Page 274 - Electrical Properties of Materials

256 Dielectric materials

The nature of eqn (10.80) now allows us to guess at some applications.
Firstly, depending on the relative values of ε P and ε M , the force may have
different signs. In positive DEP, particles are attracted towards field concentra-
tions, and in negative DEP they are repelled. In the former case, we can build a
particle concentrator. For example, in the geometry above, particles suspended
in a liquid between the electrodes will be attracted to the central wire, where
they will sediment. More generally, mixtures of particles may experience dif-
ferent forces, and it may then be possible to separate them. Large particles will
generally experience larger forces. However, particles of the same size may
still be sorted at frequencies where the factors ε M Re(f CM ) are significantly
different.
Dielectrophoresis is extensively used to manipulate biological particles such
as cells and viruses, where this is the case. Specialized microfluidic systems
with complex electrode systems have been designed that can transport, sort,
trap, rotate, rupture, and even fuse cells. Since the effect works up to optical
frequencies—where it is more commonly known as optical trapping—similar
results may be obtained using laser beams to generate the electric fields; a
phenomenon first investigated by Ashkin. As a result, DEP and optical trapping
are workhorse tools for biologists. DEP is also being used by nanotechnologists
to sort nanoparticles (for example, to separate metallic and semiconducting
carbon nanotubes), and as a basic method of nanoassembly (for example, to
place nanotubes between contact electrodes so that their transport properties
can be measured).

Exercises
10.1. Sketch qualitatively how you would expect the permit-
tivity and loss tangent to vary with frequency in those parts f = 695 Hz f = 6950 Hz
of the spectrum that illustrate the essential properties, lim- T(K) tan δ T(K) tan δ
itations, and applications of the following materials: window
glass, water, transformer oil, polythene, and alumina. 555 0.023 631 0.026
543 0.042 621 0.036
10.2. What is the atomic polarizability of argon? Its suscept- 532 0.070 612 0.043
–4
ibility at 273 K and 1 atm is 4.35 × 10 . 524 0.086 604 0.055
–3
10.3. A long narrow rod has an atomic density 5 × 10 28 m . 516 0.092 590 0.073
2
Each atom has a polarizability of 10 –40 farad m .Findthe 509 0.086 581 0.086
503 0.081 568 0.086
internal electric field when an axial field of 1 V/m is applied.
494 0.063 543 0.055
10.4. Theenergyofanelectricdipoleinanelectricfieldis 485 0.042 518 0.025
given by eqn (10.9). Derive this expression by finding the work 475 0.029 498 0.010
done by the electric field when lining up the dipole.
* Data taken from PhD thesis of J. Wachtman, University
10.5. The tables* show measured values of dielectric loss for of Maryland, 1962, quoted in Physics of solids,Wertand
thoria (ThO 2 ) containing a small quantity of calcium. For this Thomson (McGraw–Hill), 1964.
material the static and high-frequency permittivities have been
Assume that orientational polarization is responsible for the
found from other measurements to be
variation of tan δ. Use the Debye equations to show that by
s = 19.2 0 , ∞ = 16.2 0 . expressing the characteristic relaxation time as