technique relaxation times and due to end over end

technique for dielectric property
(Permittivity, ?) measurement of polar-non polar mixture. The High Temperature
Probe measurement procedure consists of Rohde & Schwarz made ZNB-20 Vector
Network Analyzer, Dielectric Assessment Kit (DAK) and DAK Evaluation software
as shown in Fig. 1. The probe will be immersed into the polar-non polar mixture
sample. The resulting measured reflections (reflection coefficient, S11)
are then converted into dielectric properties values (permittivity, ?) via DAK
Evaluation software. Prior to usage, the high temperature dielectric probe kit
needs to be calibrated using three elements and the software. The elements are
air, a metallic shorting block and water.

                  

Fig. 1. Network Analyzer Setup

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III. THEORETICAL FORMULATIONS

A.   
Estimation of ?jk and
µjk from ?ijk measurement

The straight
line equation in terms of, and  are formed from
established equation 11:

                         (1)                                              (1)

The slopes and
intercept of Eq. 1 for various wjk’s of solute at a given
frequency (f) of applied electric field were shown in Fig. 2.

Slopes of – wjk and – wjk curves in Fig. 3 & 4 are used to
calculate t 8. t’s are also calculated from the slope of of  -straight line equation of Fig. 512.

All the t’s calculated from various above mentioned method along with the
most probable, measuredt,
symmetrical ts
and asymmetric tcs
are shown in TABLE I.

The c1
and c2 for relaxation time and  can be
estimated using the relation 11, 6 as:

                                             (2)

                                             (3)

whereand provided >. All terms and symbols are depicted
elsewhere 13. All the systems show non-rigid behavior exhibiting double
relaxation times and respectively. The theoretical values of c1
and c2   are calculated from  and  of Frhlich’s equation:

                                  (4)

                                  (5)

c1
and c2  are also derived from
the plots of   and  against wjk
at wjk®0 as shown in Fig. 6 and termed as
experimental   c1 and c2.

From Eq. 4,
after simplification one gets the dipole-moment µjk as:        

                                 (6)

where b=1/(1+w2tjk2)
is the dimensionless parameter and   is the slope of
– wjk curve at  as shown in
Fig. 2. All the µ’s are placed in TABLE III.

The free energy
of activation of dielectric relaxation DFt and viscous flow DF? has been calculated using
Eyring,s equation6

                                          (7)

                                                         (8)

IV. RESULTS AND DISCUSSION

Double relaxation times and  due to end over
end rotation as well as flexible part of the molecule are derived from straight
line Eq. 1 analytically. All systems exhibit reasonable values of and  treated as
non-rigid systems. The graphs of 

x

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