**2.4. Effect of temperature**

8 Dielectric Material

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as tan *δ* ie:

summarized as in the following Figure 3:

**2.3. Relaxation and dielectric loss** 

mode of mechanism lead to the resonance spectra in the case of electronic polarization which occur at frequency beyond 1012 Hz. At below this frequency, the relaxation spectra prevail relating to the behavior of dipole polarization. This observation can best be

**Figure 3.** Dielectric constant and loss dispersion of dielectric materials against frequency (adapted from

It consist of the real part which is dielectric constant and the imaginary part which is the dielectric loss. The ratio between the dielectric loss with the dielectric constant is quantified

tan "

Dielectric loss result from the inability of polarization process in a molecules to follow the rate of change of the oscillating applied electric field. This arise from the relaxation time (τ) in a polymer which is the time taken for the dipoles to return to its original random orientation. It does not occur instatntaneously but the polarization diminished exponentially. If the relaxation time is smaller or comparable to the rate of oscillating electric field, then there would be no or minimum loss. However when the rate of electric field oscillate well faster than the relaxation time, the polarization cannot follow the oscillating frequency resulting in the energy absorption and dissipated as heat. Dipole polarisability is

<sup>d</sup> 1

*o j t* 

'

(4)

(5)

Relative permittivity can be express in complex form as in Equation (4) below:

frequency dependent and can be shown as in Equation (5)

\* *j* Temperature affect dielectric properties. As the temperature is increased the intermolecular forces between polymer chains is broken which enhances thermal agitation. The polar group will be more free to orient allowing it to keep up with the changing electric field. At lower temperature, the segmental motion of the chain is practically freezed and this will reduce the dielectric constant. At sufficiently higher temperature, the dielectric constant is again reduced due to strong thermal motion which disturb the orientation of the dipoles. At this latter stage the polarization effectively contribute minimal dielectric constant. Beside the kinetic energy acquired, free space in the polymer matrix is of necessity so as to induce segmental movement. Throughout the measured frequency and temperature, electronic and atomic polarization are spontaneous. The dipole polarization, on the other hand, would significantly be affected during heat treatment by effectively reducing the relaxation time (τ) since the polymer chain τ would reduced as the temperature is increased hence the polymer segment would be better able to follow in phase with the oscillating electric field. Significant chain and segmental motions occur in polymers and they are identified as follows [39]:


#### 10 Dielectric Material

The dielectric loss will show maxima at respective relaxation mechanisms as the temperature is increased. The loss in dielectric can be schematically represented as in the following Figure 4

where

Figure 6.

Polymeric Dielectric Materials 11

o ε

 

 

2 2

 

(6)

2 2 ' ε 1 

> o ε 2 2

 

This model relates the dielectric properties with the relaxation time. The relationship between ε'and ε'' can be formulated by eliminating the parameter ωτ to give Equation (6):

> 2 2 *s s*

 

This is a form of a semispherical plot which is popularly known as Cole-Cole plot. See

**Figure 6.** Cole-Cole Plot showing the relationship between dielectric constant and dielectric loss.

and Nagami [16]. The last modification lead to the new equation (7):

'

 

The plot shows that at dielectric constant of infinite frequency, ε∞ and static dielectric constant, εs there will be no loss. Maximum loss occur at the midpoint between the two dielectric values. The larger the different between the static and infinite dielectric constant, the higher will be the loss. This model fit very well with polar small molecular liquids. However, polymeric materials are bigger in size, higher viscosity with entanglement between chains. This contribute to visco-elastic properties which requires some modifications to the original model. It can be noted that the above relationship involved only one specific relaxation time. This is contrary in polymeric system whose relaxation time is dependent on mobility of dipoles which behave differently in varying local environments. This result in distribution in relaxtion time. Modification include Cole and Cole semiemperical equation [13] Davidson and Cole [14] Williams and Watt [15] and Navriliak

> o ε 22

  (7)

ε ( ).

 

1

ε 1 ''

 

''2

'

**Figure 4.** Schematic dielectric loss curve for polymer as temperature is increased.

The γ relaxation occur at lower temperature as it involved small entities of phenyl rings and C-H units whose motion are readily perturbed at low thermal energy. This is followed by β relaxation and finally α relaxation corresponding to the longer scale segmental motion. The broadness for each peaks signify dispersion in relaxation time as the result of different local environment of polarisable groups.
