Jørgensen
and Skibsted, 1991). The initial retrieved value κ=(1.251-0.213+0.315)×10-4 is about 20 % lower than the
value retrieved from the bulk cuvette experiment κ=(1.394±0.05)×10-4 but with overlapping uncertainty range. The
overall uncertainty in retrieved κ demonstrated in Fig. 6b is
estimated to be up to 25 % for κ≈10-4 and up to 60 %
for κ≈10-5. The gray shaded area on the ΔU/U0 plot (Fig. 6a) is the uncertainty in each ΔU/U0 data
point determined from the standard deviation on the value of U averaged
during laser off and laser on stages of each individual illumination
cycle. These experimental uncertainties, with values of 2×10-5-10×10-5 (unitless) together with point-by-point
variability of up to ±10-4, are a result of the sum of
system instabilities. These are independent of the value of ΔU/U0 and are a significant component limiting the sensitivity to
κ of this experimental approach. The experimental uncertainty
contributes up to 10 % uncertainty on the value of the retrieved κ
for values down to κ≈2×10-5 and about 30 % for
κ<2×10-5. The uncertainty on the radiant flux used in the
model calculation is the major limiting factor for the sensitivity of the
experimental approach contributing about 15 % to the uncertainty of the
retrieved κ down to κ≈2×10-5.
(a) Decay of the EDB photophoretic response (ΔU/U0)
during illumination of a slightly absorbing particle (PEG400 with 0.23 %
wt of carminic acid; CA). The decay is due to the slow photolysis of the CA.
(b) The retrieved imaginary part of the complex refractive index. Gray
shaded area in both plots represents the uncertainty in the measured and
retrieved values.
Simulated signal (and uncertainty) for a PEG400 particle, 10 µm in radius at T=20∘C, P=400 mbar,
nD=1.466,
λ=473 nm, and I=35 mW mm-2
and full thermal accommodation with the increasing imaginary part of the CRI.
(a) Transition from negligible absorptivity and negative signal (i.e.,
dominated by radiation pressure) to positive signal (i.e., dominated by
negative indirect photophoresis). (b) Increasing absorptivity leads to an
increasing positive asymmetry parameter and stronger positive signal (i.e.,
negative indirect photophoresis). Additional absorptivity leads to an asymmetry
parameter of zero as the surfaces of the upper and lower hemispheres of the
particle are effectively at equal temperature. (c) Additional increase in
absorptivity leads to an increase in a negative asymmetry parameter and
stronger positive indirect photophoresis. (d) An illustration of the
positive and negative indirect photophoresis regimes. Black arrows represent
the various forces acting on a “strongly” (lower) and “slightly” (upper)
absorbing particle when illuminated with the laser beam (blue arrow).
We determine the overall sensitivity of this approach to the imaginary RI
(within the limitation of our experimental setup) to be in the range of 1×10-5–2×10-5. The accumulated uncertainty
of κ from all other parameters in Eqs. (14) and (17) is below
10 % for κ down to κ≈2×10-5. These
include uncertainties in the particle size, real part of the CRI, density,
and thermal properties. However, the major contributor to this uncertainty
is the range of selected values of the thermal accommodation coefficient
mentioned in Sect. 2.3. An uncertainty of 18 % on the thermal
accommodation coefficient (αT=0.85±0.15) propagates to 4 %–7 % uncertainty on the retrieved κ. This small contribution to
the overall uncertainty demonstrates the usefulness of the EDB-PPS approach
for the retrieval of the imaginary RI of organic particles with unknown
composition following accurate Mie resonance spectroscopy (for determination
of size and real RI) as long as assumptions of sphericity and homogeneity
hold.
Additional potential source for uncertainty in case the particle is composed
mostly of unknown or not well-characterized substances is the particle's
thermal conductivity. A solution would be to consider that many organic
compounds are very similar with respect to their thermal properties and use
an approximated value with an appropriate uncertainty. Latini et al. (2014) published a literature survey of 4740 thermal
conductivity data sets of organic compounds at atmospheric pressure and
reduced temperature of about 0.6±0.14. A partial list of the data
from this publication (excluding 1340 data sets of refrigerant compounds) is
presented in Table 1. The list clearly shows the similarity in thermal
conductivity for many organic compounds abundant in atmospheric aerosols.
Conclusions
This study demonstrates the usefulness of the electrodynamic balance –
photophoretic spectroscopy (EDB-PPS) technique to retrieve the imaginary
component of the complex refractive index of a slightly absorbing organic
particle levitated in an environmental chamber. We showed agreement between
measurements and model calculation and reliable retrieval of the imaginary
RI at a wavelength of 473 nm, in the range of 10-5≤κ≤10-4 with uncertainty of about 25 % for κ=10-4 and
60 % for κ=10-5. The major limiting factor for sensitivity
and precision within our setup is the uncertainty in the radiant flux.
In this study, we chose to emphasize the usefulness of EDB-PPS at the lower
range of κ due to availability of other, simpler to implement,
particle phase techniques suitable for retrieval of higher values of κ. Nevertheless, EDB-PPS is not limited to 10-5≤κ≤10-4. Figure 7 shows a simulated signal (ΔU/U0) over 6
orders of magnitude of κ, from 10-8 to 10-2, for a PEG400-based particle with a radius of 10 µm. At the lower end of this range
(left side of Fig. 7a) κ is effectively zero and the simulated
signal is negative (i.e., the particle moves away from the light source) due
to direct photophoresis (radiation pressure) alone. Note how, as κ
increases, the signal increases to positive values (Fig. 7a and b) due to
an increase in the thermal asymmetry parameter that results in negative
indirect photophoresis. With additional increase in κ, more energy
is absorbed on the illuminated side of the particle. This offsets the
hot spot of absorbed energy on the surface of the dark side of the
particle. As a result, the thermal asymmetry parameter and the magnitude of
the signal are reduced. As κ continues to increase, the asymmetry
parameter changes sign from positive to negative as the illuminated side of
the particle becomes warmer than the dark side. This is shown in Fig. 7c
as a negative signal and illustrated in Fig. 7d as the particle shifts from the
regime described in the upper part of Fig. 7d to the one described by
the lower part. Based on this simulation and on our system's sensitivity
limitations, we determined the lower limit for retrieval of κ at
10-5 and do not determine an upper limit. We do however, note areas
with high uncertainty, namely, around κ≈10-3, where
the change in signal flattens and around the point where the regime changes
from negative to positive indirect photophoresis. The latter depends heavily
on the particle size. An important caveat is the non-injective behavior
observed in Fig. 7b were two values of κ could solve for the same
signal. To address the issue one would need to have prior knowledge on the
order of magnitude of the particle's absorption (for example, below or above
κ=10-3). Alternatively, in aging experiments, as κ
evolves, the direction of the change of the signal would clarify the
direction of the change of κ.
The range of environmental conditions allowed by the chamber are pressure of
400–800 hPa, RH of 0 %–90 %, and temperature of 200–300 K. This
means that we can measure and understand heterogeneous chemistry and
photochemical aging processes of a single particle in the full range of
boundary layer conditions with atmospherically relevant gas concentration
and residence time. The combination of high sensitivity and quantification
level with the wide application range of the environmental chamber enables
us to improve process level understanding of formation and degradation of
BrC aerosols resulting from chemical and photochemical aging processes that
is beyond the reach of previously available aerosol flow-through techniques.
This study laid the needed foundations for future development of a new
methodology aimed to simultaneously measure the evolution of light
absorption and the molecular composition of atmospheric aerosol proxies by
coupling photophoretic spectroscopy to electrodynamic balance–soft
ionization mass spectroscopy (EDB-MS) (Birdsall et al.,
2018). This will lead to a step change in our understanding of how such
particles evolve in the atmosphere by directly linking optical properties to
chemical composition.
Data availability
The data presented in this publication is available in the ETHZ Research Collection 10.3929/ethz-b-000419840 (Bluvshtein et al., 2020).
Author contributions
NB contributed by conceptualization, investigation, formal analysis, software development, methodology, and writing and preparation of the original draft. UKK also contributed to the conceptualization and methodology, supervision, and review and editing of the manuscript. TP contributed with review and editing of the manuscript.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Nir Bluvshtein is grateful for support from the ETH Zurich Postdoctoral Fellowship program. The authors would like to thank Thomas C. Preston and collaborators for fruitful discussions on Mie resonance mode assignment and for making their scripts available for the community.
Financial support
This research has been supported by the Swiss National Science Foundation (grant no. CRSK-2_190477).
Review statement
This paper was edited by Mingjin Tang and reviewed by two anonymous referees.
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