**3.2. Effect of cross-link between chains**

12 Dielectric Material

polyvinylchloride.

for polyvinylchloride. (From Ref 18)

where α and β is in the range 0 and 1. No physical meaning as yet is assignable to these parameters.[17] This modification result in a broader peak and smaller loss value with asymmetrical in features. The behaviour of dielectric constant and loss at variable frequencies and temperatures is exemplified in the following Figure 7 for

**Figure 7.** Plot of dielectric constant (a) and dielectric loss with the change in frequency and temperature

(a) (b)

Figure 7a shows the variation of ε' and ε" at the region of glass transition (85 0C) of polyvinylchloride. At the onset of glass transition the PVC showed a relatively low dielectric constant of 4.1 to 3.2 within the measured frequency range. With the increased in temperature, chain mobility begin to increase thus reducing the relaxation time. The dipole polarization of the polymer chain is better able to align in phase with the changing frequency and this account for the increase in dielectric constant as the temperature is increased. However this alignment with the applied oscillating field gradually failed as the frequency is increased. The optimum rate of decreased of dielectric constant occur at higher frequency as the temperature is increased. This correspond to the maximum dielectric loss in Fig 7b. Based on Cole-Cole plot, when there is a big difference in static and infinite dielectric constant, as under high thermal treatment, then the dielectric loss will be correspondingly large. It can be noted that at temperature 128 oC, there is a large dielectric loss occurring at higher frequency compared to those of lower temperature. Glass transition of polymer is a vital consideration that need to take into account during use of polymers as this affect the dielectric properties substantially. Substitution of fluorine into polyimide, for example, only affect the electronic polarization since PI is mostly used at temperature lower then its Tg (<260 oC). At this temperature, no effective polar orientation occurr which reduce any possibility of intrusion effect from this mechanism into the dielectric properties. The following Table 2 present the dielectric constant and loss of commercially used polymers.

Polymers are often cross-linked to improve their properties. The cross linking or curing process can be conveniently monitored based on relaxation time changes with the progress of reaction. This is exemplified during curing of diglycidylether bisphenol A (DGEBA) with diethyltetraamine (DETA)[19]. During the cross-linking process, the chains are covalently bonded to each other which induce chain rigidity.

Uncross-link chains Cross-link network

**Scheme 1.** Affect of crosslink network on rigidity of polymer chains

This rigidity is proportional to cross-link density henceforth affecting the change in relaxation time. This can be illustrated in the following Figure 8:

Polymeric Dielectric Materials 15

**Figure 9.** Effect of cross-link density on dielectric constant (ε' above) and dielectric loss (ε" below) for

Frequency(Hz)

DGEBA-DETA system

**Scheme 2.** Repeat unit of the polyimde (from Ref 20)

**Figure 8.** Effect of degree of reaction on the α and β relaxation time of DGEBA-DETA system

Figure 8 shows that both the α and β relaxation time increase with the increase in amount of cross-linking reaction. With the increase in cross-link density, the polymer chains are mostly bounded to each other much tighter hence inducing a longer time to return to their original equilibrium configuration. The rate of increase in α relaxation is higher as it approaches glassy state compared to β relaxation as the former relates to the segmental chain motion of larger in scale compared to the latter. The dielectric constant ε and loss is illustrated in the following Figure 9. In Figure 9a there is a significant drop in dielectric constant which correspond to the maximum frequency for dielectric loss in Figure 9b . This transition represent the frequency at which the dipole polarization is completely out of phase with the applied oscillating electric field. The maximum frequency ωmax of dielectric loss was extracted and applied into the equation τ = 1/ ωmax to yield the α relaxation time. It can be observed that as the level of curing is increased the maximum dielectric loss shift towards lower frequency while the change in dielectric constant at αstatic with αinfinity become diminished. This behaviour represent the gradual transition from the rubbery state to glassy state of the polymer with the increase of cross-link density.

#### *3.2.1. Polarizability and free volume*

Polarizability and free volume are two important factors that influence the dielectric properties as formulated in the Clausius–Mossotti equation. These effects can be exemplified by introducing fluorine into a polymer chains.[20] Fluorination of polyimide film was performed through gaseous phase in a vacuum chamber. The impregnated fluorine content was determined using XPS analysis and the dielectric constant is shown as in following Table 3:

**Figure 9.** Effect of cross-link density on dielectric constant (ε' above) and dielectric loss (ε" below) for DGEBA-DETA system

**Scheme 2.** Repeat unit of the polyimde (from Ref 20)

14 Dielectric Material

**Figure 8.** Effect of degree of reaction on the α and β relaxation time of DGEBA-DETA system

state of the polymer with the increase of cross-link density.

*3.2.1. Polarizability and free volume* 

following Table 3:

Figure 8 shows that both the α and β relaxation time increase with the increase in amount of cross-linking reaction. With the increase in cross-link density, the polymer chains are mostly bounded to each other much tighter hence inducing a longer time to return to their original equilibrium configuration. The rate of increase in α relaxation is higher as it approaches glassy state compared to β relaxation as the former relates to the segmental chain motion of larger in scale compared to the latter. The dielectric constant ε and loss is illustrated in the following Figure 9. In Figure 9a there is a significant drop in dielectric constant which correspond to the maximum frequency for dielectric loss in Figure 9b . This transition represent the frequency at which the dipole polarization is completely out of phase with the applied oscillating electric field. The maximum frequency ωmax of dielectric loss was extracted and applied into the equation τ = 1/ ωmax to yield the α relaxation time. It can be observed that as the level of curing is increased the maximum dielectric loss shift towards lower frequency while the change in dielectric constant at αstatic with αinfinity become diminished. This behaviour represent the gradual transition from the rubbery state to glassy

Polarizability and free volume are two important factors that influence the dielectric properties as formulated in the Clausius–Mossotti equation. These effects can be exemplified by introducing fluorine into a polymer chains.[20] Fluorination of polyimide film was performed through gaseous phase in a vacuum chamber. The impregnated fluorine content was determined using XPS analysis and the dielectric constant is shown as in

#### 16 Dielectric Material


Polymeric Dielectric Materials 17

to short circuit or blown fuse. This occurs when at a given applied voltage the heat generated due to the losses is greater than the heat dissipated and if the voltage is applied long enough period then the dielectric is unable to reach a state of internal thermal equilibrium. The favourable condition for the occurrence of breakdown is large thickness of the dielectric, high temperature of both the dielectric and the surrounding, continous application of high voltage and large dielectric loss (high tan δ). The last factor is the most important to occur at high frequency. The high humidity in air can similarly affect dielectric

Based on the preceding discussions, designing of polymer dielectric materials can be made using several approaches. The following examples review two approaches undertaken of

Based on Maxwell-Garnet theory, the presence of second phase of lower dielectric constant in a composite will affect a significant decrease in dielectric constant.[25] This concept was applied in generating foam structure with the introduction of air-filled pores. At least two methods were utilised. One is to synthesised block copolymer of different thermal lability [26] and the other is performing solution etching of soluble component in a composite matrix. [27] The former method involved the use of block copolymer composed of high temperature and high Tg polymer and a second component of lower thermal property which can preferentially undergoes thermal decomposition. One of such a triblock polymer

**Scheme 3.** Triblock polyimide structure illustrating the thermally labile and stable segments.

This triblock composed of thermally stable polyimide and thermally labile phosphate ester block. This copolymer is subjected to thermal treatment such that the temperature is sufficient to degrade the thermally labile block and leaving the thermally stable block intact. A small size scale of microphase saparation is then generated with spherical pore morphology, monodispersed in size and discontinuous. These nanopores are filled with air (ε = 1.0) which is responsible for the reduction in dielectric constant. Thermally labile oligomers include polymethylstyrene, polypropylene oxide and polymethylmethacrylate.

breakdown through electrolytic process.

**4. Designing of polymer dielectric materials** 

late namely free volume and copolymerization.

**4.1. Free volume** 

is shown below:

**Table 3.** The effect of Fluorine content on the dielectric constant of a polyimide

Similar result was obtained in a series of polyimides synthesised from starting monomers bearing varying percentage of fluorine content. [21] The decreased in dielectric constant as the fluorine content is increased can be explained as due to the low polarizability of fluorine. The electrons of fluorine being very tightly held and close to the nucleus. The polarizability of the fluorinated polyimides is decreased as the number of fluorine atoms is increased, due to the lower electronic polarizability of a C–F bond relative to that of a C–H bond that has been displaced. [22,23] The free volume concomitantly increases due to the relatively large volume of fluorine compared with hydrogen, which reduces the number of polarizable groups per unit volume.

The effect of free volume can be seen when introducing adamantane into a polyimide chain. [24] Adamantane is a bulky group which induce an increase in the free volume. The dielectric constant achieved was 2.7 at 1 KHz. This value is well below the commercial Kapton H film (25.4 *μ*m) with a dielectric constant of approximately 3.5 at 1 kHz and 3.3 at 10 MHz. Besides, hydrophobicity was reduced thus preventing absorption of moisture. Low dielectric loss is important for a good capacitors and insulation. The strategy of introducing bulky substituents is further exemplified in a commercial Avatrel™ dielectric polymer made up of polynorbonene for passivation applications. It has a dielectric constant of 2.55, a loss tangent less than 0.002. These electrical properties held constant up to above 1 GHz. The bulky structures in these polymers are illustrated in the following Figure 10:

**Figure 10.** Adamantane structure incorporated into polyimide chain (a, from Ref 12) and the generic structure for polynorbonene (b).
