This is brief summary of my current reseach. 
You can find more information from the following pdf file.
dielectric_spectroscopy.pdf 

     Dielectric spectroscopy is a well established analytical method in material characterization.
Such material properties as viscosity, molecular weight distribution, chemical composition, 
density, porosity, presence of contaminants, and other can be correlated to the broad-band
dielectric spectrum of materials. The models which provide the correlation between the
dielectric spectrum and material property of interest can be based on physical theories or can
be generated using statistical correlations. For instance, the correlation between dielectric 
spectrum and the molecular weight distribution (MWD) is predicted by the de Gennes'/Doi--
Edwards' theory of reptational relaxation of long molecular chains.

For the model of any origin, the dielectric properties are often secondary to a material property of interest (such as 
a MWD or chemical composition) that we are trying to estimate, and, thus, the solution of an inverse problem 
becomes a necessary part the analytical technique. The inverse problem is defined as the task of determining either
material properties or associated geometry, or both, as the external excitations and admittance measurements are 
provided. On the other hand, the forward problem is the task of determining the electric field distribution and 
admittance when the geometry, material properties, and external excitations are given.

     Dielectric spectroscopy has been widely used for a long time. Traditionally, dielectric spectrograms are taken by
placing the material sample (liquid, gaseous or solid) between the capacitor electrodes, typically arranged in the 
parallel plate configuration. The broad-band excitation signal (usually a sine voltage sweep) is applied to the 
capacitor, the current is measured and the complex impedance as a function of frequency is calculated. 
The impedance is then used to calculate the complex dielectric permittivity using the established correlation. 
The obtained dielectric (loss and storage) spectra allows us to solve a variety of problems in measuring material 
properties, ranging from simple monitoring of a sample to determination of the physical and chemical properties by
solving an inverse problem  using theoretical or statistical models.

     Dielectric spectroscopy received renewed interest in the 1980's with the advent of microdielectric fringe-effect 
sensors by a group of MIT researchers. These sensors are not only miniature (though large devices can also be 
used) but also planar by design and, therefore, provide us with the interfacial measurements.
The planar structure of the interdigitated sensors also allows for in situ sensor placement, including elaborate 
laboratory measurements, placement inside a process (such as a polymerization reactor or bioreactor) or a tool
(extruder or a mold being two examples) or human body.

Figure 1. 
Schematic diagram of 
a parallel and 
an interdigited sensor

     Figure 1 illustrates two different types of sensors. The left one is a conventional parallel-plate sensor, and the other
one is called an interdigitated sensor which is formed by photolithographic deposition of interdigitated-comb electrodes
on an insulating substrate. The electrodes contact  with a dielectric material of interest from above and with an
insulating substrate from below

Figure 2.
Top view of interdigitated sensor.
The dark lines are the electrodes.
For clear view, the total number of 
lines has been reduced

Figure 3. 
(A) Capacitor filled with a dielectric.
(B) Equivalent circuit of A.
The subscript p represents that 
two circuit components, a resistor 
and a capacitor, are in parallel

Figure 4. Potential distribution (A) and electric filed (B) created by parallel plate sensor.
               The spacing between the electrode is 0.3 mm. 
               The applied potential differnce between two neighboring electrodes is 2 volt.

Figure 5. Potential distribution (A) and electric field (B) created by the interdigitated sensor.
               The spacing between the electrodes is 50 micro meter, the width of each electrode is 
               50 micro meter. The applied potential difference between two neighboring electrodes is 2 volt.

Figure 6.
The capacitance Cp, resistance Rp,
and dielectric permittivity (loss and
storage) of the polyisoprene, cis,
made from natural rubber.
It was measured by the parallel-plate
sensor.

Figure 7. 
The molecular weight distribution
of the polyisoprene, cis, made 
from natural rubber. 
Inversions of experimental dielectric
loss spectra were performed by 
Tikhonov regularization method.
Second plot gives the comparison of
the predicted loss spectrum with the
experimental data.