Ph.D. thesis (pdf) - dirac

48 Experimental techniques and observables
viscous liquids. Particularly the studies of relaxation time as a function of pressure,
which have lead to the scaling law presented in section 3.2 are to a very high degree
obtained by dielectric spectroscopy. The drawback of dielectric spectroscopy, is that
the exact relation between the macroscopic measured quantity and the microscopic
dynamics is not totally understood. Also the relation between dielectric relaxation
and other more fundamental macroscopic properties, such as the frequency dependent
shear response remains unresolved.
In this section we present the basic principle of the dielectric spectroscopy as well as
give a brief discussion of the physical interpretation. The details of our experimental
setup are given in section 5.1.1.
4.2.1 Basic principle
The basic principle of dielectric spectroscopy is the measurement of a frequency dependent
capacitance of a capacitor filled by the sample. The measuring capacitance
is usually made up of two equally sized parallel plates. This gives the following
capacitance of the empty capacitor,
C 0 = ǫ 0A
d , (4.2.1)
where ǫ 0 is the vacuum permittivity, A is the area of the electrodes and d is the
distance between the plates. The capacitance of the capacitor filled sample with
sample is given by
C(ω) = ǫ(ω) ǫA d = ǫ(ω)C 0 (4.2.2)
where ǫ(ω) is the frequency dependent dielectric constant of the sample. Hence,
ǫ(ω) is determined by dividing the frequency dependent capacitance of the filled
capacitor by the capacitance of the empty capacitor.
The dielectric constant, ǫ, of a sample is defined from the ratio between the applied
electric field, E, and the displacement field, D,
P = ǫ 0 χE m , D = P + ǫ 0 E m = ǫ 0 (χ + 1)E m = ǫ 0 ǫE m , (4.2.3)
where P is the polarization per unit volume. Thus, ǫ(ω) is the response function (see
section 4.1.1), when the applied macroscopic field is the input and the displacement
field is the output.
The experiments reported and discussed in this study are all performed with low