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COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 67 (2007) 2363–2368 www.elsevier.com/locate/compscitech
Dielectric behavior of CCTO/epoxy and Al-CCTO/epoxy composites B. Shri Prakash, K.B.R. Varma
*
Materials Research Centre, Indian Institute of Science, Bangalore 560012, India Received 16 March 2006; received in revised form 5 January 2007; accepted 19 January 2007 Available online 31 January 2007
Abstract A composite of epoxy embedded with a giant dielectric constant material CaCu3Ti4O12 (CCTO) was fabricated. Various theoretical models were employed to rationalize the dielectric behavior of these biphasic composites. Amongst different models that were employed to predict the dielectric properties of the composites, the effective dielectric constants (eeff), obtained via Yamada model were in close agreement with the experimental values. A metallic inclusion in CCTO/epoxy composite was found to be effective way to enhance its dielectric constant. A three phase percolative composite (Al-CCTO/epoxy) was fabricated and percolation theory was employed to describe its dielectric behavior. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: A. Metals; Oxides; Polymers B. Electrical properties; Optical microscopy
1. Introduction In recent years, there has been an increasing interest on high dielectric constant flexible particulate composites (0–3 composites) made up of a ferroelectric ceramic and a polymer for high density energy storage and capacitor applications [1,2]. However, invariably the dielectric constant of such polymer based 0–3 composites is rather low (about 50) because of the lower dielectric constant of the matrix (usually below 10) [1–5]. For instance, in BaTiO3/epoxy composite, though BaTiO3 has relatively high dielectric constant (>1000), the effective dielectric constant (eeff) of the composite was as low as 50, even when the highest possible volume fraction of ceramic was incorporated [2]. As the volume fraction of ceramic increases, the composite loses its flexibility, which is undesirable. Metal/polymer composites are yet another class of materials exhibiting moderately high dielectric constants [6,7]. Metal/ceramic composites such as Ni/BaTiO3 appears to be interesting as these have dielectric constants
*
Corresponding author. Tel.: +91 80 2293 2914; fax: + 91 80 2360 0683. E-mail address: [email protected] (K.B.R. Varma).
0266-3538/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2007.01.010
as high as 80,000 [8]. The effect of Ag on the dielectric properties of SrBi2Nb2O9 and BaTiO3 has been reported in the literature [9,10]. In general, electrical transport characteristics of these composites containing conducting components could be understood based on the percolation phenomenon. The percolation phenomenon is a well known mechanism in the conductor–insulator systems to explain an anomalous change in the electrical properties in the vicinity of the percolation threshold. The divergence in the electrical properties of the composite with metallic filler is attributed to the formation of infinite number of tiny capacitors with many conducting particles separated by thin insulating layers. Thus, a heterogeneous system of this kind can result in a capacitor with excellent characteristics for charge storage. Usually, only a small improvement in the dielectric constant was observed at the lower concentration of metallic particles, unless the metal concentration is very close to the percolation threshold [8,11–17]. In this paper, we report the details pertaining to the fabrication and characterization of a composites associated with high dielectric constants (>700). It is made up of an epoxy resin dispersed with small amounts of homogeneously distributed CaCu3Ti4O12 (CCTO) and metallic aluminium (Al) powders. CCTO was chosen for
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the study owing to its reported high dielectric constant (>104) [18–22]. This three-phase epoxy based composite is flexible, and can easily be fabricated into various shapes and sizes at relatively low processing temperatures. 2. Experimental The starting materials used for the preparation of the composite samples were epoxy, CCTO powder (0.3– 0.5 lm) and Aluminum powder (100 nm). CCTO was prepared by the conventional solid-state reaction route by heating a stoichiometric mixture of CaCO3, CuO, and TiO2 at 1000 °C for 10 h with an intermittent grinding. The formation of the monophasic compound was confirmed via X-ray powder diffraction (XRD) using Cu Ka radiation. CCTO powder was then ball milled for 10 h in a planetary mill using agate container to obtain submicron sized particles. To prepare epoxy used in the experiment; resin and hardener were mixed in 9:1 volume ratio. For fabricating a composite under study, the CCTO powder was added to the previously prepared epoxy. The resultant product was mixed thoroughly by ultrasonication to have the uniform distribution of CCTO particles in the matrix. The mixture was then poured into an aluminium mould of 20 mm in diameter and 2 mm in thickness to obtain circular shaped specimens to carry out electrical characterization. The samples were cured at 50 °C for 2 h to get well shaped hard discs. A series of CCTO/epoxy composite with CCTO volume varying from 0% to 40% were fabricated. For dielectric constant measurements, samples were polished using emery papers containing successively finer abrasives to achieve perfectly parallel and smooth surfaces. The surfaces of the disc were painted with silver paste and cured at 50 °C. The copper leads were glued on to the surface for making capacitance measurements. These were carried out on the sample as a function of frequency (100 Hz–1 MHz) using impedance gain phase analyzer (HP 4194A) at a signal strength of 5 mV. Dielectric constants were evaluated by taking the dimensions of the sample into account. Epoxy with 20 vol% of CCTO was considered for further studies to visualize the effect of metallic inclusions on the dielectric properties of CCTO/ epoxy composite. A series of Al-CCTO/epoxy samples in which the vol% of Al varying from 0 to 25 were prepared.
Fig. 1. Frequency dependence of effective dielectric constant (eeff) (measured at 300 K) of CCTO/epoxy composite for various volume fractions of CCTO (fCCTO).
loss of the composite is much lower than that of the pure CCTO. Fig. 2 shows the room temperature (300 K) dielectric constant of the composite at 10 kHz (experimental) for different volume fractions of CCTO. For comparison, the dielectric constants calculated based on various models are also included in the figure. The open circles in the figure are the experimental results. According to the well-known Maxwell–Garnett model, the effective dielectric constant (eeff) of above mentioned composite is given by [15,23], 3f CCTO b eeff ¼ e1 1 þ ð1Þ 1 fCCTO b where b ¼ ðe2 e1 Þ=ðe2 þ 2e1 Þ Here, e1 and e2 are, respectively, the dielectric constants of the epoxy and CCTO ceramics and fCCTO is the volume
3. Results and discussion Fig. 1 shows the frequency dependence of the effective dielectric constant (eeff) of CCTO/epoxy composite for different volume fractions of CCTO. For pure epoxy, the dielectric constant is nearly independent of frequency. As expected, the dielectric constant increases with increase in the volume fraction of CCTO at all the frequencies considered. However, the low frequency dielectric dispersion increases with increase in the CCTO content. The reason for increased low frequency dielectric dispersion is due to high dielectric loss of CCTO. Nevertheless, the dielectric
Fig. 2. Variation of effective dielectric constant (eeff) (measured at 300 K and 10 kHz) of CCTO/epoxy composite as a function of volume fraction of CCTO particles (fCCTO). For comparison, the calculations by using Maxwell–Garnett, Bruggeman equation and Yamada model are also shown.
B. Shri Prakash, K.B.R. Varma / Composites Science and Technology 67 (2007) 2363–2368
fraction of the CCTO phase in the matrix. The values that are substituted for e1 and e2 are 4.81 and 6000 (at 10 kHz), respectively. The values obtained for eeff by using the above expressions are in close agreement with experimental values at lower volume fractions of CCTO in epoxy. It is consistent with this model as it is applicable to a system wherein the matrix is continuous with embedded inclusions of CCTO. As the volume fraction of CCTO increases in the matrix, these particles aggregate and the eeff behavior deviates significantly from that of experimental values. In order to see whether the experimental data fits well into the model which is due to the Bruggeman, in which medium is assumed to consist of homogeneous isotropic elements of the two substances. The equation that is given for evaluating eeff in this model is [15,23], e2 eeff e2 eeff ð1 fCCTO Þ þ fCCTO ¼0 ð2Þ e1 þ 2eeff e2 þ 2eeff The eeff values obtained using above equation for different volume fractions of CCTO are also shown in Fig. 2. In the lower volume fraction regime, the experimental results are consistent with those obtained using Bruggeman self-consistent effective medium approximation. The eeff value for fCCTO = 0.1 is 6.89, which is comparable with the experimental eeff (8.3). However, when the volume fraction of the CCTO increases in matrix, the ceramic particles, which were well separated at lower volume fractions, start clustering and as in the earlier case, at higher volume fractions of CCTO, the eeff obtained by this model deviates remarkably from those of experimental values. However, the experimental data were found to fit well in the expression developed by Yamada. According to which [24,25], nfCCTO ðe2 e1 Þ eeff ¼ e1 1 þ ð3Þ ne1 þ ðe2 e1 Þð1 fCCTO Þ where fCCTO is the volume fraction of the CCTO added, and ‘n’ is the parameter related to the geometry of the ceramic particles [24]. The parameter n was evaluated to fit the theoretical value obtained from Eq. (3) to the observed values. The dielectric constant of the epoxy (e1) and CCTO (e2) used are 4.81 and 6000, respectively. The theoretical values agreed well with the experimental values of the dielectric constant when the parameter n is 10.2, which is in agreement with the one simulated based on the theory [24]. The Yamada model is based on the assumption that the epoxy characteristics are very different from those of CCTO. The solid line passing through the experimental points (Fig. 2) clearly demonstrates the effective applicability of this model to rationalize the dielectric characteristics of the present composite. The samples with higher volume fractions of CCTO (fCCTO > 0.4) could not be prepared as mixing of the two components became difficult. Therefore, in the present work, epoxy with 20 vol% of CCTO was considered for further investigations to study the effect of the Al particles addition on the dielectric properties of CCTO/epoxy composite. Before fabricating and characterizing the three phase composite (Al-CCTO/epoxy), it was
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felt that a priori knowledge about the dielectric behavior of metal/polymer composite is desirable. Therefore, Al/ epoxy composites of various compositions were fabricated and characterized. The variation of room temperature (300 K) dielectric constant of Al/epoxy composite with frequency for various concentration of Al is shown in Fig. 3. The dielectric constant increases with increase in the volume fraction of Al throughout the frequency region studied. Also, the dielectric constant for a given volume fraction of the metal is nearly frequency independent and eeff vs frequency curve is almost parallel to the frequency axis in the log scale for smaller volume fraction of the metal. However, the slope of these lines increases with increase in the volume fraction of metal and is more remarkable at higher concentrations. The variation of room temperature (300 K) dielectric constant for Al/epoxy composite as a function of the volume fraction of Al at 10 kHz is shown in Fig. 4. A small increase in the dielectric constant is observed till the volume fraction of Al reaches 0.08 and the subsequent increase is very rapid. Such a behavior of the composite could be explained based on the percolation phenomenon and a limit called percolation threshold [12,13]. The variation in the dielectric constant in the neighborhood of the percolation threshold could be explained based on the power law as given by the equation [11,15], q fc fAl eeff ¼ e1 ð4Þ fc where eeff and e1 are, respectively, the dielectric constants of the composite and the matrix (4.81 at 10 kHz), fc is the percolation threshold, fAl is the volume fraction of the Al powder in the composite and q is the critical exponent. The experimental values of effective dielectric constant (eeff) are in good agreement with those obtained using the above equation for q = 0.98 and fc = 0.18. The observed value of
Fig. 3. Frequency dependence of effective dielectric constant (eeff) (measured at 300 K) of Al/epoxy composite for various volume fractions of aluminium (fAl).
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Fig. 4. Variation of effective dielectric constant (eeff) (measured at 300 K and 100 kHz) of Al/epoxy composite as a function of volume fraction of aluminium particles (fAl). Circles (O) are data points and the solid line denotes the fit of the experimental data using power law.
percolation threshold is little higher than the one predicted for the random composites (fc = 0.16). The maximum eeff achieved in the composite near the percolation threshold is 48. On further increase in the Al content, the metallic particles form continuous network and the composite becomes conducting. Fig. 5a–c shows the optical micrographs
of the composite containing 5, 10 and 15 vol% of Al. The white regions are Al particles, which are almost homogeneously distributed in the epoxy matrix. However, when their volume fraction increases, the particles start clustering. Fig. 6 shows the variation of the dielectric constant with frequency for different volume fractions of Al in the Al-CCTO/epoxy composite. With increase in the addition of the Al, the dielectric constant increases throughout the frequency range under consideration. As the volume fraction of Al increases from 0.20 to 0.25, the dielectric constant increases dramatically. Fig. 7a and b shows the variation of the dielectric constant and the dielectric loss with volume fraction of Al for the three-phase AlCCTO/epoxy composites at 10 kHz. The variation of the dielectric constant could be explained based on the percolation phenomenon and nature of the curve for the dielectric constant vs. Al volume fraction follows the power law equation given by Eq. (4) near percolation threshold [11]. Usually only a small increase in the dielectric constant is expected unless the metallic particle concentration is very close to the percolation threshold. Here, e1 is the dielectric constant of the CCTO/epoxy matrix with fCCTO = 0.2, which is 17 at 10 kHz. As can be seen in Fig 7, the experimental values of the dielectric constant are in good agreement with those obtained using
Fig. 5. Optical micrographs of the Al/epoxy composite containing different volume fractions of Al (a) 5 vol%; (b) 10 vol%; (c) 15 vol%.
B. Shri Prakash, K.B.R. Varma / Composites Science and Technology 67 (2007) 2363–2368
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(Fig. 7b). At the same percolation threshold, tand also sharply increases. For example, tan d value for composite with no metallic inclusion is 0.009 and at the percolation threshold, it is 0.237. Though the dielectric loss is slightly higher at percolation threshold, these high dielectric constant flexible composites may still be potential candidates for charge storage applications as the value is still within the acceptable limits. 4. Conclusions
Fig. 6. Frequency dependence of effective dielectric constant (eeff) (measured at 300 K) of Al-CCTO/epoxy composite for various volume fractions of Al (fAl).
A two phase composite containing CCTO particles dispersed in the epoxy matrix was fabricated for different volume fractions of CCTO. The dielectric constant of the composite was simulated based on different models. The values obtained by Yamada model are in close agreement with the experimental values. A two phase composite with Al particles dispersed in epoxy matrix was prepared for different volume fractions of Al. The dielectric constant of the composite was found to be enhanced greatly near the percolation threshold. The maximum dielectric constant of 50 was achieved with this biphasic composite. This limitation was due to the low dielectric constant of the epoxy host matrix. By using CCTO/epoxy composite as a base matrix, a three-phase percolative composite was fabricated by adding metallic Al particles, which has dielectric constant as high as 700 at 300 K. The easy processing, flexibility and good dielectric behavior of the three-phase particulate composites that are reported in this paper are attractive as potential candidates for the practical applications in charge storage devices, capacitors etc.
References
Fig. 7. (a and b) Variation of effective dielectric constant (eeff) (a) and dielectric loss (tan d); (b) (measured at 300 K and 100 kHz) of Al-CCTO/ epoxy composite with the volume fraction of aluminium particles (fAl). In (a), circles (O) are data points and the solid line denotes the fit of the experimental data using power law.
Eq. (4). The values for fc and q are 0.208 and 0.98, respectively. The experimentally determined percolation threshold is little higher than the theoretically predicted value of 16.4% for a composite system consisting of conducting hard spheres dispersed within an insulating matrix. The increase in the value of the percolation threshold could be due to the presence of the CCTO particles in the epoxy matrix, which prevent Al particles from coming closer to form a continuous chain. The dielectric constant reaches a value as high as 700 at 300 K at 10 kHz. Similar to the change in the dielectric constant (eeff) with fAl, the dielectric loss (tan d) of the composite increases with fAl
[1] Bai Y, Cheng Z-Y, Bharti V, Xu HS, Zhang QM. High-dielectricconstant ceramic-powder polymer composites. Appl Phys Lett 2000;76(25):3804–6. [2] Kuo D-H, Chang C-C, Su T-Y, Wang W-K, Lin B-Y. Dielectric behaviour of multi-doped BaTiO3 epoxy composites. J Eur Ceram Soc 2001;21(9):1171–7. [3] Gregorio R, Cestari JM, Bernardino FE. Dielectric behaviour of thin films of b-PVDF/PZT and b-PVDF/BaTiO3 composites. J Mater Sci 1996;31(11):2925–30. [4] Chan HLW, Chan WK, Zhang Y, Choy CL. Pyroelectric and piezoelectric properties of lead titanate/polyvinylidene fluoride-trifluoroethylene 0–3 composites. IEEE Trans Dielectr Electr Insul 1998;5(4):505–12. [5] Dias CJ, Das-Gupta DK. Inorganic ceramic/polymer ferroelectric composite electrets. IEEE Trans Dielectr Electr Insul 1996;3(5): 706–34. [6] Mamunya YP, Muzychenko YV, Pissis P, Lebedev EV, Shut MI. Percolation phenomena in polymers containing dispersed iron. Polym Eng Sci 2002;42(1):90–100. [7] Baziard Y, Breton S, Toutain S, Gourdenne A. Dielectric properties of aluminium powder-epoxy resin composites. Eur Polym J 1988;24(6):521–6. [8] Pecharroman C, Esteban-Betegon F, Bartolome JF, Lopez-Esteban S, Moya JS. New percolative BaTiO3-Ni composites with a high and frequency-independent dielectric constant 80 000). Adv Mat 2001;13(20):1541–4.
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[9] Wang C, Fang QF, Zhu ZG. Enhanced dielectric properties of lowtemperature sintered SrBi2Nb2O9/Ag composites. Appl Phys Lett 2002;80(19):3578–80. [10] Chen R, Wang X, Gui Z, Li LT. Effect of silver addition on the dielectric properties of barium titanate-based X7R ceramics. J Am Ceram Soc 2003;86(6):1022–4. [11] Efros AL, Shklovskii BI. Critical behaviour of conductivity and dielectric constant near the metal-non-metal transition threshold. Phys Status Solidi B 1976;76(2):475–85. [12] Grannan DM, Garland JC, Tanner DB. Critical behavior of the dielectric constant of a random composite near the percolation threshold. Phys Rev Lett 1981;46(5):375–8. [13] Song Y, Noh TW, Lee S-I, Gaines JR. Experimental study of the three-dimensional AC conductivity and dielectric constant of a conductor–insulator composite near the percolation threshold. Phys Rev B 1986;33(2):904–8. [14] Pecharroman C, Moya JS. Experimental evidence of a giant capacitance in insulator–conductor composites at the percolation threshold. Adv Mater 2000;12(4):294–7. [15] Nan C-W. Physics of inhomogeneous inorganic material physics. Prog Mater Sci 1993;37(1):1–116. [16] Wu J, McLachlan DS. Percolation exponents and thresholds obtained from the nearly ideal continuum percolation system graphite-boron nitride. Phys Rev B 1997;56(3): 1236–48.
[17] Wu J, McLachlan DS. Scaling behavior of the complex conductivity of graphite-boron nitride percolation systems. Phys Rev B 1998;58(22):14880–7. [18] Subramanian MA, Li D, Duan N, Reisner BA, Sleight AW. High dielectric constant in Cu3Ti4O12 and ACu3Ti3FeO12 phases. J Solid State Chem 2000;151(2):323–5. [19] Subramanian MA, Sleight AW. ACu3Ti4O12 and ACu3Ru4O12 perovskites: high dielectric constants and valence degeneracy. Solid State Sci 2002;4(3):347–51. [20] Sinclair DC, Adams TB, Morrison FD, West AR. CaCu3Ti4O12: onestep internal barrier layer capacitor. Appl Phys Lett 2002;80(12):2153–5. [21] Wang CC, Zhang LW. Oxygen-vacancy-related dielectric anomaly in CaCu3Ti4O12: post-sintering annealing studies. Phys Rev B 2006;74(2):024106-1–6-4. [22] Ke S, Huang H, Fan H. Relaxor behavior in CaCu3Ti4O12 ceramics. Appl Phys Lett 2006;89(18):182904-1–4-3. [23] Nan C-W. Comment on Effective dielectric function of a random medium. Phys Rev B 2001;63(17):176201-1–1-3. [24] Yamada T, Ueda T, Kitayama T. Piezoelectricity of a high-content lead zircontate titanate/polymer composite. J Appl Phys 1982;53(6):4328–32. [25] Furukawa T, Ishida K, Fukada E. Piezoelectric properties in the composite systems of polymers and PZT ceramics. J Appl Phys 1979;50(7):4904–12.
Dielectric behavior of CCTO/epoxy and Al-CCTO/epoxy composites B. Shri Prakash, K.B.R. Varma
*
Materials Research Centre, Indian Institute of Science, Bangalore 560012, India Received 16 March 2006; received in revised form 5 January 2007; accepted 19 January 2007 Available online 31 January 2007
Abstract A composite of epoxy embedded with a giant dielectric constant material CaCu3Ti4O12 (CCTO) was fabricated. Various theoretical models were employed to rationalize the dielectric behavior of these biphasic composites. Amongst different models that were employed to predict the dielectric properties of the composites, the effective dielectric constants (eeff), obtained via Yamada model were in close agreement with the experimental values. A metallic inclusion in CCTO/epoxy composite was found to be effective way to enhance its dielectric constant. A three phase percolative composite (Al-CCTO/epoxy) was fabricated and percolation theory was employed to describe its dielectric behavior. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: A. Metals; Oxides; Polymers B. Electrical properties; Optical microscopy
1. Introduction In recent years, there has been an increasing interest on high dielectric constant flexible particulate composites (0–3 composites) made up of a ferroelectric ceramic and a polymer for high density energy storage and capacitor applications [1,2]. However, invariably the dielectric constant of such polymer based 0–3 composites is rather low (about 50) because of the lower dielectric constant of the matrix (usually below 10) [1–5]. For instance, in BaTiO3/epoxy composite, though BaTiO3 has relatively high dielectric constant (>1000), the effective dielectric constant (eeff) of the composite was as low as 50, even when the highest possible volume fraction of ceramic was incorporated [2]. As the volume fraction of ceramic increases, the composite loses its flexibility, which is undesirable. Metal/polymer composites are yet another class of materials exhibiting moderately high dielectric constants [6,7]. Metal/ceramic composites such as Ni/BaTiO3 appears to be interesting as these have dielectric constants
*
Corresponding author. Tel.: +91 80 2293 2914; fax: + 91 80 2360 0683. E-mail address: [email protected] (K.B.R. Varma).
0266-3538/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2007.01.010
as high as 80,000 [8]. The effect of Ag on the dielectric properties of SrBi2Nb2O9 and BaTiO3 has been reported in the literature [9,10]. In general, electrical transport characteristics of these composites containing conducting components could be understood based on the percolation phenomenon. The percolation phenomenon is a well known mechanism in the conductor–insulator systems to explain an anomalous change in the electrical properties in the vicinity of the percolation threshold. The divergence in the electrical properties of the composite with metallic filler is attributed to the formation of infinite number of tiny capacitors with many conducting particles separated by thin insulating layers. Thus, a heterogeneous system of this kind can result in a capacitor with excellent characteristics for charge storage. Usually, only a small improvement in the dielectric constant was observed at the lower concentration of metallic particles, unless the metal concentration is very close to the percolation threshold [8,11–17]. In this paper, we report the details pertaining to the fabrication and characterization of a composites associated with high dielectric constants (>700). It is made up of an epoxy resin dispersed with small amounts of homogeneously distributed CaCu3Ti4O12 (CCTO) and metallic aluminium (Al) powders. CCTO was chosen for
2364
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the study owing to its reported high dielectric constant (>104) [18–22]. This three-phase epoxy based composite is flexible, and can easily be fabricated into various shapes and sizes at relatively low processing temperatures. 2. Experimental The starting materials used for the preparation of the composite samples were epoxy, CCTO powder (0.3– 0.5 lm) and Aluminum powder (100 nm). CCTO was prepared by the conventional solid-state reaction route by heating a stoichiometric mixture of CaCO3, CuO, and TiO2 at 1000 °C for 10 h with an intermittent grinding. The formation of the monophasic compound was confirmed via X-ray powder diffraction (XRD) using Cu Ka radiation. CCTO powder was then ball milled for 10 h in a planetary mill using agate container to obtain submicron sized particles. To prepare epoxy used in the experiment; resin and hardener were mixed in 9:1 volume ratio. For fabricating a composite under study, the CCTO powder was added to the previously prepared epoxy. The resultant product was mixed thoroughly by ultrasonication to have the uniform distribution of CCTO particles in the matrix. The mixture was then poured into an aluminium mould of 20 mm in diameter and 2 mm in thickness to obtain circular shaped specimens to carry out electrical characterization. The samples were cured at 50 °C for 2 h to get well shaped hard discs. A series of CCTO/epoxy composite with CCTO volume varying from 0% to 40% were fabricated. For dielectric constant measurements, samples were polished using emery papers containing successively finer abrasives to achieve perfectly parallel and smooth surfaces. The surfaces of the disc were painted with silver paste and cured at 50 °C. The copper leads were glued on to the surface for making capacitance measurements. These were carried out on the sample as a function of frequency (100 Hz–1 MHz) using impedance gain phase analyzer (HP 4194A) at a signal strength of 5 mV. Dielectric constants were evaluated by taking the dimensions of the sample into account. Epoxy with 20 vol% of CCTO was considered for further studies to visualize the effect of metallic inclusions on the dielectric properties of CCTO/ epoxy composite. A series of Al-CCTO/epoxy samples in which the vol% of Al varying from 0 to 25 were prepared.
Fig. 1. Frequency dependence of effective dielectric constant (eeff) (measured at 300 K) of CCTO/epoxy composite for various volume fractions of CCTO (fCCTO).
loss of the composite is much lower than that of the pure CCTO. Fig. 2 shows the room temperature (300 K) dielectric constant of the composite at 10 kHz (experimental) for different volume fractions of CCTO. For comparison, the dielectric constants calculated based on various models are also included in the figure. The open circles in the figure are the experimental results. According to the well-known Maxwell–Garnett model, the effective dielectric constant (eeff) of above mentioned composite is given by [15,23], 3f CCTO b eeff ¼ e1 1 þ ð1Þ 1 fCCTO b where b ¼ ðe2 e1 Þ=ðe2 þ 2e1 Þ Here, e1 and e2 are, respectively, the dielectric constants of the epoxy and CCTO ceramics and fCCTO is the volume
3. Results and discussion Fig. 1 shows the frequency dependence of the effective dielectric constant (eeff) of CCTO/epoxy composite for different volume fractions of CCTO. For pure epoxy, the dielectric constant is nearly independent of frequency. As expected, the dielectric constant increases with increase in the volume fraction of CCTO at all the frequencies considered. However, the low frequency dielectric dispersion increases with increase in the CCTO content. The reason for increased low frequency dielectric dispersion is due to high dielectric loss of CCTO. Nevertheless, the dielectric
Fig. 2. Variation of effective dielectric constant (eeff) (measured at 300 K and 10 kHz) of CCTO/epoxy composite as a function of volume fraction of CCTO particles (fCCTO). For comparison, the calculations by using Maxwell–Garnett, Bruggeman equation and Yamada model are also shown.
B. Shri Prakash, K.B.R. Varma / Composites Science and Technology 67 (2007) 2363–2368
fraction of the CCTO phase in the matrix. The values that are substituted for e1 and e2 are 4.81 and 6000 (at 10 kHz), respectively. The values obtained for eeff by using the above expressions are in close agreement with experimental values at lower volume fractions of CCTO in epoxy. It is consistent with this model as it is applicable to a system wherein the matrix is continuous with embedded inclusions of CCTO. As the volume fraction of CCTO increases in the matrix, these particles aggregate and the eeff behavior deviates significantly from that of experimental values. In order to see whether the experimental data fits well into the model which is due to the Bruggeman, in which medium is assumed to consist of homogeneous isotropic elements of the two substances. The equation that is given for evaluating eeff in this model is [15,23], e2 eeff e2 eeff ð1 fCCTO Þ þ fCCTO ¼0 ð2Þ e1 þ 2eeff e2 þ 2eeff The eeff values obtained using above equation for different volume fractions of CCTO are also shown in Fig. 2. In the lower volume fraction regime, the experimental results are consistent with those obtained using Bruggeman self-consistent effective medium approximation. The eeff value for fCCTO = 0.1 is 6.89, which is comparable with the experimental eeff (8.3). However, when the volume fraction of the CCTO increases in matrix, the ceramic particles, which were well separated at lower volume fractions, start clustering and as in the earlier case, at higher volume fractions of CCTO, the eeff obtained by this model deviates remarkably from those of experimental values. However, the experimental data were found to fit well in the expression developed by Yamada. According to which [24,25], nfCCTO ðe2 e1 Þ eeff ¼ e1 1 þ ð3Þ ne1 þ ðe2 e1 Þð1 fCCTO Þ where fCCTO is the volume fraction of the CCTO added, and ‘n’ is the parameter related to the geometry of the ceramic particles [24]. The parameter n was evaluated to fit the theoretical value obtained from Eq. (3) to the observed values. The dielectric constant of the epoxy (e1) and CCTO (e2) used are 4.81 and 6000, respectively. The theoretical values agreed well with the experimental values of the dielectric constant when the parameter n is 10.2, which is in agreement with the one simulated based on the theory [24]. The Yamada model is based on the assumption that the epoxy characteristics are very different from those of CCTO. The solid line passing through the experimental points (Fig. 2) clearly demonstrates the effective applicability of this model to rationalize the dielectric characteristics of the present composite. The samples with higher volume fractions of CCTO (fCCTO > 0.4) could not be prepared as mixing of the two components became difficult. Therefore, in the present work, epoxy with 20 vol% of CCTO was considered for further investigations to study the effect of the Al particles addition on the dielectric properties of CCTO/epoxy composite. Before fabricating and characterizing the three phase composite (Al-CCTO/epoxy), it was
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felt that a priori knowledge about the dielectric behavior of metal/polymer composite is desirable. Therefore, Al/ epoxy composites of various compositions were fabricated and characterized. The variation of room temperature (300 K) dielectric constant of Al/epoxy composite with frequency for various concentration of Al is shown in Fig. 3. The dielectric constant increases with increase in the volume fraction of Al throughout the frequency region studied. Also, the dielectric constant for a given volume fraction of the metal is nearly frequency independent and eeff vs frequency curve is almost parallel to the frequency axis in the log scale for smaller volume fraction of the metal. However, the slope of these lines increases with increase in the volume fraction of metal and is more remarkable at higher concentrations. The variation of room temperature (300 K) dielectric constant for Al/epoxy composite as a function of the volume fraction of Al at 10 kHz is shown in Fig. 4. A small increase in the dielectric constant is observed till the volume fraction of Al reaches 0.08 and the subsequent increase is very rapid. Such a behavior of the composite could be explained based on the percolation phenomenon and a limit called percolation threshold [12,13]. The variation in the dielectric constant in the neighborhood of the percolation threshold could be explained based on the power law as given by the equation [11,15], q fc fAl eeff ¼ e1 ð4Þ fc where eeff and e1 are, respectively, the dielectric constants of the composite and the matrix (4.81 at 10 kHz), fc is the percolation threshold, fAl is the volume fraction of the Al powder in the composite and q is the critical exponent. The experimental values of effective dielectric constant (eeff) are in good agreement with those obtained using the above equation for q = 0.98 and fc = 0.18. The observed value of
Fig. 3. Frequency dependence of effective dielectric constant (eeff) (measured at 300 K) of Al/epoxy composite for various volume fractions of aluminium (fAl).
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Fig. 4. Variation of effective dielectric constant (eeff) (measured at 300 K and 100 kHz) of Al/epoxy composite as a function of volume fraction of aluminium particles (fAl). Circles (O) are data points and the solid line denotes the fit of the experimental data using power law.
percolation threshold is little higher than the one predicted for the random composites (fc = 0.16). The maximum eeff achieved in the composite near the percolation threshold is 48. On further increase in the Al content, the metallic particles form continuous network and the composite becomes conducting. Fig. 5a–c shows the optical micrographs
of the composite containing 5, 10 and 15 vol% of Al. The white regions are Al particles, which are almost homogeneously distributed in the epoxy matrix. However, when their volume fraction increases, the particles start clustering. Fig. 6 shows the variation of the dielectric constant with frequency for different volume fractions of Al in the Al-CCTO/epoxy composite. With increase in the addition of the Al, the dielectric constant increases throughout the frequency range under consideration. As the volume fraction of Al increases from 0.20 to 0.25, the dielectric constant increases dramatically. Fig. 7a and b shows the variation of the dielectric constant and the dielectric loss with volume fraction of Al for the three-phase AlCCTO/epoxy composites at 10 kHz. The variation of the dielectric constant could be explained based on the percolation phenomenon and nature of the curve for the dielectric constant vs. Al volume fraction follows the power law equation given by Eq. (4) near percolation threshold [11]. Usually only a small increase in the dielectric constant is expected unless the metallic particle concentration is very close to the percolation threshold. Here, e1 is the dielectric constant of the CCTO/epoxy matrix with fCCTO = 0.2, which is 17 at 10 kHz. As can be seen in Fig 7, the experimental values of the dielectric constant are in good agreement with those obtained using
Fig. 5. Optical micrographs of the Al/epoxy composite containing different volume fractions of Al (a) 5 vol%; (b) 10 vol%; (c) 15 vol%.
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(Fig. 7b). At the same percolation threshold, tand also sharply increases. For example, tan d value for composite with no metallic inclusion is 0.009 and at the percolation threshold, it is 0.237. Though the dielectric loss is slightly higher at percolation threshold, these high dielectric constant flexible composites may still be potential candidates for charge storage applications as the value is still within the acceptable limits. 4. Conclusions
Fig. 6. Frequency dependence of effective dielectric constant (eeff) (measured at 300 K) of Al-CCTO/epoxy composite for various volume fractions of Al (fAl).
A two phase composite containing CCTO particles dispersed in the epoxy matrix was fabricated for different volume fractions of CCTO. The dielectric constant of the composite was simulated based on different models. The values obtained by Yamada model are in close agreement with the experimental values. A two phase composite with Al particles dispersed in epoxy matrix was prepared for different volume fractions of Al. The dielectric constant of the composite was found to be enhanced greatly near the percolation threshold. The maximum dielectric constant of 50 was achieved with this biphasic composite. This limitation was due to the low dielectric constant of the epoxy host matrix. By using CCTO/epoxy composite as a base matrix, a three-phase percolative composite was fabricated by adding metallic Al particles, which has dielectric constant as high as 700 at 300 K. The easy processing, flexibility and good dielectric behavior of the three-phase particulate composites that are reported in this paper are attractive as potential candidates for the practical applications in charge storage devices, capacitors etc.
References
Fig. 7. (a and b) Variation of effective dielectric constant (eeff) (a) and dielectric loss (tan d); (b) (measured at 300 K and 100 kHz) of Al-CCTO/ epoxy composite with the volume fraction of aluminium particles (fAl). In (a), circles (O) are data points and the solid line denotes the fit of the experimental data using power law.
Eq. (4). The values for fc and q are 0.208 and 0.98, respectively. The experimentally determined percolation threshold is little higher than the theoretically predicted value of 16.4% for a composite system consisting of conducting hard spheres dispersed within an insulating matrix. The increase in the value of the percolation threshold could be due to the presence of the CCTO particles in the epoxy matrix, which prevent Al particles from coming closer to form a continuous chain. The dielectric constant reaches a value as high as 700 at 300 K at 10 kHz. Similar to the change in the dielectric constant (eeff) with fAl, the dielectric loss (tan d) of the composite increases with fAl
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