Polymer Physics

Thus the complex dielectric constant can be obtained as

e^ ¼

D^

E^

¼

D

E

expðidÞ¼eðcosdisindÞ¼e^0 ie^00 (6.35)

Correspondingly,e^0 is the storage dielectric constant, ande^00 is the loss dielectric
constant. The dielectric loss factor is

tand¼

e^00

e^0

(6.36)

The re-orientation of the dipoles on the typical motion of the chain unit gives rise
to the peak of internal dissipation as its response to the external electric field.
Therefore, one obtains a characteristic relaxation spectrum as a function of either
the frequency or the temperature.
In the whole frequency range, the dynamic mechanical relaxation spectroscopy
for typical non-crystalline high-molecular-weight linear polymers is illustrated in
Fig. 6.13. The storage moduli show a rubbery plateau in the intermediate
frequencies or temperatures, while the loss moduli exhibit wide peaks separately
around the glass transition region and the fluid transition region. In the high
frequency (or low temperature) region, non-crystalline polymers are in the glass
state, exhibiting the elastic solid. Therefore, the storage modulus is higher than the
loss modulus. In the intermediate frequency (or temperature) region, there occurs
the rubber state, and the storage modulus is still higher than the loss modulus. In the
low frequency (or high temperature) region, polymers enter the fluid state, and
the loss modulus becomes higher than the storage modulus. In this region, since the
zero-shear viscosity

Fig. 6.13Illustration of the whole-frequency spectroscopy for the dynamic mechanical relaxation
of the typical non-crystalline high-molecular-weight linear polymers

6.2 Relaxation of Polymer Deformation 107