Storage and light scattering of microparticles in a ring-type
electrodynamic trap
Al. A. Kolomenskii,
a͒
S. N. Jerebtsov, J. A. Stoker, M. O. Scully, and H. A. Schuessler
Department of Physics, Texas A&M University, College Station, Texas 77843-4242, USA
͑Received 26 April 2007; accepted 10 September 2007; published online 1 November 2007͒
We employ a Paul-Straubel ring-type electrodynamic trap for studies of single microparticles. Such
a trap provides ready access for laser beams to a stored species and is especially suited for scattering
and spectroscopic studies of fine particles. We derive the pseudopotential for such a trap and
determine the stability regions for confinement of charged particles considering also the viscous
force of a buffer medium and the force of gravity. The dynamics of microparticles in such a trap is
numerically simulated. The diffraction pattern of light scattered on a polystyrene particle of about
10
m diameter was registered. For measuring Raman spectra from a single dipicolinic acid
microparticle, we used excitation at 488 nm and detection with a fiber optics spectrometer. To
improve the collection of light, the trap with the stored particle was placed inside an elliptical
mirror. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2802287͔
I. INTRODUCTION
The technique of electrodynamic traps was introduced
by Paul and Steinwedel
1
͑a mass spectrometer with a quad-
rupole trap͒ and as a mass filter by Paul and Raether.
2
The
trap design based on an inhomogeneous electric rf field was
used by Dehmelt for storage and spectroscopy of ions.
3
Straubel
4
modified Millikan’s electrostatic balance
5
by add-
ing an additional electrode providing an ac field and used
this device to levitate and analyze microparticles. Different
modifications of such a Paul-Straubel trap are of interest be-
cause of the strong localization of the field, enabling conve-
nient study of single stored ions
6
and their simple electrode
configuration allowing trap microfabrication.
7
The necessity of analyzing small particles is encountered
in different applications, for instance, such as detection and
identification of aerosols,
8
studies of spectral properties of
cells in biology,
9
and investigation of the particles formed as
a result of chemical reactions.
10
Coulomb fission of evapo-
rating charged droplets was investigated
11,12
and formation
of Rayleigh jets was studied in detail.
13
The technique of “optical tweezers” pioneered by Ash-
kin et al.
14
provides a possibility to work with neutral par-
ticles. Charged particles have an additional handle and can
be levitated in electromagnetic fields.
4,15
Using levitation in
suitable ac and dc fields, the characteristics of Rayleigh and
Mie scattering
8,16
and Raman scattering
10,17,18
of micropar-
ticles were studied. While the elastic ͑Rayleigh and Mie͒
light scattering reflects mainly the size, shape, and complex
refractive index of the particle, the measurements of the in-
elastic ͑Raman͒ scattering provide information on the chemi-
cal composition of the particle material, since the frequency
shifts of the Raman peaks in the spectrum correspond to
certain characteristic vibrational bands of the molecules.
We employ a simple ring-type trap similar to the one
discussed in Ref. 6 for studying single microparticles. The
trap consists of a ring electrode with an ac potential, and the
potential at infinity is taken to be zero. In such a trap the
gravitational force is compensated by an average electrical
force which is not zero, since the particle spends more time
in the region with a higher electric field. In this case the
particle must oscillate to maintain a stationary state. When
the ring is in the horizontal plane, the gravity force can be
also balanced by the addition of two electrodes above and
below the ring electrode with a dc potential applied to them,
as was originally realized by Straubel,
4
and later a modified
version was used by Kiefer et al.
18
The simple geometry of
the trap allows obtaining explicit analytical formulas for the
field in such a trap.
19
For a small particle moving in a gas
environment ͑air͒, the viscous ͑drag͒ force of the medium
becomes significant, as was first demonstrated by Millikan
20
and later thoroughly studied by Dahneke
21
and Lea and
Loyalka.
22
In the atmosphere, the relative role of the drag
force increases with the decrease of the size of a particle. The
charge/mass ratio also tends to increase with the reduction of
particle size. Therefore, much higher frequencies of the ac
field are needed for trapping of very small particles, such as
nanoparticles.
A detailed study of the unstable regions for axial con-
finement of a microparticle storage in a quadrupole trap ͑or
as it was called in this case, an electrodynamic levitator͒ in
the plane of ͑field strength parameter͒-͑drag coefficient͒ was
carried out by Frickel et al.
23
and Davis.
24,25
We study the
regions of stable trapping by taking also the viscosity and the
force of gravity into account. We obtain unstable regions that
combine instabilities for the axial and radial motions. From
the theory of Mathieu functions
26
we identify also several
regions exhibiting the highest stability for combined motion
in both the radial and axial directions. It was shown
23
that the
force of gravity leads to a phase shift between the particle
motion in the vertical direction and the applied ac field. This
phase shift was proposed to be used for “weighing” or size
determination of a particle.
27
In this case, the electrodynamic
trap plays a role of an electrodynamic balance that uses an ac
a͒
Electronic mail: a-kolomenski@physics.tamu.edu
JOURNAL OF APPLIED PHYSICS 102, 094902 ͑2007͒
0021-8979/2007/102͑9͒/094902/7/$23.00 © 2007 American Institute of Physics102, 094902-1