**5.1. Polyimide-ceramic composites**

Of late several attempts were made towards this strategy. Incorporation of alumina (Al2O3), barium titanate (BaTiO3), titania (TiO2) and zirconia (ZrO2) into PI matrix were attempted.. [33,34] Several methods were employed in preparing these nanocomposites. It has been established that method of preparation affect the dielectric properties of these materials. A nanocomposite of PI/Al2O3 was prepared by mechanical stirring of prepolymer polyamic acid with the inorganic filler followed by thermal curing. [35] The nanocomposite showed an improved dielectric constant compared to a neat polymer material from about 3.0 to 3.4 at 1 MHz. This values increases correspondingly with the amount of filler loading. A further increase in dielectric constant was achieved when mixing was performed using ultrasonication. It has been shown from SEM result that this improvement was due to a better mixing during the latter treatment. Under these processes, the crystal structure of the inorganic fillers remains intact as shown by XRD data. The effect of good miscibility in improving the dielectric constant was proven when using a 3-Aminopropyltrimethoxysilanetreated (APS) ultrasonication. The APS served as an interface layer between the two immiscible organic PI with inorganic filler which reduced any agglomeration between the different phases. This is brought about possibly through the formation of hydrogen bond between the amine moeity of APS with the polar group of polyimide while the inorganic part of the methoxysilane of APS form secondary interaction with the inorganic fillers. Figure 13 reveals the SEM images of PI/ Al2O3 composites doped by the treated Al2O3 powder.

PA0 demonstrated a neat and clean morphology. The Al2O3 particles were homogeneously dispersed into PI matrix in all PA10, PA20 and PA30. The inset images revealed the average size of Al2O3 was around 2µm - 4µm. There was no obvious aggregation observed suggesting the improved compatibility between PI matrix and Al2O3 attributed to the APS coupling agent. The bahaviour of PI-nanocomposites for BaTiO3, TiO2 and ZrO2 displayed similar trend with that of PI-Al2O3 nanocomposites. They can be summarized as in the following Figures 14:

#### 22 Dielectric Material

Polymeric Dielectric Materials 23

All composite systems displayed a decreased in dielectric constant with the increase in frequencies. The dielectric constants increased as the inorganic filler content were increased. This can be attributed to the increase in polarizability group with the incorporation of the inorganic fillers which replace significant part of the PI in the matrix. As the result the polarizable units per unit volume and the space charge polarizability which occurred at the interfaces between PI matrix and inorganic particles were increased. Fig 13(a) shows the dielectric constant of PI/BaTiO3 composite films demonstrating the highest value of dielectric constant followed by PI/TiO2, PI/Al2O3, PI/ZrO2 and neat PI films. Apparently this property is dependent on the dielectric constant of the respective fillers. BaTiO3 was known to display highest value of dielectric constant [36] followed by TiO2, ZrO2 and Al2O3 in their neat form. BaTiO3 possesed perovskite structure which is capable to polarize in the absence of electric field. This feature remains in the composite as the crystal structure remains intact as established in XRD data. The low dielectric constant for PI/ZrO2 was attributed to the poor compatibility between phases resulted in the presence of voids and even led to cracks.

Several models were proposed in predicting the dielectric constant of the composites which include Maxwell-Wagner model, Logarithmic Mixing Law and Bruggeman Model. [37] These models allow designing of composite materials based on respective dielectric constant of the polymer, inorganic filler, composition ratio as well as the filler sizes. The slight discrepancy of these models which do not fit to most composite systems are mainly due to inconsistency in treatment for the interphase interaction hence further modification is required. An interphase interaction factor, K, was introduced during fitting into this models.[38] A typical plot of composite dielectric constant with respect to the volume

**Figure 15.** The prediction of the effective dielectric constant as a function of filler volume fraction for different K values. (a) The case of εpolymer > εfiller. (b) The case of εpolymer > εfiller (Adapted from Ref 38)

The presence of voids naturally induce a low dielectric constant.

fraction of the fillers is illustrated in the following Figure 15:

**5.2. Composite models** 

**Figure 13.** The morphology of PA0, PA10, PA20 and PA30 (a, b, c and d), respectively.

**Figure 14.** Dielectric constant of PI/inorganic (a) with 30 wt% inorganic content at varying frequency and (b) at 1MHz for several type of inorganic fillers.

All composite systems displayed a decreased in dielectric constant with the increase in frequencies. The dielectric constants increased as the inorganic filler content were increased. This can be attributed to the increase in polarizability group with the incorporation of the inorganic fillers which replace significant part of the PI in the matrix. As the result the polarizable units per unit volume and the space charge polarizability which occurred at the interfaces between PI matrix and inorganic particles were increased. Fig 13(a) shows the dielectric constant of PI/BaTiO3 composite films demonstrating the highest value of dielectric constant followed by PI/TiO2, PI/Al2O3, PI/ZrO2 and neat PI films. Apparently this property is dependent on the dielectric constant of the respective fillers. BaTiO3 was known to display highest value of dielectric constant [36] followed by TiO2, ZrO2 and Al2O3 in their neat form. BaTiO3 possesed perovskite structure which is capable to polarize in the absence of electric field. This feature remains in the composite as the crystal structure remains intact as established in XRD data. The low dielectric constant for PI/ZrO2 was attributed to the poor compatibility between phases resulted in the presence of voids and even led to cracks. The presence of voids naturally induce a low dielectric constant.

#### **5.2. Composite models**

22 Dielectric Material

**Figure 13.** The morphology of PA0, PA10, PA20 and PA30 (a, b, c and d), respectively.

**Figure 14.** Dielectric constant of PI/inorganic (a) with 30 wt% inorganic content at varying frequency

and (b) at 1MHz for several type of inorganic fillers.

Several models were proposed in predicting the dielectric constant of the composites which include Maxwell-Wagner model, Logarithmic Mixing Law and Bruggeman Model. [37] These models allow designing of composite materials based on respective dielectric constant of the polymer, inorganic filler, composition ratio as well as the filler sizes. The slight discrepancy of these models which do not fit to most composite systems are mainly due to inconsistency in treatment for the interphase interaction hence further modification is required. An interphase interaction factor, K, was introduced during fitting into this models.[38] A typical plot of composite dielectric constant with respect to the volume fraction of the fillers is illustrated in the following Figure 15:

**Figure 15.** The prediction of the effective dielectric constant as a function of filler volume fraction for different K values. (a) The case of εpolymer > εfiller. (b) The case of εpolymer > εfiller (Adapted from Ref 38)

#### 24 Dielectric Material

At K = 0, there is no interaction between phases while a high K values showed a strong interaction. This interaction also dependent on the filler sizes. For a given volume fraction filler, a smaller particle size has a larger fraction of interphase volume in the region between the filler and the matrix granting more polarization to operate. Thus they lead to a relative increase in dielectric constant.

Polymeric Dielectric Materials 25

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[2] Alfred S C and Charles E W Jr, Electric Capacitor and method of Making the same, US

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[4] Tummala R R and Rymaszewski E J. Microelectronics Packaging Handbook. Van Nostrand Reinhold. New York, 1989. Chap. I; Numata S, Fujisaki K. Makino D and Kinjo N. Proceedings of the 2nd Technical Conference on Polyimides, Society of Plastic

[5] Ranjan V, Yu L , Nardelli M B and Bernholc J , Phase Equilibria in High Energy Density

[6] Xie S H, Zhu B K, Li J B, Wei X Z and Xu Z K, Preparation and properties of polyimide/aluminum nitride composites. Polymer Testing, 2004, 23(7), 797-801. [7] Liu L, Liang B, Wang, W. and Lei Q. Preparation of polyimide/inorganic nanoparticle hybrid films by sol-gel method. Journal of Composite Materials, 2006, 40(23), 2175-2183 [8] Li H, Liu G, Liu B, Chen W and Chen S, Dielectric properties of polyimide/Al2O3 hybrids synthesized by in-situ polymerization. Materials Letters, 2007, 61(7), 1507-1511. [9] Indulkar C S and Thiruvengadam S, An Introduction to Electronic Engineering

[10] Blythe T and Bloor D, Electrical Proeprties of Polymers, 2nd Ed., (2005) Cambridge

[11] Hougham G, Tesoro G, Viehbeck A, Chapple-Sokol J D, Polarization Effects of Fluorine

[12] Debye P, Polar molecules, (1929) Chemical Cataloque Company, reprinted in New York

[13] Cole R R and Cole K S, Dispersion and Absorption in Dielectrics I. Alternating Current

[14] Davidson D W and Cole R H, Dielectric relaxation of glycerine, 1950, J. Chem Phys., 18,

[15] Williams G and Watt D C, Non-symmetrical dielectric relaxation behaviour arising

[16] Navriliak S and Havriliak S J, Dielectric and Mechanical Relaxation in Materials – Analysis, Interpretation and Application to Polymers, 1997, Munich, Hanser. [17] Lukichev A A, Graphical method for the Debye-like relaxation spectra analysis, Journal

[20] Park S J, Cho K S and Kim S H, A study on dielectric characteristics of fluorinated polyimide thin film Journal of Colloid and Interface Science, 2004, 272, 384–390

on the Relative Permittivity in Polyimides, *Macromolecules,* 1994*,* 27, 5964.

from a simple empirical decay function 1970, Trans Faraday Soc 66, 80

[19] Oplicki M and Kenny J M, Makromol Chem. Makromol Symp, 1993, 68, 41

Patent 3252830 assigned to General Electric Company, NY may 1966

Engineers, Inc., October 1985, Ellenville, New York, p. 164.

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A major concern with polymer/ceramic composites is the heterogeneity in phase which lead to formation of cracks and voids. This effect is known as Maxwell-Wagner effect which reduce the dielectric constant. A more serious type of heterogeneity is that the composite comprised of conductive inorganic fillers which could lead to a mistaken interpretation of dipole polarization occurring at very low frequency region.
