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Acta Materialia 59 (2011) 5593–5602 www.elsevier.com/locate/actamat
Nano- and microsize effect of CCTO fillers on the dielectric behavior of CCTO/PVDF composites Wenhu Yang a, Shuhui Yu a,⇑, Rong Sun a,⇑, Ruxu Du a,b a b
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China Institute of Precision Engineering, The Chinese University of Hong Kong, Hong Kong 999077, China Received 21 September 2010; received in revised form 11 April 2011; accepted 17 May 2011 Available online 14 June 2011
Abstract The microstructure and dielectric properties of composites comprising polyvinylidene fluoride (PVDF) and calcium copper titanate (CCTO) particles have been investigated. Nano- and microsized CCTO were employed separately and investigated comparatively. The effective dielectric constant (er) of the composite containing 40 vol.% nanosized CCTO filler is over 106 at 102 Hz and room temperature, which is substantially higher than that of the composite containing microsized CCTO, of which the er value is 35.7 (with 40 vol.%). The er and loss tangent (tan d) decrease with temperature for the composite containing nanosized CCTO, while the one with microsized CCTO shows the opposite tendency. For the composite with nanosized CCTO, the conductivity decreases sharply with increasing temperature in the low frequency range (100–104 Hz) and slightly increases in the high frequency range, while the conductivity of the composite with microsized CCTO is nearly independent of temperature. The theoretical calculations demonstrate that the activation energies of the composites containing nano- or microsized CCTO are 0.52 and 0.051 eV, indicating active interfaces and insulated grain boundaries in these two composites, respectively. Theoretical analysis also shows that the dielectric performance of the composite with nanosized CCTO does not follow the conventional mixing rules and the giant dielectric constant comes mainly from the interfacial polarization. The dielectric property of the composite containing microsized CCTO matches well with the Maxwell–Garnett and effective medium theory models, indicating insulate interfaces between the fillers and the matrix. The results obtained in this study indicate that the composite containing microsized CCTO may be suitable for embedded device applications, while the one with nanosized CCTO may find a new application in the temperature sensor field. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: CCTO; PVDF; Dielectric; Size effect
1. Introduction Ceramic materials with a high dielectric constant (er), such as oxides with perovskite and related structures, are widely used in capacitors, memory devices, power systems and the automotive industry [1,2]. High dielectric constants allow smaller capacitive components, thus offering the opportunity to decrease the size of electronic devices. One important role for ceramic materials with a high ⇑ Corresponding authors.
E-mail addresses: [email protected] (W. Yang), sh.yu@siat. ac.cn, [email protected] (S. Yu), [email protected] (R. Sun).
dielectric constant is as fillers in the ceramic–polymer composites [3]. These composites exhibit high er, relatively low dielectric loss (tan d) and good flexibility at low temperatures. Therefore, polymeric composites with ceramic fillers have attracted considerable interest and have been studied widely, because of their potential applications in the electronics industry, especially as embedded devices. Generally, ceramic–polymer composites are good insulators, with a low dielectric constant (usually less than 10). A common way to enhance the er of such composites is to use fillers with high permittivity, such as BaTiO3 [3], Pb(Zr, Ti)O3 [4] and NiO [5], among which BaTiO3 is the most widely used ceramic filler. The er of ceramic–polymer
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.05.034
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composites is mainly dependent on the filler loading amount [6,7]. However, the dielectric constant of this kind of composite is usually less than 50 even at a high ceramic loading [3]. In the past few years, much attention has been paid to a cubic perovskite ceramic–calcium copper titanate (CCTO), which has a very large dielectric permittivity (over 104). The calcium copper titanate belongs to the ACu3Ti4O12 family (where A = Ca, Cd), which has been extended to the general formula, (AC3)(B4)O12, (where A = Ca, Cd, Sr, Na or Th; B = Ti or (Ti + M5+), in which M = Ta, Sb or Nb; and C = Cu2+or Mn3+) [8]. The crystal structure of CCTO has been refined with the space group Im3 (lattice ˚ , Z = 2), which remains centrosymparameter a = 7.391 A metric body-centered cubic over a wide range of temperatures. CCTO was reported by Deschanvres et al. [9] as early as in 1967; however, the origins of the extraordinarily high er are still not very clear despite being discussed intensively in the literature. Several models have been proposed to explain the unusual dielectric responses, one of which, the Maxell–Wagner (M–W) polarization (originated from internal barrier layer capacitor), is widely accepted as the principal mechanism leading to the high permittivity. Some reports show that there is a relationship between the dielectric constant and the grain size of the CCTO ceramic. For example, Adams et al. [10] reported that, with the grain size increasing from 10 to 300 lm, the dielectric constant of the CCTO bulk material improved from 9000 to 280,000. Saji and Choe [11] reported a CCTO film on a silica substrate that had a dielectric constant of about 2000 with a grain size of 200 nm. However, Fu et al. [12] suggested that the size dependence of the dielectric property was related to the defect density in the CCTO grains. In various models [13,14] proposing a mechanism for the large dielectric constant of CCTO, researchers assume a model of a conducting or semiconducting grain surrounded by a thin insulating grain boundary and the er depends on the size of the grain divided by the grain boundary. In fact, the grain boundary of the CCTO crystal is also conductive or semiconductive due to O defects [12]. The dielectric constant of the nanosized CCTO is more sensitive to the defects of Ti on the Cu site and O defects due to the thinner grain boundary compared with microsized ones. Another outstanding property of the nanosized CCTO material is its exceptionally large surface area. Therefore, extraordinary properties are expected when introducing nanosized CCTO into a polymer to form a nanocomposite material. Many studies of CCTO/polymer composites have been carried out. Arbatti et al. [15] reported that CCTO/ P(VDF-TrFE) composite had a sandwich configuration, with a dielectric constant of more than 610 at 102 Hz and room temperature when the ceramic filler is 50 vol.%. Dang et al. [16] fabricated a CCTO/polyimide composite film (with 40 vol.% ceramic filler) with a dielectric permittivity of about 49 at 100 Hz and room temperature. A similar result was reported by Shri Prakash and Varma [17] with epoxy as the matrix. However, the CCTO filler of the com-
posites mentioned above was mostly prepared by the traditional solid-state reaction with a grain size ranging from a few to tens of micrometers. Composites containing nanosized CCTO have rarely been reported. The purpose of this study is to systematically investigate the dielectric property of a CCTO/PVDF composite, especially the effect of the CCTO’s particle dimensions on the dielectric properties of the composite. CCTO ceramic fillers with two grain sizes were introduced separately into a polyvinylidene fluoride (PVDF) matrix. One was uniform, with an average grain size of about a few hundreds of nanometers, which was synthesized via a wet chemical precursor route by our group. The other powder was microsized and prepared by the traditional solid-state reaction, and obtained from an industrial source. The microstructure and interfacial effect of the two composites were investigated. Theoretical models, including Maxwell’s, the effective medium theory and the percolation theory, were employed to explain the dielectric behavior of the composite. 2. Experimental 2.1. Preparation of CCTO nanoparticles The nano-CCTO ceramic particles (called CCTO-1) were synthesized via a wet chemical route [18]. Titanium tetrachloride (TiCl4, 99.98%) (Fuchen, China), calcium carbonate (Luoyang Chemical Reagent Co., Ltd., China) cupric chloride (Damao, China, proanalyse grade), oxalic acid (Caitong, China, analytical grade) and acetone (pure) were employed as raw materials. In the first step, a titania gel was obtained via the controlled reaction of ice-cold distilled water with titanium tetrachloride, with the pH value kept at 8.0 with NH4OH. After the reaction, the NH4Cl was removed by a filter funnel. Oxalic acid (1:2 ratio of Ti2þ : C2 O2 4 ) was added to the obtained gel, which was kept warm at 45 °C until the solution was clear. Then calcium carbonate was added under constant stirring. The aqueous solution, now containing titanyl oxalic acid together with calcium titanyl oxalate, was cooled to 10 °C. Cupric chloride was dissolved in acetone, added to the above solution and stirred continuously. The thick precipitate was separated by the further addition of acetone. Subsequently, the precipitate was filtered, washed several times with acetone to make it chloride-free and dried in air. The precursor was isothermally heat-treated at 700 °C to get phase-pure CCTO nanoparticles. 2.2. Preparation of PVDF/CCTO composite The prepared CCTO-1 and purchased micro-CCTO powders (CCTO-2; DYC Industry Co., Ltd., China) were thoroughly mixed with PVDF powder (3F, Shanghai, China) separately, by grinding the mixtures for 20 min. The mixtures were then molded by hot pressing at about 200 °C under a pressure of 50 MPa to get tablet samples
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3. Results and discussion 3.1. Characterization of CCTO powders
Fig. 1. Simultaneous DSC/TGA curves for the complex precursor of CCTO-1 measured at a heating rate of 10 °C min1 in air.
12 mm in diameter and about 0.8 mm in thickness. The CCTO/PVDF composites with the nano- and microsized CCTO particles were named composite-1 and composite2, respectively. 2.3. Characterization techniques Differential scanning calorimetry/thermogravimetric analysis (DSC/TGA; QS600, TA, USA) was used to characterize the thermal behavior of the precursor. The crystal structure of CaCu3Ti4O12 was analyzed using X-ray diffraction (XRD; X’Pert PRO MPD, Philips) with Cu Ka radiation, at a scanning speed of 2° min1 in steps of 0.02°. The cross-section of the composite samples was examined by scanning electron microscopy (SEM; 4800S, Hitachi). For dielectric measurements, electrodes were painted on both sides using silver paste. The dielectric properties were measured with an impedance analyzer (Agilent 4294A) in the frequency range from 102 to 106 Hz and the temperature range from 25 to 150 °C. The dielectric constant was calculated based on the measured thickness and capacitance. A sourcemeter (Keithly 2410) was employed for the I–V measurement.
Fig. 1 shows the simultaneous DSC/TGA curves of the complex precursor for CCTO-1 measured at a heating rate of 10 °C min1 in air. The TGA curve shows a minor weight loss step between 30 and 200 °C, which is related to the losses of moisture, hydrate decomposition and trapped solvent (water and carbon dioxide). A major weight loss is observed between 250 and 400 °C, and there is almost no obvious weight loss above 400 °C. Over the temperature of 250 °C, all the weight loss was related to the decomposition of the complex precursor. Each step of the oxalate decomposition involved a complex set of reactions, such as decomposition of the oxalate and oxidation of CO to form CO2. More details of the decomposition process of the CCTO precursor have been reported by Thomas et al. [18]. Two major decalescence peaks are present in the DSC curve. The first endothermic reaction appears in the temperature range of 250–350 °C, which complies with the temperature of major weight loss. The second appears in the temperature range of 680–700 °C, corresponding to the formation of crystalline CCTO. This implies that there will be no weight loss above 700 °C, which is consistent with the TGA curve. Fig. 2 shows the SEM morphology of the two kinds of CCTO ceramic powers. As shown in Fig. 2a, the diameter of the CCTO-1 particles prepared in this study is a few hundreds of nanometers, while the CCTO-2 is microsize, as shown in Fig. 2b. Some tiny grain particles are found in Fig. 2b, and the grinding traces are obvious. Fig. 3 shows the XRD patterns of the CCTO-1 and CCTO-2 powers. The main peaks of these two kinds of CCTO powder are assigned according to the standard powder XRD pattern of CCTO in the ICDD PDF Card No. 21-0140. It shows that the compound has a cubic perovskite-related structure (group: Im3). The calculated lattice parameters of the CCTO-1 and CCTO-2 powers ˚ , respectively, which agree are a = 7.374 and a = 7.375 A
Fig. 2. SEM morphology of the CCTO ceramic powders for (a) CCTO-1 and (b) CCTO-2.
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Fig. 3. XRD patterns of CCTO-1 and CCTO-2 powders.
well with the reported values [19]. Some minor diffraction peaks of TiO2, CaTiO3 and CuO are detected in both CCTO-1 and CCTO-2, which is in accordance with the previous work; it is commonly known that it is difficult to acquire a pure perovskite structure in CCTO [18,20]. The diffraction peak intensity of the CCTO-1 was relatively weak. According to Fig. 2, the particle size of CCTO-1 is much smaller than that of CCTO-2. It is well known that the diffraction intensity is associated with the grain size, crystallinity and surface state. Finer particles lead to a greater surface area and more serious structure defects on the surface layer, which results in a lower diffraction intensity and broader diffraction peaks. The calcination temperature also affects the crystallinity. The CCTO-1 prepared in this study was calcinated at 700 °C, which was much lower
Fig. 4. SEM images of the fresh fractured cross-section of CCTO/PVDF composites with various CCTO volume fractions: (a) pure PVDF, (b) with 20 vol.% CCTO-1, (c) with 40 vol.% CCTO-1, (d) with 20 vol.% CCTO-2 and (e) with 52 vol.% CCTO-2.
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than the calcination temperature of the industrial CCTO-2 (over 1000 °C).
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Fig. 5 shows the frequency dependence of er and tan d of composite-1 containing various volumetric fractions of CCTO-1 fillers at room temperature. The er is about 738 and the loss value is 1.8 at 102 Hz and room temperature
when the filler volume fraction is 20%. However, the er exhibits a giant value of 2.49 106 with a dielectric loss of 48 when the CCTO-1 filler loading is increased to 40 vol.%. The er of the composite dramatically decreases to 2.4 103 when the frequency is increased from 100 to 104 Hz, and to 49 at 1 MHz. Correspondingly, the tan d decreases to 4.7 at 104 Hz and 0.65 at 1 MHz. This dramatic change in dielectric behavior with frequency in composite-1 indicates that the giant dielectric constant and loss tangent at low frequencies result mainly from the interfacial polarization. For comparison, Fig. 6 presents the frequency dependence of the dielectric properties of composite-2 containing various amounts of CCTO-2 at room temperature. Both the er and tan d of the composites increase gradually with the CCTO-2 content. As shown in Fig. 6a, the er of the pure PVDF is 10.5 at 100 Hz, which is increased to 16.5 with 20 vol.% CCTO-2 loading. As the concentration is further increased to fCCTO = 30, 40 and 52 vol.%, the values of er increase to 26, 35 and 49, respectively. However, the er decreases to 39 when the CCTO-2 loading is further increased to 55 vol.%. This may be caused by inhomogeneous dispersion or porosity in the system. This slight tendency the er of the composites to decrease with frequency becomes more obvious when the filler loading is high. The tan d of composite-2 measured in the frequency range from 100 to 106 Hz at room temperature is shown
Fig. 5. Variation of the (a) effective dielectric constant er and (b) dielectric loss tan d of composite-1 with various volume fractions (fCCTO) at room temperature.
Fig. 6. Frequency dependence of (a) the effective dielectric constant (er) and (b) the loss tangent of composite-2 with various volume fractions of CCTO-2 filler at room temperature.
3.2. Microstructure of CCTO/PVDF composites Fig. 4 presents the SEM images of the fresh fractured cross-section of the CCTO/PVDF composites containing various CCTO volume fractions. Fig. 4a is the microstructure of pure PVDF, which shows that the PVDF molecules form a continuous phase. The images in Fig. 4b–e show that both the CCTO-1 and CCTO-2 particles are dispersed homogeneously in the PVDF matrix without aggregation when the filler content is 20 vol.%. The CCTO particles are surrounded by the PVDF network. As the concentration increases, a slight aggregation is observed in composites-1 and -2 with 40 and 52 vol.% filler loading, respectively. According to earlier work by other researchers [21], this slight non-uniformity of particle distribution would not affect the macroscopic dielectric properties of the ceramic–polymer composites. 3.3. Dielectric properties of CCTO/PVDF composites
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in Fig. 6b. The maximum of tan d is 0.23 at 100 Hz and room temperature. It decreases in the frequency range from 100 to 105 Hz, then increases substantially over 105 Hz. The er and tan d of composite-2 with 40 vol.% filler are 24.5 and at 0.13 at 1 MHz, respectively, both of which are much lower than those of composite-1 with the same filler loading. The increase in tan d at high frequency is believed to be related to the glass transition relaxation of PVDF [22]. 3.4. Temperature dependence of the dielectric properties of CCTO/PVDF composites Fig. 7 shows the frequency dependence of the er and tan d of composite-1 with 40 vol.% CCTO-1 measured at various temperatures. The er decreases from 2.49 106 to 285 with an increase in temperature from 25 to 130 °C. Correspondingly, the tan d decreases from 48 to 1.6. In contrast, for the composite-2 with 52 vol.% loading, both er and tan d increase with temperature, as shown in Fig. 8. The er increases from 49 to 111 and the tan d from 0.23 to 0.3 when the temperature is increased from 25 to 150 °C. This phenomenon indicates different polarization mechanisms in composites-1 and -2, which are induced by the nano- and micro-CCTO size effects. Fig. 8. Frequency dependence of (a) er and (b) tan d of composite-2 with 52 vol.% CCTO-2 measured at different temperatures.
3.5. Temperature dependence of the conductivity of CCTO/ PVDF composites
Fig. 7. Frequency dependence of (a) er and (b) tan d of composite-1 with 40 vol.% CCTO-1 measured at different temperatures. The inset in (b) shows the tan d at 25 and 30 °C.
The influence of temperature is more pronounced in the low frequency range, while at high frequency the values of conductivity r display proximity for composite-1. As shown in Fig. 9a, the r of composite-1 with 40 vol.% CCTO-1 decreases sharply with increasing temperature in the low frequency range (100–104 Hz). The phenomenon should be attributed to the interfacial relaxation that occurs at the interface of dissimilar materials. The free charges available in different phases of the composite are trapped at the interface. It is easy for the charges to move when the electric field is applied. In addition, the r is more sensitive to temperature at low frequency. Similar behavior was observed in metal–polymer composites [23]. At high frequency (105–106 Hz), the r is nearly independent of temperature in the range from 30 to 90 °C but increases slightly with temperature from 100 to 150 °C. This transition may be attributed to trapped charges, such as impurity ions and vacancies, which are only active in the higher frequency and higher temperature region. This is similar to typical semiconducting fillers [24]. In contrast, the r vs. temperature curves of composite-2 with 52 vol.% filler loading are nearly flat at different frequencies, as presented in Fig. 9b, which indicates no significant changes in conductivity with increasing temperature.
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Eq. (1). The calculated activation energy EA1 of composite-1 is 0.51 eV, and the negative value indicates that a lot of electrons are present in composite-1. In contrast, the activation energy of composite-2 is 0.052 eV, implying that insulated grain boundaries exist in the composite and the movement of electrons is restricted. This is consistent with the result that the conductivity of composite-2 with 52 vol.% filler loading is nearly independent of temperature, as shown in Fig. 9b. 3.6. The leakage current density vs. electric field of composite-1 Fig. 10 shows the current density as a function of the applied electric field for composite-1. The value of the leakage current density (ID) increases with the applied electric field (E). The ID–E loop shows a nonlinear ferroelectriclike behavior. A similar result was reported for a CCTO ceramic material [25]. It is obvious from Fig. 10a and b that, at a given applied electric field, the leakage current density is increased considerably by increasing the volume fraction of the nanosized CCTO filler. This implies that the electron density increases in the composite. This is consistent with the changes in the dielectric constant and loss
Fig. 9. Temperature dependence of the conductivity of (a) composite-1 with 40 vol.% filler loading and (b) composite-2 with 52 vol.% filler loading at different frequencies; (c) conductivity data in Arrhenius format for composite-1 (40 vol.%) and composite-2 (52 vol.%) at 100 Hz.
According to the Arrhenius equation, electrical conductivity is strongly dependent on temperature, which can be written as: EA rðT Þ ¼ r0 exp ð1Þ kT where r0 is the high temperature limit of conductivity and EA, k and T are the activation energy, Boltzmann constant and absolute temperature, respectively. Fig. 9c shows the plot of ln r vs. 1/T, in which the solid lines show the results fitted using Eq. (1) for composites-1 and -2. The experimental data approximately obeys
Fig. 10. Variation in leakage current density as a function of the applied electric field for composite-1, with various CCTO-1 loadings. The measurements were conducted at room temperature.
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tangent. It suggests that the conductive nanosized CCTO grain boundary and the high electron density are responsible for the giant dielectric constant of the composite. 3.7. Theoretical models of CCTO/PVDF composites In order to clarify the mechanism of the electrical properties of the composites, the percolation theory [26], the Maxwell–Garnett model (M–G) and the effective medium theory model (EMT) [27] are used to predict the er of composites-1 and -2 at 100 Hz and room temperature, through Eqs. (2), (3) and (4), respectively. The results are shown in Fig. 11. q
er ¼ e1 jðfc fCCTO Þ=fc j 3f CCTO b er ¼ e1 1 þ 1 fCCTO b fCCTO ðe2 e1 Þ er ¼ e1 1 þ e1 þ nð1 fCCTO Þðe2 e1 Þ
ð2Þ ð3Þ ð4Þ
Here b = (e2 e1)/(e2 + 2e1); er is the dielectric constant of the CCTO/PVDF composite; and e1, e2, fCCTO, n and q are the dielectric constants of the PVDF and CCTO, the volume fraction of the CCTO particles, the ceramic morphology fitting factor and a critical exponent of about 1, respectively. fc is the percolation threshold. The er was measured at 100 Hz and room temperature. It is worth noting that the percolation theory was initially introduced in the mathematical literature by Broadbent and Hammersley
[28], and is widely used to predict the electrical properties of the percolative composites [26]. As shown in Fig. 11a, for composite-1, the percolation theory (the fitting parameter fc and q are 29.9 vol.% and 1, respectively), M–G and EMT models all deviate from the experimental data. However, the dielectric constant of the composites increases dramatically with the filler loading. This behavior indicates that the nanosized fillers possess “conductor” properties. Nevertheless, the structure of the nanosized CCTO with semiconductor grains and their conductive grain boundaries make a clear difference from traditional conductivity fillers [26] in composite-1. Therefore, the dielectric behavior of composite-1 does not strictly follow the percolation theory. The M–G and EMT models suggest that the filler particles should be homogeneously distributed, non-interacting and roughly spherical. In practice, with the filler size decreasing from micro- to nanosize, the interaction between the fillers becomes apparent and should not be ignored. Unlike the conventional ceramics filler [3], the conducting grain boundary also contributes to the giant dielectric constant of composite-1. The results thus clearly indicate that the interfacial polarization mechanisms play a crucial role in composite-1. For composite-2, the experimental results are in good agreement with those calculated using Eqs. (3) and (4), where e1 = 10.7, e2 = 12,000 [8] and the derived n is 0.3. It is worth noting that the value of the morphology fitting factor n (0.3) obtained from the fitting is much higher than that reported previously, where the derived n is 0.13 or 0.11 [29], which indicates that the dielectric constant of composite-2 in this study is more closely associated with the filler size and shape. For the calculation based on Eq. (2), the experimental results are in good agreement with the percolation theory, with q = 0.7 and fc = 0.38 when f 6 20 vol.%. However, the discrepancy increases for higher volume fractions. The insulation–conduction transition near fc is not observed, which could be ascribed to the barrier effect on electron movement in composite-2. 3.8. Effect of filler size on the dielectric properties of CCTO/ PVDF composites
Fig. 11. Comparison of experimental and theoretical dielectric constants of composite-1 (a) and composite-2 (b) at 100 Hz and room temperature.
Composites containing nano- and microsized CCTO exhibit different dielectric and conductive properties in this study. For composite-1 containing nanosized CCTO-1, the er and loss tangent (tan d) decrease with temperature, and the conductivity decreases sharply with increasing temperature. The leakage current density is increased considerably by increasing the volume fraction of the nanosized CCTO filler. For composite-2 containing microsized CCTO-2, the er and tan d increase with temperature, while the conductivity is nearly independent of temperature. All the results indicate that for the nano-CCTO-1, the grains are semiconductive inside, but with a conductive grain boundary. In comparison, semiconducting grains with insulating grain boundaries are suggested for the micro-CCTO-2 [30].
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This special structure is derived from the higher defect density of the nanosized CCTO compared with the microsized ones. Previous studies showed that the semiconducting behavior of CCTO grain originates from the cation nonstoichiometry [31]. Partial occupation of excess Ti4+ at the Cu sites leads to a reduction in Cu2+ to Cu+ at high temperatures by charge compensation, as indicated by Eq. (5). The monovalent copper is oxidized to Cu2+ on cooling by Eq. (6): 3Cu þ
2þ
þ
! 2Cu þ Ti
Cu þ Ti
4þ
2þ
! Cu
4þ
þ Ti
ð5Þ 3þ
ð6Þ
Oxygen defects are also possible, and in particular are responsible for the conductive grain boundary that occurs upon reducing the gas atmosphere and at high temperatures: 1 Oxo ! O2 þ V 00o þ 2e0 2
ð7Þ
For the CCTO/PVDF composite, the CCTO particles are surrounded by the insulating polymer, as shown in Fig. 12a and b. The interfacial effect is significantly enhanced when the size of the CCTO filler decreases from microsize to nanosize. The area of CCTO/PVDF interface in 1 m3 of the composite was calculated by assuming a
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spherical shape and taking the average size of CCTO particles, as shown in Fig. 12c. The average distance d between neighboring particles (inset of Fig. 12c) for composites-1 and -2 was calculated using the relation [32]: " 1 # 4p 3 2 ð8Þ d¼r 3f where f is the volume fraction and r is the average radius of the CCTO particles. For composite-1, d is 18 nm while f = 40 vol.%, which is much lower than for composite-2 (about 0.1 um) with the same f, and the interfacial area is much larger. This implies that the interfacial polarization is the dominant mechanism in composite-1. As the filler is in nanosize, the trapped electrons by Cu+ and Ti3+ ions as well as oxygen vacancies will accumulate at the interface between the filler and the matrix. The calculated negative active energy (0.52 eV) implies that the conduction band and valence band of composite-1 overlap partially due to the interaction of the nanosized fillers. Moreover, the fillers introduced in the matrix could destroy the homogeneity of the matrix, which would increase the interaction between the filler and the matrix. As a result, the overlapping of the effective tunneling range increases and electron hopping becomes easy at the interface between the nanosized CCTO and PVDF. This band structure is similar to that of metal. As shown in Fig. 9a, the r of composite-1 (40 vol.%) decreases with increasing temperature from 30 to 130 °C at 100 Hz, and the er, and tan d also decrease with increasing temperature from 25 to 130 °C (Fig. 7). All the results for composite-1 demonstrate metallic characteristics in this temperature range, so the giant dielectric loss at room temperature is not surprising. For composite-2 (52 vol.%), the changes in er and tan d with temperature (Fig. 8) are opposite those for composite-1 (40 vol.%). The r (Fig. 9b) is nearly independent of temperature. This can be attributed mainly to the relatively stable active energy of 0.051 eV at 100 Hz, which as a barrier prevents the electrons from transferring between the particles or clusters. 4. Conclusions
Fig. 12. An illustration of (a) nanosized filler (small circle) and (b) microsized filler (large circle) in composite; (c) the interfacial area and interparticle distance (inset) with various volume fractions of CCTO in composites-1 and -2.
In conclusion, nanosized CCTO fillers possess active and “conductive” interfaces while microsized CCTO exhibits “insulating” boundaries in the PVDF matrix, which results in differences in the er, tan d and r of these two groups of CCTO/PVDF composites. For composite-1 containing 40 vol.% nanosized CCTO fillers, the er and tan d reach 2.49 106 and 48, respectively, at 100 Hz and room temperature. The er and tan d decrease with increasing frequency and temperature, especially from 30 to 130 °C. The r decreases sharply with increasing temperature in the low frequency range (100–104 Hz) and increases slightly at high frequencies. In contrast, the values of er and tan d for composite-2 with microsized CCTO fillers are much lower and are more stable at the same temperatures. The maximum values are
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49 and 0.23, respectively, at 100 Hz and room temperature, when f = 52 vol.%. The er and tan d increase with temperature, which is opposite of composite-1. The r is nearly independent of temperature, which is also clearly different with composite-1. Theoretical calculations using the Arrhenius equation demonstrate that the activation energies of the composites containing nanosized or microsized CCTO are 0.52 and 0.051 eV, indicating active interfaces and insulated grain boundaries in these two composites, respectively. When the size of CCTO filler decreases from micro- to nanosize, the interfacial effect is significantly enhanced and interfacial polarization becomes the dominant mechanism. Electron tunneling forms readily and is sensitive to temperature in composite-1 when this nanosized filler volume fraction reaches a certain value. The conductive grain boundary derived from the large number of defects in the CCTO filler is the main mechanism for this giant dielectric constant of composite-1. While composite-2 is suitable for embedded capacitors in high-density electronic packaging, composite-1 may find a new potential application in the temperature sensor field. Acknowledgements The present research is supported by the National Natural Science Foundation of China (Nos. 50807038 and 20971089) and research funding from National S&T Major Project under Contract No. 2009ZX02038. References [1] Shimada T, Touji K, Katsuyama Y, Takeda H, Shiosaki T. J Eur Ceram Soc 2007;27:3877. [2] Kobayashi Y, Kurosawa A, Nagao D, Konno M. Polym Eng Sci 2009;49:1069. [3] Dang ZH, Lin YQ, Xu HP, Shi CY, Li SH, Bai JB. Adv Funct Mater 2008;18:1509.
[4] Firmino MS, Costa CM, Sencadas V, Serrado Nunes J, Costa P, Gregorio Jr R, Lanceros-Me´ndez S. Appl Phys A 2009;96:899. [5] Maensiri S, Thongbai P. Appl Phys Lett 2007;90:202908. [6] Bai Y, Cheng ZY, Bharti V, Xu HS, Zhang QM. Appl Phys Lett 2000;76:3804. [7] Pant HC, Patra MK, Verma Aditya, Vadera SR, Kumar N. Acta Mater 2006;54:3163–9. [8] Subramanian MA, Li D, Duan N, Reisnerc BA, Sleight AW. J Solid State Chem 2000;151:323. [9] Deschanvres A, Raveau B, Tollermer M. Bull Soc Chim Fr 1967;11:4077. [10] Adams TB, Sinclair DC, West AR. Adv Mater 2002;14:1312–23. [11] Saji VS, Choe HC. Bull Mater Sci 2010;33(3):203–7. [12] Fu DS, Taniguchi, Taniyama H, Itoh M, Koshihara SY. Chem Mater 2008;20:1694–8. [13] He L, Neaton JB, Cohen MH, Vanderbilt D. Phys Rev 2002;65:214112. [14] Bender BA, Pan MJ. Mater Sci Eng, B 2005;117:339–47. [15] Arbatti M, Shan XB, Cheng ZY. Adv Mater 2007;19:1369. [16] Dang ZM, Zhou T, Yao SH, Yuan JK, Zha JW, Song TH, et al. Adv Mater 2009;21:2077. [17] Shri Prakash B, Varma KBR. Compos Sci Technol 2007;67:2363. [18] Thomas P, Dwarakanath K, Varma KBR, Kutty TRN. J Phys Chem Solids 2008;69:2594. [19] Ramireza AP, Subramanianb MA, Gardela M, Blumberga G, Lib D, Vogtc T, et al. Solid State Commun 2000;115:217. [20] Loı¨c M, Sophie GF, Bernard D. J Am Ceram Soc 2008;91:485. [21] Devaraju NG, Kim ES, Lee BI. Microelectron Eng 2005;82:71. [22] Gregorio RJ, Cestari MJ. Polym Sci Part B Polym Phys 1994;32:859. [23] Xu HP, Dang ZM, Bing NC, Wu YH, Yang DD. J Appl Phys 2010;107:034105. [24] Kaiser AB. Adv Mater 2001;13:927. [25] Chung SY, Kim ID, Kang SJ. Nat Mater 2004;3(11):774–8. [26] Nan CW, Shen Y, Ma J. Annu Rev Mater Res 2010;40:131–51. [27] Rao Y, Qu J, Marinis T, Wong CP. IEEE Trans Compon Packag Technol 2000;23:680. [28] Broadbenta SR, Hammersley JM. Math Proc Camb Philos Soc 1957;53:629–41. [29] Thomas P, Varughese KT, Dwarakanath K, Varma KBR. Compos Sci Technol 2010;70:539. [30] Ma YZ, Liu JJ, Gao CX, Mei WN, White AD, Rasty JJ. Appl Phys Lett 2006;88:191903. [31] Li M, Feteira A, Sinclair DC, West AR. Appl Phys Lett 2006;88:232903. [32] Deepa KS, Sebastian MT, Jamesa J. Appl Phys Lett 2007;91:202904.
Acta Materialia 59 (2011) 5593–5602 www.elsevier.com/locate/actamat
Nano- and microsize effect of CCTO fillers on the dielectric behavior of CCTO/PVDF composites Wenhu Yang a, Shuhui Yu a,⇑, Rong Sun a,⇑, Ruxu Du a,b a b
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China Institute of Precision Engineering, The Chinese University of Hong Kong, Hong Kong 999077, China Received 21 September 2010; received in revised form 11 April 2011; accepted 17 May 2011 Available online 14 June 2011
Abstract The microstructure and dielectric properties of composites comprising polyvinylidene fluoride (PVDF) and calcium copper titanate (CCTO) particles have been investigated. Nano- and microsized CCTO were employed separately and investigated comparatively. The effective dielectric constant (er) of the composite containing 40 vol.% nanosized CCTO filler is over 106 at 102 Hz and room temperature, which is substantially higher than that of the composite containing microsized CCTO, of which the er value is 35.7 (with 40 vol.%). The er and loss tangent (tan d) decrease with temperature for the composite containing nanosized CCTO, while the one with microsized CCTO shows the opposite tendency. For the composite with nanosized CCTO, the conductivity decreases sharply with increasing temperature in the low frequency range (100–104 Hz) and slightly increases in the high frequency range, while the conductivity of the composite with microsized CCTO is nearly independent of temperature. The theoretical calculations demonstrate that the activation energies of the composites containing nano- or microsized CCTO are 0.52 and 0.051 eV, indicating active interfaces and insulated grain boundaries in these two composites, respectively. Theoretical analysis also shows that the dielectric performance of the composite with nanosized CCTO does not follow the conventional mixing rules and the giant dielectric constant comes mainly from the interfacial polarization. The dielectric property of the composite containing microsized CCTO matches well with the Maxwell–Garnett and effective medium theory models, indicating insulate interfaces between the fillers and the matrix. The results obtained in this study indicate that the composite containing microsized CCTO may be suitable for embedded device applications, while the one with nanosized CCTO may find a new application in the temperature sensor field. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: CCTO; PVDF; Dielectric; Size effect
1. Introduction Ceramic materials with a high dielectric constant (er), such as oxides with perovskite and related structures, are widely used in capacitors, memory devices, power systems and the automotive industry [1,2]. High dielectric constants allow smaller capacitive components, thus offering the opportunity to decrease the size of electronic devices. One important role for ceramic materials with a high ⇑ Corresponding authors.
E-mail addresses: [email protected] (W. Yang), sh.yu@siat. ac.cn, [email protected] (S. Yu), [email protected] (R. Sun).
dielectric constant is as fillers in the ceramic–polymer composites [3]. These composites exhibit high er, relatively low dielectric loss (tan d) and good flexibility at low temperatures. Therefore, polymeric composites with ceramic fillers have attracted considerable interest and have been studied widely, because of their potential applications in the electronics industry, especially as embedded devices. Generally, ceramic–polymer composites are good insulators, with a low dielectric constant (usually less than 10). A common way to enhance the er of such composites is to use fillers with high permittivity, such as BaTiO3 [3], Pb(Zr, Ti)O3 [4] and NiO [5], among which BaTiO3 is the most widely used ceramic filler. The er of ceramic–polymer
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.05.034
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composites is mainly dependent on the filler loading amount [6,7]. However, the dielectric constant of this kind of composite is usually less than 50 even at a high ceramic loading [3]. In the past few years, much attention has been paid to a cubic perovskite ceramic–calcium copper titanate (CCTO), which has a very large dielectric permittivity (over 104). The calcium copper titanate belongs to the ACu3Ti4O12 family (where A = Ca, Cd), which has been extended to the general formula, (AC3)(B4)O12, (where A = Ca, Cd, Sr, Na or Th; B = Ti or (Ti + M5+), in which M = Ta, Sb or Nb; and C = Cu2+or Mn3+) [8]. The crystal structure of CCTO has been refined with the space group Im3 (lattice ˚ , Z = 2), which remains centrosymparameter a = 7.391 A metric body-centered cubic over a wide range of temperatures. CCTO was reported by Deschanvres et al. [9] as early as in 1967; however, the origins of the extraordinarily high er are still not very clear despite being discussed intensively in the literature. Several models have been proposed to explain the unusual dielectric responses, one of which, the Maxell–Wagner (M–W) polarization (originated from internal barrier layer capacitor), is widely accepted as the principal mechanism leading to the high permittivity. Some reports show that there is a relationship between the dielectric constant and the grain size of the CCTO ceramic. For example, Adams et al. [10] reported that, with the grain size increasing from 10 to 300 lm, the dielectric constant of the CCTO bulk material improved from 9000 to 280,000. Saji and Choe [11] reported a CCTO film on a silica substrate that had a dielectric constant of about 2000 with a grain size of 200 nm. However, Fu et al. [12] suggested that the size dependence of the dielectric property was related to the defect density in the CCTO grains. In various models [13,14] proposing a mechanism for the large dielectric constant of CCTO, researchers assume a model of a conducting or semiconducting grain surrounded by a thin insulating grain boundary and the er depends on the size of the grain divided by the grain boundary. In fact, the grain boundary of the CCTO crystal is also conductive or semiconductive due to O defects [12]. The dielectric constant of the nanosized CCTO is more sensitive to the defects of Ti on the Cu site and O defects due to the thinner grain boundary compared with microsized ones. Another outstanding property of the nanosized CCTO material is its exceptionally large surface area. Therefore, extraordinary properties are expected when introducing nanosized CCTO into a polymer to form a nanocomposite material. Many studies of CCTO/polymer composites have been carried out. Arbatti et al. [15] reported that CCTO/ P(VDF-TrFE) composite had a sandwich configuration, with a dielectric constant of more than 610 at 102 Hz and room temperature when the ceramic filler is 50 vol.%. Dang et al. [16] fabricated a CCTO/polyimide composite film (with 40 vol.% ceramic filler) with a dielectric permittivity of about 49 at 100 Hz and room temperature. A similar result was reported by Shri Prakash and Varma [17] with epoxy as the matrix. However, the CCTO filler of the com-
posites mentioned above was mostly prepared by the traditional solid-state reaction with a grain size ranging from a few to tens of micrometers. Composites containing nanosized CCTO have rarely been reported. The purpose of this study is to systematically investigate the dielectric property of a CCTO/PVDF composite, especially the effect of the CCTO’s particle dimensions on the dielectric properties of the composite. CCTO ceramic fillers with two grain sizes were introduced separately into a polyvinylidene fluoride (PVDF) matrix. One was uniform, with an average grain size of about a few hundreds of nanometers, which was synthesized via a wet chemical precursor route by our group. The other powder was microsized and prepared by the traditional solid-state reaction, and obtained from an industrial source. The microstructure and interfacial effect of the two composites were investigated. Theoretical models, including Maxwell’s, the effective medium theory and the percolation theory, were employed to explain the dielectric behavior of the composite. 2. Experimental 2.1. Preparation of CCTO nanoparticles The nano-CCTO ceramic particles (called CCTO-1) were synthesized via a wet chemical route [18]. Titanium tetrachloride (TiCl4, 99.98%) (Fuchen, China), calcium carbonate (Luoyang Chemical Reagent Co., Ltd., China) cupric chloride (Damao, China, proanalyse grade), oxalic acid (Caitong, China, analytical grade) and acetone (pure) were employed as raw materials. In the first step, a titania gel was obtained via the controlled reaction of ice-cold distilled water with titanium tetrachloride, with the pH value kept at 8.0 with NH4OH. After the reaction, the NH4Cl was removed by a filter funnel. Oxalic acid (1:2 ratio of Ti2þ : C2 O2 4 ) was added to the obtained gel, which was kept warm at 45 °C until the solution was clear. Then calcium carbonate was added under constant stirring. The aqueous solution, now containing titanyl oxalic acid together with calcium titanyl oxalate, was cooled to 10 °C. Cupric chloride was dissolved in acetone, added to the above solution and stirred continuously. The thick precipitate was separated by the further addition of acetone. Subsequently, the precipitate was filtered, washed several times with acetone to make it chloride-free and dried in air. The precursor was isothermally heat-treated at 700 °C to get phase-pure CCTO nanoparticles. 2.2. Preparation of PVDF/CCTO composite The prepared CCTO-1 and purchased micro-CCTO powders (CCTO-2; DYC Industry Co., Ltd., China) were thoroughly mixed with PVDF powder (3F, Shanghai, China) separately, by grinding the mixtures for 20 min. The mixtures were then molded by hot pressing at about 200 °C under a pressure of 50 MPa to get tablet samples
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3. Results and discussion 3.1. Characterization of CCTO powders
Fig. 1. Simultaneous DSC/TGA curves for the complex precursor of CCTO-1 measured at a heating rate of 10 °C min1 in air.
12 mm in diameter and about 0.8 mm in thickness. The CCTO/PVDF composites with the nano- and microsized CCTO particles were named composite-1 and composite2, respectively. 2.3. Characterization techniques Differential scanning calorimetry/thermogravimetric analysis (DSC/TGA; QS600, TA, USA) was used to characterize the thermal behavior of the precursor. The crystal structure of CaCu3Ti4O12 was analyzed using X-ray diffraction (XRD; X’Pert PRO MPD, Philips) with Cu Ka radiation, at a scanning speed of 2° min1 in steps of 0.02°. The cross-section of the composite samples was examined by scanning electron microscopy (SEM; 4800S, Hitachi). For dielectric measurements, electrodes were painted on both sides using silver paste. The dielectric properties were measured with an impedance analyzer (Agilent 4294A) in the frequency range from 102 to 106 Hz and the temperature range from 25 to 150 °C. The dielectric constant was calculated based on the measured thickness and capacitance. A sourcemeter (Keithly 2410) was employed for the I–V measurement.
Fig. 1 shows the simultaneous DSC/TGA curves of the complex precursor for CCTO-1 measured at a heating rate of 10 °C min1 in air. The TGA curve shows a minor weight loss step between 30 and 200 °C, which is related to the losses of moisture, hydrate decomposition and trapped solvent (water and carbon dioxide). A major weight loss is observed between 250 and 400 °C, and there is almost no obvious weight loss above 400 °C. Over the temperature of 250 °C, all the weight loss was related to the decomposition of the complex precursor. Each step of the oxalate decomposition involved a complex set of reactions, such as decomposition of the oxalate and oxidation of CO to form CO2. More details of the decomposition process of the CCTO precursor have been reported by Thomas et al. [18]. Two major decalescence peaks are present in the DSC curve. The first endothermic reaction appears in the temperature range of 250–350 °C, which complies with the temperature of major weight loss. The second appears in the temperature range of 680–700 °C, corresponding to the formation of crystalline CCTO. This implies that there will be no weight loss above 700 °C, which is consistent with the TGA curve. Fig. 2 shows the SEM morphology of the two kinds of CCTO ceramic powers. As shown in Fig. 2a, the diameter of the CCTO-1 particles prepared in this study is a few hundreds of nanometers, while the CCTO-2 is microsize, as shown in Fig. 2b. Some tiny grain particles are found in Fig. 2b, and the grinding traces are obvious. Fig. 3 shows the XRD patterns of the CCTO-1 and CCTO-2 powers. The main peaks of these two kinds of CCTO powder are assigned according to the standard powder XRD pattern of CCTO in the ICDD PDF Card No. 21-0140. It shows that the compound has a cubic perovskite-related structure (group: Im3). The calculated lattice parameters of the CCTO-1 and CCTO-2 powers ˚ , respectively, which agree are a = 7.374 and a = 7.375 A
Fig. 2. SEM morphology of the CCTO ceramic powders for (a) CCTO-1 and (b) CCTO-2.
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Fig. 3. XRD patterns of CCTO-1 and CCTO-2 powders.
well with the reported values [19]. Some minor diffraction peaks of TiO2, CaTiO3 and CuO are detected in both CCTO-1 and CCTO-2, which is in accordance with the previous work; it is commonly known that it is difficult to acquire a pure perovskite structure in CCTO [18,20]. The diffraction peak intensity of the CCTO-1 was relatively weak. According to Fig. 2, the particle size of CCTO-1 is much smaller than that of CCTO-2. It is well known that the diffraction intensity is associated with the grain size, crystallinity and surface state. Finer particles lead to a greater surface area and more serious structure defects on the surface layer, which results in a lower diffraction intensity and broader diffraction peaks. The calcination temperature also affects the crystallinity. The CCTO-1 prepared in this study was calcinated at 700 °C, which was much lower
Fig. 4. SEM images of the fresh fractured cross-section of CCTO/PVDF composites with various CCTO volume fractions: (a) pure PVDF, (b) with 20 vol.% CCTO-1, (c) with 40 vol.% CCTO-1, (d) with 20 vol.% CCTO-2 and (e) with 52 vol.% CCTO-2.
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than the calcination temperature of the industrial CCTO-2 (over 1000 °C).
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Fig. 5 shows the frequency dependence of er and tan d of composite-1 containing various volumetric fractions of CCTO-1 fillers at room temperature. The er is about 738 and the loss value is 1.8 at 102 Hz and room temperature
when the filler volume fraction is 20%. However, the er exhibits a giant value of 2.49 106 with a dielectric loss of 48 when the CCTO-1 filler loading is increased to 40 vol.%. The er of the composite dramatically decreases to 2.4 103 when the frequency is increased from 100 to 104 Hz, and to 49 at 1 MHz. Correspondingly, the tan d decreases to 4.7 at 104 Hz and 0.65 at 1 MHz. This dramatic change in dielectric behavior with frequency in composite-1 indicates that the giant dielectric constant and loss tangent at low frequencies result mainly from the interfacial polarization. For comparison, Fig. 6 presents the frequency dependence of the dielectric properties of composite-2 containing various amounts of CCTO-2 at room temperature. Both the er and tan d of the composites increase gradually with the CCTO-2 content. As shown in Fig. 6a, the er of the pure PVDF is 10.5 at 100 Hz, which is increased to 16.5 with 20 vol.% CCTO-2 loading. As the concentration is further increased to fCCTO = 30, 40 and 52 vol.%, the values of er increase to 26, 35 and 49, respectively. However, the er decreases to 39 when the CCTO-2 loading is further increased to 55 vol.%. This may be caused by inhomogeneous dispersion or porosity in the system. This slight tendency the er of the composites to decrease with frequency becomes more obvious when the filler loading is high. The tan d of composite-2 measured in the frequency range from 100 to 106 Hz at room temperature is shown
Fig. 5. Variation of the (a) effective dielectric constant er and (b) dielectric loss tan d of composite-1 with various volume fractions (fCCTO) at room temperature.
Fig. 6. Frequency dependence of (a) the effective dielectric constant (er) and (b) the loss tangent of composite-2 with various volume fractions of CCTO-2 filler at room temperature.
3.2. Microstructure of CCTO/PVDF composites Fig. 4 presents the SEM images of the fresh fractured cross-section of the CCTO/PVDF composites containing various CCTO volume fractions. Fig. 4a is the microstructure of pure PVDF, which shows that the PVDF molecules form a continuous phase. The images in Fig. 4b–e show that both the CCTO-1 and CCTO-2 particles are dispersed homogeneously in the PVDF matrix without aggregation when the filler content is 20 vol.%. The CCTO particles are surrounded by the PVDF network. As the concentration increases, a slight aggregation is observed in composites-1 and -2 with 40 and 52 vol.% filler loading, respectively. According to earlier work by other researchers [21], this slight non-uniformity of particle distribution would not affect the macroscopic dielectric properties of the ceramic–polymer composites. 3.3. Dielectric properties of CCTO/PVDF composites
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in Fig. 6b. The maximum of tan d is 0.23 at 100 Hz and room temperature. It decreases in the frequency range from 100 to 105 Hz, then increases substantially over 105 Hz. The er and tan d of composite-2 with 40 vol.% filler are 24.5 and at 0.13 at 1 MHz, respectively, both of which are much lower than those of composite-1 with the same filler loading. The increase in tan d at high frequency is believed to be related to the glass transition relaxation of PVDF [22]. 3.4. Temperature dependence of the dielectric properties of CCTO/PVDF composites Fig. 7 shows the frequency dependence of the er and tan d of composite-1 with 40 vol.% CCTO-1 measured at various temperatures. The er decreases from 2.49 106 to 285 with an increase in temperature from 25 to 130 °C. Correspondingly, the tan d decreases from 48 to 1.6. In contrast, for the composite-2 with 52 vol.% loading, both er and tan d increase with temperature, as shown in Fig. 8. The er increases from 49 to 111 and the tan d from 0.23 to 0.3 when the temperature is increased from 25 to 150 °C. This phenomenon indicates different polarization mechanisms in composites-1 and -2, which are induced by the nano- and micro-CCTO size effects. Fig. 8. Frequency dependence of (a) er and (b) tan d of composite-2 with 52 vol.% CCTO-2 measured at different temperatures.
3.5. Temperature dependence of the conductivity of CCTO/ PVDF composites
Fig. 7. Frequency dependence of (a) er and (b) tan d of composite-1 with 40 vol.% CCTO-1 measured at different temperatures. The inset in (b) shows the tan d at 25 and 30 °C.
The influence of temperature is more pronounced in the low frequency range, while at high frequency the values of conductivity r display proximity for composite-1. As shown in Fig. 9a, the r of composite-1 with 40 vol.% CCTO-1 decreases sharply with increasing temperature in the low frequency range (100–104 Hz). The phenomenon should be attributed to the interfacial relaxation that occurs at the interface of dissimilar materials. The free charges available in different phases of the composite are trapped at the interface. It is easy for the charges to move when the electric field is applied. In addition, the r is more sensitive to temperature at low frequency. Similar behavior was observed in metal–polymer composites [23]. At high frequency (105–106 Hz), the r is nearly independent of temperature in the range from 30 to 90 °C but increases slightly with temperature from 100 to 150 °C. This transition may be attributed to trapped charges, such as impurity ions and vacancies, which are only active in the higher frequency and higher temperature region. This is similar to typical semiconducting fillers [24]. In contrast, the r vs. temperature curves of composite-2 with 52 vol.% filler loading are nearly flat at different frequencies, as presented in Fig. 9b, which indicates no significant changes in conductivity with increasing temperature.
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Eq. (1). The calculated activation energy EA1 of composite-1 is 0.51 eV, and the negative value indicates that a lot of electrons are present in composite-1. In contrast, the activation energy of composite-2 is 0.052 eV, implying that insulated grain boundaries exist in the composite and the movement of electrons is restricted. This is consistent with the result that the conductivity of composite-2 with 52 vol.% filler loading is nearly independent of temperature, as shown in Fig. 9b. 3.6. The leakage current density vs. electric field of composite-1 Fig. 10 shows the current density as a function of the applied electric field for composite-1. The value of the leakage current density (ID) increases with the applied electric field (E). The ID–E loop shows a nonlinear ferroelectriclike behavior. A similar result was reported for a CCTO ceramic material [25]. It is obvious from Fig. 10a and b that, at a given applied electric field, the leakage current density is increased considerably by increasing the volume fraction of the nanosized CCTO filler. This implies that the electron density increases in the composite. This is consistent with the changes in the dielectric constant and loss
Fig. 9. Temperature dependence of the conductivity of (a) composite-1 with 40 vol.% filler loading and (b) composite-2 with 52 vol.% filler loading at different frequencies; (c) conductivity data in Arrhenius format for composite-1 (40 vol.%) and composite-2 (52 vol.%) at 100 Hz.
According to the Arrhenius equation, electrical conductivity is strongly dependent on temperature, which can be written as: EA rðT Þ ¼ r0 exp ð1Þ kT where r0 is the high temperature limit of conductivity and EA, k and T are the activation energy, Boltzmann constant and absolute temperature, respectively. Fig. 9c shows the plot of ln r vs. 1/T, in which the solid lines show the results fitted using Eq. (1) for composites-1 and -2. The experimental data approximately obeys
Fig. 10. Variation in leakage current density as a function of the applied electric field for composite-1, with various CCTO-1 loadings. The measurements were conducted at room temperature.
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tangent. It suggests that the conductive nanosized CCTO grain boundary and the high electron density are responsible for the giant dielectric constant of the composite. 3.7. Theoretical models of CCTO/PVDF composites In order to clarify the mechanism of the electrical properties of the composites, the percolation theory [26], the Maxwell–Garnett model (M–G) and the effective medium theory model (EMT) [27] are used to predict the er of composites-1 and -2 at 100 Hz and room temperature, through Eqs. (2), (3) and (4), respectively. The results are shown in Fig. 11. q
er ¼ e1 jðfc fCCTO Þ=fc j 3f CCTO b er ¼ e1 1 þ 1 fCCTO b fCCTO ðe2 e1 Þ er ¼ e1 1 þ e1 þ nð1 fCCTO Þðe2 e1 Þ
ð2Þ ð3Þ ð4Þ
Here b = (e2 e1)/(e2 + 2e1); er is the dielectric constant of the CCTO/PVDF composite; and e1, e2, fCCTO, n and q are the dielectric constants of the PVDF and CCTO, the volume fraction of the CCTO particles, the ceramic morphology fitting factor and a critical exponent of about 1, respectively. fc is the percolation threshold. The er was measured at 100 Hz and room temperature. It is worth noting that the percolation theory was initially introduced in the mathematical literature by Broadbent and Hammersley
[28], and is widely used to predict the electrical properties of the percolative composites [26]. As shown in Fig. 11a, for composite-1, the percolation theory (the fitting parameter fc and q are 29.9 vol.% and 1, respectively), M–G and EMT models all deviate from the experimental data. However, the dielectric constant of the composites increases dramatically with the filler loading. This behavior indicates that the nanosized fillers possess “conductor” properties. Nevertheless, the structure of the nanosized CCTO with semiconductor grains and their conductive grain boundaries make a clear difference from traditional conductivity fillers [26] in composite-1. Therefore, the dielectric behavior of composite-1 does not strictly follow the percolation theory. The M–G and EMT models suggest that the filler particles should be homogeneously distributed, non-interacting and roughly spherical. In practice, with the filler size decreasing from micro- to nanosize, the interaction between the fillers becomes apparent and should not be ignored. Unlike the conventional ceramics filler [3], the conducting grain boundary also contributes to the giant dielectric constant of composite-1. The results thus clearly indicate that the interfacial polarization mechanisms play a crucial role in composite-1. For composite-2, the experimental results are in good agreement with those calculated using Eqs. (3) and (4), where e1 = 10.7, e2 = 12,000 [8] and the derived n is 0.3. It is worth noting that the value of the morphology fitting factor n (0.3) obtained from the fitting is much higher than that reported previously, where the derived n is 0.13 or 0.11 [29], which indicates that the dielectric constant of composite-2 in this study is more closely associated with the filler size and shape. For the calculation based on Eq. (2), the experimental results are in good agreement with the percolation theory, with q = 0.7 and fc = 0.38 when f 6 20 vol.%. However, the discrepancy increases for higher volume fractions. The insulation–conduction transition near fc is not observed, which could be ascribed to the barrier effect on electron movement in composite-2. 3.8. Effect of filler size on the dielectric properties of CCTO/ PVDF composites
Fig. 11. Comparison of experimental and theoretical dielectric constants of composite-1 (a) and composite-2 (b) at 100 Hz and room temperature.
Composites containing nano- and microsized CCTO exhibit different dielectric and conductive properties in this study. For composite-1 containing nanosized CCTO-1, the er and loss tangent (tan d) decrease with temperature, and the conductivity decreases sharply with increasing temperature. The leakage current density is increased considerably by increasing the volume fraction of the nanosized CCTO filler. For composite-2 containing microsized CCTO-2, the er and tan d increase with temperature, while the conductivity is nearly independent of temperature. All the results indicate that for the nano-CCTO-1, the grains are semiconductive inside, but with a conductive grain boundary. In comparison, semiconducting grains with insulating grain boundaries are suggested for the micro-CCTO-2 [30].
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This special structure is derived from the higher defect density of the nanosized CCTO compared with the microsized ones. Previous studies showed that the semiconducting behavior of CCTO grain originates from the cation nonstoichiometry [31]. Partial occupation of excess Ti4+ at the Cu sites leads to a reduction in Cu2+ to Cu+ at high temperatures by charge compensation, as indicated by Eq. (5). The monovalent copper is oxidized to Cu2+ on cooling by Eq. (6): 3Cu þ
2þ
þ
! 2Cu þ Ti
Cu þ Ti
4þ
2þ
! Cu
4þ
þ Ti
ð5Þ 3þ
ð6Þ
Oxygen defects are also possible, and in particular are responsible for the conductive grain boundary that occurs upon reducing the gas atmosphere and at high temperatures: 1 Oxo ! O2 þ V 00o þ 2e0 2
ð7Þ
For the CCTO/PVDF composite, the CCTO particles are surrounded by the insulating polymer, as shown in Fig. 12a and b. The interfacial effect is significantly enhanced when the size of the CCTO filler decreases from microsize to nanosize. The area of CCTO/PVDF interface in 1 m3 of the composite was calculated by assuming a
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spherical shape and taking the average size of CCTO particles, as shown in Fig. 12c. The average distance d between neighboring particles (inset of Fig. 12c) for composites-1 and -2 was calculated using the relation [32]: " 1 # 4p 3 2 ð8Þ d¼r 3f where f is the volume fraction and r is the average radius of the CCTO particles. For composite-1, d is 18 nm while f = 40 vol.%, which is much lower than for composite-2 (about 0.1 um) with the same f, and the interfacial area is much larger. This implies that the interfacial polarization is the dominant mechanism in composite-1. As the filler is in nanosize, the trapped electrons by Cu+ and Ti3+ ions as well as oxygen vacancies will accumulate at the interface between the filler and the matrix. The calculated negative active energy (0.52 eV) implies that the conduction band and valence band of composite-1 overlap partially due to the interaction of the nanosized fillers. Moreover, the fillers introduced in the matrix could destroy the homogeneity of the matrix, which would increase the interaction between the filler and the matrix. As a result, the overlapping of the effective tunneling range increases and electron hopping becomes easy at the interface between the nanosized CCTO and PVDF. This band structure is similar to that of metal. As shown in Fig. 9a, the r of composite-1 (40 vol.%) decreases with increasing temperature from 30 to 130 °C at 100 Hz, and the er, and tan d also decrease with increasing temperature from 25 to 130 °C (Fig. 7). All the results for composite-1 demonstrate metallic characteristics in this temperature range, so the giant dielectric loss at room temperature is not surprising. For composite-2 (52 vol.%), the changes in er and tan d with temperature (Fig. 8) are opposite those for composite-1 (40 vol.%). The r (Fig. 9b) is nearly independent of temperature. This can be attributed mainly to the relatively stable active energy of 0.051 eV at 100 Hz, which as a barrier prevents the electrons from transferring between the particles or clusters. 4. Conclusions
Fig. 12. An illustration of (a) nanosized filler (small circle) and (b) microsized filler (large circle) in composite; (c) the interfacial area and interparticle distance (inset) with various volume fractions of CCTO in composites-1 and -2.
In conclusion, nanosized CCTO fillers possess active and “conductive” interfaces while microsized CCTO exhibits “insulating” boundaries in the PVDF matrix, which results in differences in the er, tan d and r of these two groups of CCTO/PVDF composites. For composite-1 containing 40 vol.% nanosized CCTO fillers, the er and tan d reach 2.49 106 and 48, respectively, at 100 Hz and room temperature. The er and tan d decrease with increasing frequency and temperature, especially from 30 to 130 °C. The r decreases sharply with increasing temperature in the low frequency range (100–104 Hz) and increases slightly at high frequencies. In contrast, the values of er and tan d for composite-2 with microsized CCTO fillers are much lower and are more stable at the same temperatures. The maximum values are
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49 and 0.23, respectively, at 100 Hz and room temperature, when f = 52 vol.%. The er and tan d increase with temperature, which is opposite of composite-1. The r is nearly independent of temperature, which is also clearly different with composite-1. Theoretical calculations using the Arrhenius equation demonstrate that the activation energies of the composites containing nanosized or microsized CCTO are 0.52 and 0.051 eV, indicating active interfaces and insulated grain boundaries in these two composites, respectively. When the size of CCTO filler decreases from micro- to nanosize, the interfacial effect is significantly enhanced and interfacial polarization becomes the dominant mechanism. Electron tunneling forms readily and is sensitive to temperature in composite-1 when this nanosized filler volume fraction reaches a certain value. The conductive grain boundary derived from the large number of defects in the CCTO filler is the main mechanism for this giant dielectric constant of composite-1. While composite-2 is suitable for embedded capacitors in high-density electronic packaging, composite-1 may find a new potential application in the temperature sensor field. Acknowledgements The present research is supported by the National Natural Science Foundation of China (Nos. 50807038 and 20971089) and research funding from National S&T Major Project under Contract No. 2009ZX02038. References [1] Shimada T, Touji K, Katsuyama Y, Takeda H, Shiosaki T. J Eur Ceram Soc 2007;27:3877. [2] Kobayashi Y, Kurosawa A, Nagao D, Konno M. Polym Eng Sci 2009;49:1069. [3] Dang ZH, Lin YQ, Xu HP, Shi CY, Li SH, Bai JB. Adv Funct Mater 2008;18:1509.
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