# Active aerosols

Charles A. Rohde  U.S. Naval Research Laboratory
4555 Overlook Ave. Southwest, Washington, DC 20375, USA  Kristin M. Charipar
U.S. Naval Research Laboratory
4555 Overlook Ave. Southwest, Washington, DC 20375, USA  Paul Johns  U.S.
Naval Research Laboratory
4555 Overlook Ave. Southwest, Washington, DC 20375, USA  Ashlin G. Porter
U.S. Naval Research Laboratory
4555 Overlook Ave. Southwest, Washington, DC 20375, USA  Nicholas J. Greybush
U.S. Naval Research Laboratory
4555 Overlook Ave. Southwest, Washington, DC 20375, USA  Jake Fontana
<EMAIL_ADDRESS>U.S. Naval Research Laboratory
4555 Overlook Ave. Southwest, Washington, DC 20375, USA

###### Abstract

We unite the research fields of active plasmonics and aerosols to create an
active aerosol. We demonstrate control of the orientational and positional
order of ensembles of gold nanorods suspended in air at standard temperature
and pressure using externally applied electric fields. Light filter, valve and
gradient responses are shown, establishing active aerosols as a unique type of
optical element we term _component-less optics_.

††preprint: APS/123-QED

The interaction between aerosols and light is a fundamental problem throughout
physics. The consequences are wide ranging from influencing astronomical
observations through cosmic dust Bohren and Huffman (1983); Schlegel  _et al._
(1998), to affecting the climate by altering earth’s albedo Albrecht (1989);
Hansen and Nazarenko (2004), and impairing vision in navigation Choi  _et al._
(2011); Popoff  _et al._ (2010). Although aerosols have ubiquitous impact,
often limiting the ability to make observations, they are commonly regarded as
disordered media. Understanding the relationships that define order in
aerosols is key to governing their optics.

Individual aerosol particles are routinely ordered using external fields
Ashkin (1970); Jauffred  _et al._ (2015); Reimann  _et al._ (2018); Conangla
_et al._ (2020); Smalley  _et al._ (2018); Shvedov  _et al._ (2010). To date,
control of the optics of an aerosol ensemble has yet to be realized, generally
due to the need for low pressure environments or substantial particle-field
coupling.

Plasmonic nanoparticles resonantly couple to light, giving rise to large and
unique optical responses as a result of their free carrier density and
geometry Prodan  _et al._ (2003); Miller  _et al._ (2014). Active plasmonics
have further enabled the spatial, spectral and temporal ordering of these
properties with external stimuli Jiang  _et al._ (2018); Shaltout  _et al._
(2019). The orientational order of a gold nanorod can be controlled if the
potential energy of the nanorod in a externally applied AC electric field is
comparable to the energy of thermal excitations Fontana  _et al._ (2016);
Etcheverry  _et al._ (2017); Greybush  _et al._ (2019). The positional order
of a nanorod can be directed by the electrophoretic force when the frequency
of the applied electric field is reduced from AC to DC. Recently, isotropic
suspensions of gold nanorods were transitioned from the liquid to gas state
and optically characterized, creating a plasmonic aerosol Geldmeier  _et al._
(2019). These materials are optically homogeneous and thermodynamically
stable.

In this Letter, we report the experimental dynamics and control of ensembles
of gold nanorods suspended in air by varying the magnitude and frequency of
externally applied electric fields, thereby demonstrating an active aerosol.
We utilize active aerosols to establish the concept of _component-less optics_
using three illustrative paradigms to traditional optics: (i) The isotropic
response of the aerosol behaves as a stop-band filter, absorbing discrete
wavelength bands. (ii) A light valve response is shown by controlling the
orientational order of the nanorods in air with electric fields, temporally
opening or closing spectral bands and polarization states. (iii) The spatial
distribution of the aerosolized nanorods was varied by electrophoretic force,
providing a mechanism to tailor the gradient-index profile within the aerosol.

Experiments were carried out to understand the dynamics of gold nanorods
suspended in air when external electric fields are applied. Gold nanorods with
a length to diameter aspect ratio of 5.7 (114 nm/20 nm) were synthesized to
overlap the longitudinal absorption peak of the nanorods in air with the probe
laser wavelength (1030 nm, 0.5 mW diode laser) Park  _et al._ (2017). Aqueous
suspensions of nanorods initially stablized with CTAB
(hexadecyltrimethylammonium bromide) were phase transferred into ethyl acetate
by coating the surface of the nanorods with thiol terminated polystyrene
(Polymer Source, Inc., $M_{n}=29k$, $M_{w}=31k$) Fontana  _et al._ (2016),
allowing for rapid evaporation of the solvent droplets upon aerosolization.
The liquid suspension of nanorods (40 mL, 0.5 nM) were aerosolized into the
gas phase, creating a plasmonic aerosol, using a Venturi based atomizer
Geldmeier  _et al._ (2019).

The plasmonic aerosol at standard temperature and pressure (nanorod volume
fraction, $\phi=4.90\times 10^{-10}$) filled a probe cell (3D printed
polyamide, cross-section = 1000 mm2, length = 150 mm) from the bottom port
[Fig. 1(a)]. A pair of rectangular copper electrodes (length = 150 mm, height
= 12 mm, spacing = 3 mm) along the long axis of the probe cell applied a
uniform electric field across the aerosol.

Figure 1: Schematic of the experiment and aerosol light filter. (a) The
apparatus used to measure the evolution of the plasmonic aerosols. (b) A
representative spectrum of a stop-band filter, consisting of an isotropic
plasmonic aerosol and NIR probe laser.

Upon exiting the probe cell from the top port, the aerosol flowed into a
control cell, with identical dimensions to the probe cell. The aerosol
spectrum was collected (tungsten halogen unpolarized light, Ocean Optics
HL-2000-HP, QE-Pro and NIRQuest) and used to determine the absolute magnitude
of the absorption [Fig. 1(b)]. The aerosol passed through a filter (HEPA)
removing the nanorods from the air after exiting the control cell.

The longitudinal and transverse absorption peaks of the nanorods in air were
spectrally resolved at 1020 nm and 520 nm, respectively [Fig. 1(b)], showing a
stop-band light filter response at the absorption peak wavelengths. The stop-
or pass-bands can be further tailored by tuning the aspect ratio of the
nanorods Geldmeier  _et al._ (2019). The large transverse absorption peak,
relative to liquid suspensions, is due to increased Rayleigh scattering from
the polymer coated nanorods in air Cox  _et al._ (2002).

Figure 2: Active aerosol light valve. (a) The applied sine-envelope electric
field pulse (50 cycle, 200 Hz, 0 to 2.3 $V/\mu m$). (b) The dynamic response
of the relative absorption spectrum for gold nanorods suspended in air as a
function of applied electric field. (c) Order parameter versus the square of
the applied electric field. The solid black lines are the calculated fits from
the experimentally determined $A=0.108~{}m^{-1}$, $B=0.363~{}m^{-1}$, and
$E_{c}=0.560~{}V/\mu m$ parameters. (d) Absorption versus order parameter.

To demonstrate control of the orientational order of an ensemble of gold
nanorods suspended in air and resulting active aerosol light valve, a
collimated (RC02FC-P01) near infrared laser diode source (QFLD-1030-10S, beam
diameter = 2 mm) was incident upon a $1/2$-waveplate and polarizer, creating a
linearly polarized beam parallel to the applied electric field in the probe
cell. Using a 50:50 beamsplitter, half of the light irradiated the aerosol in
the probe cell and the other half was used as a reference beam. The light
exiting the probe cell was collected on the negative sensor of the balanced
photodiode (BPD210A) and the reference beam was collected on the positive
sensor. The balanced photodiode voltage difference was adjusted to zero with a
variable neutral density attenuator prior to the aerosols being introduced
into the probe cell.

The intensity difference between the balanced photodiode signals determined
the relative change in the absorption, $\alpha_{on}/\alpha_{off},$ of the
aerosols as a function of an applied sine-envelope electric field pulse
[Fig.2(a)]. At 1030 nm Rayleigh scattering is small, therefore the extinction
is assumed to be dominated by absorption. The measurements of absorption at
1030 nm [Fig. 1(b)] were used to calibrate $\alpha_{on}$/$\alpha_{off}$ from
relative to absolute changes in magnitude.

For the experimental geometry, as the 1020 nm longitudinal axis of the
nanorods begin to align in the applied electric field and probe laser
polarization direction, an increase in the relative absorption at 1030 nm is
measured [Fig. 2(b)].

The absorption of the aerosol depends linearly on the orientational order of
the nanorods Fontana  _et al._ (2016),

$\alpha=AS+B,$ (1)

where $A=\frac{4\pi\phi}{3\lambda
n_{h}}\left(\chi^{"}_{\parallel}-\chi^{"}_{\perp}\right)$,
$B=\frac{2\pi\phi}{3\lambda,n_{h}}\left(\chi^{"}_{\parallel}+2\chi^{"}_{\perp}\right)$,
$\lambda$ is the probe wavelength, $n_{h}$ is the refractive index of the
host, $\chi^{"}_{\parallel,\perp}$ are the imaginary parts of the longitudinal
and transverse principal values of the nanorod susceptibility and $S$ is the
scalar orientational order parameter,

$S=\frac{\int_{0}^{1}\frac{1}{2}\left(3cos^{2}\theta-1\right)e^{\frac{E^{2}}{E^{2}_{c}}cos^{2}\theta}\,d(cos\theta)}{\int_{0}^{1}e^{\frac{E^{2}}{E^{2}_{c}}cos^{2}\theta}\,d(cos\theta)},$
(2)

where $\theta$ is angle between the applied electric field direction and the
longitudinal axis of the nanorod. The critical magnitude of the electric field
needed for alignment is
$E_{c}=\sqrt{2k_{B}T/\left(\left(\frac{1}{L_{\parallel}}-\frac{1}{L_{\perp}}\right)\epsilon_{0}\epsilon_{h}V\right)}$,
where $k_{B}$ is Boltzmann’s constant, $T$ is absolute temperature,
$L_{\parallel,\perp}$ are the depolarization factors for fields parallel and
perpendicular to the long axis of the nanorod, $\epsilon_{0,h}$ are the
permittivites of free space and host material and $V$ is the volume of a
nanorod.

The measurement of $\alpha$ versus E was fit to Eq. (1), with fitting
parameters A, B and $E_{c}$ [Fig. 2(c,d)]. The solid black lines are the
calculated fits from the fitted parameters. We find the absorption of the
aerosol is linear in the order parameter [Fig. 2(d)], verifying the
relationship in Eq. (1). The order parameter maximum is $S_{max}=0.96$.
Inverting the $A$ and $B$ parameters and solving for the imaginary principal
values of the nanorod susceptibility at 200 Hz yields;
$\chi^{"}_{\parallel}=164$, $\chi^{"}_{\perp}=107$. The magnitude of
$E_{c}=0.560~{}V/\mu m$ and ensuing potential energy of the nanorod, relative
to the thermal energy, is expected for nanorod alignment Fontana  _et al._
(2016).

To guide the positional order of an ensemble of gold nanorods suspended in air
and show an active aerosol gradient response, a DC electric field was applied
across the electrodes in the probe cell [Fig. 3]. The scattered light from the
nanorods was imaged with a 4x microscope objective (Nikon MRP00042) onto a
CMOS camera (Thorlabs DCC3240N, 10 Hz) through a window inserted in the top of
the probe cell. A second diode laser (QFLD-520-10S) at 520 nm wavelength was
co-propagated, using dichroic mirrors, along the NIR beam axis through the
probe cell to increase the sensitivity of the CCD measurement [Fig. 1(a)].

In Fig. 3(a) we present an image of the scattered light from the nanorods
suspended in air. A DC pulse (3 s on, 30 s off) was applied across the
aerosol. To ensure the images continuously captured the translation of the
nanorods in the relatively small volume between the electrodes, small voltages
(0-30 V) were applied to minimize the electrophoretic force and resulting
nanorod velocities. Software was used to analyze the motion of the nanorods
between images Allan  _et al._ (2021).

As the magnitude of the DC electric field increased, the displacement of the
nanorods increased in the applied field direction ($y$-axis) [Fig. 3(b)]. The
nanorods translated in both the plus and minus field directions due to
residual surfactant encased in the ligand shell coating the nanorods, leading
to a net positive or negative charge on the nanorods and the bipolar
translation along the field direction. The nanorod translation along the
aerosol flow direction ($x$-axis) was constant and unaffected by the electric
field.

Figure 3: Active aerosol gradient (color online). (a) Representative image of
the plasmonic aerosol. Evolution of the vertical displacement (b) and ensemble
root mean square displacement (c) of the aerosol versus the magnitude of the
DC electric field. The inset table is the fitted values of the electrophoretic
mobility.

The ensemble root mean square displacement (RMSD) of the nanorod aerosol
depends linearly on the magnitude of the applied electric field [Fig 3(c)].
The datasets are fitted using the ensemble RMSD,

$\sqrt{\frac{1}{N}\sum_{i=0}^{N}(y_{i}(t)-y_{i}(0))^{2}}=\mu Et,$ (3)

where $N$ is the number of nanorods, $\mu$ is the electrophoretic mobility and
$y_{i}(t)$ is the $y$-position of a nanorod at time, $t$. The model was fit at
different electric field magnitudes and in the constant velocity regime
$t=0.6-3~{}s$. An average ensemble electrophoretic mobility of
$\bar{\mu}=1.1\pm 1.3\times 10^{-8}~{}m^{2}/(V\cdot s)$ was retrieved from the
fits.

In conclusion, we have experimentally demonstrated an active aerosol by
controlling the order of gold nanorods suspended in air using electric fields.
We applied active aerosols to realize _component-less optics_ and highlighted
three illustrative paradigms. Further investigations may lead to additional
_component-less optics_ such as diffusers, lenses or holographic elements
Palmer (1980, 1983), as well as their integration for signal processing
Engheta  _et al._ (2005); Silva  _et al._ (2014). These results open up the
possibility to govern electrodynamic effects in the atmosphere.

J.F. thanks Rohith Chandrasekar and Richard Vaia for insightful discussions.
This work was supported by the Office of Naval Research (N0001421WX00025,
N0001422WX00600).

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