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Effect of curing on activation energy and dielectric properties of carbon black–epoxy composites at different temperatures
Journal of Non-Crystalline Solids 421 (2015) 1–13
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Effect of curing on activation energy and dielectric properties of carbon black–epoxy composites at different temperatures Manindra Trihotri a,b,⁎, U.K. Dwivedi c, Fozia Haque Khan a, M.M. Malik a, M.S. Qureshi a a b c
Department of Physics and Nanotechnology, Maulana Azad National Institute of Technology, Bhopal 462003, M.P. India Department of Physics, Truba Institute of Engineering & Information Technology, Bhopal 462038, M.P., India Department of Physics, Amity University, Jaipur 302006, Rajasthan, India
a r t i c l e
i n f o
Article history: Received 18 December 2014 Received in revised form 8 April 2015 Accepted 10 April 2015 Available online xxxx Keywords: Activation energy; Electron tunneling; Polymer Matrix Composite (PMC); Dielectric properties; Curing effect
a b s t r a c t The effect of curing on activation energy and dielectric properties of carbon black–epoxy (CB–EP) composites has been reported at different temperatures and frequencies. The activation energy was found to be higher for the room temperature cured CB–EP samples as compared with the thermally cured CB–EP samples. Curing behavior of epoxy nanocomposites prove that epoxide molecules contribute to the curing reaction and reacted with them to form a cross-linked network. Dielectric constants of thermally cured CB–EP samples were higher than the room temperature cured samples. The results showed that activation energy, decreased with an increase in the concentration of carbon black in the composite, which may be due to an increase of polarization energy and/or charge carrier density leading to a decrease of the domain boundary potential of carbon black aggregates into the epoxy matrix. At room temperature, the electrical conductivity is due to electron tunneling and hopping. Dielectric constant of the CB–EP composite increase with increase in temperature and decreases with an increase in frequency from 0.5 kHz to 10 kHz for both room temperature cured and thermally cured specimens. The peak height of the dielectric constant curve of both cured samples decreases with increasing frequency. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Development of nanocomposites is a fast growing field owing to the excellent properties at low concentration of filler. Epoxy based nanocomposites have attracted much interest, as there is an enhancement in the physical properties of epoxy composites due to dispersion of conducting particles within an insulating matrix [1–6]. Epoxy resin a thermosetting material is widely used in advanced structures of composite materials. This is because of the attractive physical and chemical properties. It contains two or more oxirane rings or epoxy groups in their molecular structure. The performance of an epoxy-based nanocomposite significantly depends on its curing circumstance. Studies on curing behavior of epoxy based nanocomposites conclude that epoxide molecules contribute to the curing reaction and react with themselves to form a cross linked network and/or with other reactive molecules whether a catalyst is used or not [7]. Curing of epoxy plays a vital role in its composite properties. The electrical, mechanical, and chemical properties possessed by the epoxy-based composites are due to the curing reaction. Curing refers to an irreversible exothermic chemical reaction by which the composite is transformed from a soft, multi-layered mixture of resin to a hard structural component [8]. During curing low ⁎ Corresponding author at: Department of Physics and Nanotechnology, Maulana Azad National Institute of Technology, Bhopal 462003, M.P., India. E-mail address: [email protected] (M. Trihotri).
http://dx.doi.org/10.1016/j.jnoncrysol.2015.04.020 0022-3093/© 2015 Elsevier B.V. All rights reserved.
molecular weight, resin is converted to an infinite molecular weight polymer with a three-dimensional network structure through chemical reaction or physical interlocking or both. Hence, the study of cure behavior of epoxy composites is significant for the design and analysis of processing parameters [9]. The electrical properties of such systems are dependent on various factors like the curing of composites, the degree of dispersion, the interaction between components, the volume fraction of the filler and percolation [10–14]. Electrical conductivity of polymer nanocomposites strongly depends on the filler content and can be explained in terms of the percolation theory. Below the percolation threshold, the electrically conducting composite materials behave either as insulators or semiconductors, whereas the raise in conductivity with increase of temperature is determined by thermally assisted hopping or, possibly, charge tunneling between the conducting particles [15]. Among the available fillers, carbon black (CB) has been widely used because of its ability to give high electrical conductivity to an insulating polymer at relatively low filler content. Conductivity of an insulating polymeric material using CB as filler is enhanced by free electron transport through a continuous network in the polymer matrix. Carbon black as filler is used to reduce the tunneling distance and increase the number of tunneling contacts, which have to be overcome by charge carriers, determining the overall conductivity [16–18]. The dependence of conductivity σ on temperature can be explained by Arrhenius equation. It expresses the dependence of the conductivity
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σ over a wide range of temperatures in terms of two parameters, first is the preexponential factor A depending on mobilities of charge carriers and second is the experimental activation energy Ea in joules [19]. The equation is given by −Ea σ ¼ A exp KBT
ð1Þ
where KB is the Boltzmann's constant; and T is the temperature in Kelvin. Recent investigation has shown that epoxy/nanocomposites exhibit some advantages for both mechanical and dielectric properties when compared with pure resin system [10,20–22]. An enhancement in the electrical properties of the epoxy nanocomposites can be attributed to the relaxation processes. The relaxation processes correlate to dipolar orientation effects or space charge migration [23,24]. The dielectric effect of the epoxy nanocomposites is due to the charge mobility and interfacial polarization. At lower temperatures, polar side groups enhance the electrical performance of the system. Interfacial polarization is the result of the heterogeneity of the system e.g., mobile charges assembled at the polymer–filler interface form large dipoles. The volume concentrations of the conductive charges are proved crucial parameter governing the electrical behaviour of the polymer composites [25]. When the filler content is low, the mean distance between charge particles or clusters is large and conductance is limited due to the presence of the dielectric polymer matrix. At a critical volume fraction (or percolating threshold) of the filler, a physical path is formed in a way that the current can flow, percolating the whole system [26]. The effect of CB on the network structure of epoxy composites, like volume fraction of the network, the extent of CB reinforcing, and the interparticle distance between conductive particles, has been investigated in detail for thermally cured and as prepared samples. It is found that the conductivity of an insulating epoxy matrix increases continuously with CB content and is well explained by percolation theory. The temperature dependence of the dielectric response has been analyzed below and at near the epoxy glass transition temperature for various CB concentrations. The aim of the present study is to obtain new information on the curing effect on the activation energy and dielectric properties of CB–epoxy composite under different conditions of different temperatures and frequencies. In addition, we attempt to give extensive experimental results that may lead to a better understanding of network structure and electrical properties of carbon black–epoxy (CB–EP) composites for practical applications as heating devices and/or conducting composites. 2. Experimental details 2.1. Materials The carbon black used in this study was Ketjenblack EC-600 JD (Supplied by Akzonoble) with a total surface area, BET 1400 m2/g, diameter 36 nm, apparent bulk density 0.12 g/cm3, iodine absorption 1000–1100 mg/g, pore volume DBP 480–510 ml/100 g and ash content b 0.1 (as specified). The thermosetting matrix used in this study was unmodified epoxy resin provided by Atul Pvt. Ltd. Valsad, India. Fig. 1 (a, b) shows the structure of unmodified epoxy prepolymer resin and structure of a hardener. The density of the resin, cured at room temperature was 1.15 g/cm3.
Fig. 1. (a) Structure of unmodified epoxy pre-polymer resin. (b) Structure of a hardener.
reducing the viscosity of resin and then the weighed amount of CB was mixed with the resin. The mixture was then sonicated for 30 min using an ultrasonic bath sonicator. The mixture was again heated for 15 min and sonicated for another 30 min. This dispersed mixture of CB and epoxy resin was then stirred for 1 h with 50 °C temperature using a hot plate stirrer. After cooling, hardener was added to the mixture in the abovementioned ratio and then stirred for complete mixing. For preventing air entrapment in the prepared mixture, vacuum mixing was used and the mixture was then poured in the mould for making the sheets. The sample sheet was cured at room temperature for 7 days and another set of samples having a same w/v % was cured at 125 °C for 1 h. 2.3. Preparation of test sample Sample sheets of 0.5, 1, 1.5, 2, 2.25, and 2.5 w/v % of CB–EP composite cured at room temperature and at 125 °C were prepared. Test samples, are then cut from the sheets in a square, having the each side of 9 mm and with 2 mm thickness. Uniformity of surface was obtained by polishing the sample. Both surfaces of the sample were coated by airdrying conducting paint in such a way that both the surfaces should not connect electrically with each other. The test samples were then heated at 60 °C for 10 min, to remove the solvent of the silver conducting paste. 3. Characterization 3.1. Activation energy The Arrhenius equation plays a dominant role in classical studies of chemical kinetics. Ea is in practice taken as the slope of an Arrhenius plot of ln (σ) versus 1/T in Kelvin [27,28]. The term (− Ea/KBT) is the slope and Eq. (1) can be rewritten as 1 ln ðσ Þ ¼ ln ðAÞSlope : T
ð2Þ
Now the value of the slope can be computed from the linear graph of ln (σ) V/s 1/T in Kelvin as follows [15]: Slope ¼
Δ ln ðσ Þ . :
Δ
1
ð3Þ
T
The activation energy (Ea) is now calculated as Ea ¼ −K B slope:
ð4Þ
2.2. Composite preparation The slope being negative, a positive value of Ea is obtained [19]. Composite was prepared using a resin/hardener ratio of 10:1. Carbon black was first heated to 60 °C for 30 min in order to remove the moisture. The carbon black–epoxy (CB–EP) composite samples of 0.5, 1, 1.5, 2, 2.25, and 2.5 w/v % respectively were prepared. For the proper dispersion of the CB, initially the resin was heated at 60 °C for 30 min for
3.2. Dielectric measurements Dielectric constant (ε′) refers to the measure of the reduction of coulomb interaction between the ion pairs in polymer electrolytes.
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Fig. 2. (a, b) Shows the Arrhenius plot between log (σ) versus 1/T in K−1 for room temperature cured and thermally cured CB–EP 0.5 w/v % samples at 0.5 kHz, 5 kHz And 10 kHz frequency respectively.
Fig. 3. (a, b) Shows the Arrhenius plot between log (σ) versus 1/T in K−1 for room temperature cured and thermally cured CB–EP 2.5 wt.% samples at 0.5 kHz, 5 kHz And 10 kHz frequency respectively.
Thus the dielectric property of any material/composites provides valuable information such as characteristics of the ionic/molecular interaction of the polymer electrolyte and the understanding of ion transport behavior as well. In all cases, the increase in dielectric constant implies the increase in the number of ions [29]. The method of measuring the dielectric properties of the epoxy composite is explained elsewhere [30].
molecule, the higher is the dielectric constant [30]. Therefore, the polarizability decreases with increase in volume of filler.
4. Results and discussions Thermal curing significantly affects the activation energy and dielectric properties of polymer composites. The dielectric constant of polymeric materials depends on the contribution of interfacial, dipole, electronic and atomic polarizations. The interfacial polarization can explain the behaviour at low frequencies. This type of polarization is due to the heterogeneity present as an impurity in the composite material. Interfacial relaxation occurs when charge carriers are trapped at the interfaces of heterogeneous systems. It decreases with increasing frequency and influences the low frequency dielectric properties. The dielectric constant of the material directly depends upon the polarizability in such a manner that the greater the polarizability of the
4.1. Activation energy Figs. 2 (a, b) and 3 (a, b) indicate the variation of AC conductivity as a function of temperature for 0.5 and 2.5 w/v % prepared CB–EP composite samples respectively at three different frequencies. Resins have a thermally activated character of conductivity. A change of the slope in curve is observed at the temperature above Tg and can be formally connected with the changes of activation energy. With the help of these Arrhenius plots, the corresponding parts of ln (σ) versus 1/T plots were interpolated and from the slope and intercept, the activation energies were estimated. The slope of the linear curve was calculated using Eq. (3) and Ea is calculated using Eq. (4). It is clear that, as the temperature increases the conductivity decreases. The increase in frequency decreases the slope of the straight line. Comparing the room temperature cured samples and thermally cured samples; it was found that the slope decreases as the sample is thermally cured. This behaviour of decrease in slope may be due to the reduction of activation energy Ea. The linear curves called Arrhenius plots shown as a straight line are obtained using curve fitting.
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Table 1 (a, b, c): Activation energies of room temperature and thermally cured samples at 0.5 kHz, 5 kHz and 10 kHz Frequency. Sample
Room temp. cured
Thermally cured
Activation energy Ea at 0.5 kHz EP-00 0.667 EP-0.5 0.686 EP-1 0.705 EP-1.5 0.690 EP-2 0.707 EP-2.25 0.480 EP-2.5 0.580
0.685 0.615 0.685 0.678 0.650 0.575 0.707
Activation energy Ea at 5 kHz EP-00 0.482 EP-0.5 0.436 EP-1 0.465 EP-1.5 0.490 EP-2 0.466 EP-2.25 0.317 EP-2.5 0.448
0.438 0.253 0.420 0.485 0.404 0.386 0.453
Activation energy Ea at 10 kHz EP-00 0.387 EP-0.5 0.370 EP-1 0.405 EP-1.5 0.433 EP-2 0.377 EP-2.25 0.320 EP-2.5 0.361
0.374 0.151 0.347 0.469 0.368 0.292 0.413
The above graphs show that there is a decrease in the activation energy as the filler concentration increases. This may be due to saturation of the dangling bonds; i.e., there is reduction in the density of state. Table 1 (a, b, c) shows the values of activation energies at three different frequencies (0.5 kHz, 5 kHz and 10 kHz) for room temperature cured and thermally cured samples. From these data, we can conclude that the activation energy value is less for room temperature cured samples as compared to the thermally cured samples. It was also observed that the activation energy decreases as the frequency increases. The Ea values for 2.25 w/v % and 2.5 w/v % CB–EP samples were found to be almost the same for both the room temperature cured and thermally cured samples. Fig. 4 (a, b, c) shows the variation of Ea values with respect to filler concentration at three different frequencies (0.5 kHz, 5 kHz and 10 kHz). As seen in Fig. 4 (a, b, c) the values of Ea for room temperature cured and thermally cured samples decrease with increasing CB content and frequency. Decrease in Ea values with CB content may be due to an increase of polarization energy and/or charge carrier density leading to a decrease of the domain boundary potential of CB aggregates into the epoxy matrix [31]. The Ea value shows almost constancy at 2.25 and 2.5 w/v % samples. 4.2. Dielectric constant (ε′) 4.2.1. Effect of volume concentration (Vf) The volume concentration of the fillers in composites has been proved to be a crucial parameter governing the dielectric behaviour of the polymer composites. Figs. 5 (a, b, c) and 6 (a, b, c) show the effect of volume concentration, frequency and temperature on the dielectric constant (ε′) of the prepared CB–EP composites at room temperature cured and thermally cured composites respectively. When the content of filler in polymer matrix is low the dielectric constant (ε′) of the EP– CB composite changes slightly in both types of cured samples at all frequencies (Figs. 5 and 6). The composites exhibit insulating properties due to the large mean distance between charged particles (carbon black as filler) or clusters and limited conductance due to the presence of the filler in polymer matrix. This effect is shown in Fig. 5 (a, b, c) for room temperature cured samples and in Fig. 6 (a, b, c) for thermally cured samples. The conductive CB particles form a finite cluster in the
Fig. 4. (a, b, c) shows the curve of CB concentration versus Ea for room temperature cured and thermally cured samples at 0.5 kHz, 5 kHz, and 10 kHz frequency respectively.
epoxy matrix hence the conductive network paths cannot form in the matrix due to the physical barriers between the gaps. These gaps hinder the flow of charge carriers through the epoxy matrix. A small increase in
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Fig. 5. (a, b, c) Shows the variation of dielectric constant (ε′) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP room temperature cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
conductivity of polymer composite may be attributed to the transportation of the small number of charged particles through the polymer matrix without having any continuous conductive path [10,31]. At a critical volume concentration (or percolating threshold) of the filler, a physical path percolating the whole system is formed within the matrix in a way that the current can flow [26]. It is evident from the three graphs of Figs. 5 and 6 that the volume fraction of the filler affects the dielectric constant (ε′) of the polymer composite considerably. In Fig. 5(a) the value of ε′ with 0.5 w/v% of filler concentration starts increasing from 3.5 and attains a maximum value of 6 at 95 °C and 0.5 kHz frequency, after that it starts decreasing up to 5.2 at 180 °C. The same trend was followed by another w/v % of filler concentration. The effect of postcuring of the sample on ε′ is also clear from Fig. 6 (a, b, c). As the weight percent of the filler increases in both types of room temperature cured and thermally cured samples, dielectric constant (ε′) increases. For thermally cured sample as shown in the curves of Fig. 6(a), ε′ with
0.5 w/v % of filler concentration starts increasing from 5.6 for 0.5 kHz frequency to a maximum value of 8.43 at 95 °C, after that it starts decreasing up to 7.23 at 180 °C. The level of dielectric constant (ε′) for thermally cured samples is higher which supports that the thermal curing maturates the conductive network density and increases the shrinkability among conductive filaments in the epoxy matrix. Comparing the thermally cured to room temperature cured samples, it reflects that the thermal curing acts as an additional cross-linking agent and/ or charge carriers reservoir into the epoxy matrix [31]. The value of the dielectric constant (ε′) of room temperature cured sample raises up to 2.25 w/v % of filler concentration, after that the (ε′) value is almost constant. 4.2.2. Effect of frequency The three graphs (a, b, c) of Figs. 5 and 6 show that dielectric constant decreases with increase in frequency from 0.5 to 10 kHz for both
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Fig. 6. (a, b, c) Shows the variation of dielectric constant (ε′) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP thermally cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
room temperature and thermally cured batches respectively. The peak height at the transition temperature decreases with increasing frequency as shown in Figs. 5 (a, b, c) and 6 (a, b, c). At low frequencies the mobile ions accumulate at the interface which gives a high value of dielectric constant as it is a measure of stored charge directly related to charge carriers. Also, all the dipole groups in the epoxy molecular chains can orient themselves at low frequencies again resulting in higher dielectric constant (ε′). With an increase in the frequency of ac voltage, the polarization fails to settle completely and the values of dielectric constant of epoxy resin begin to drop at the higher frequencies. At high frequencies, periodic reversal of the electric field occurs so fast that there is no room for excess ion diffusion in the direction of the field and polarization due to charge accumulation decreases, leading to the decrease in dielectric constant.
4.2.3. Effect of temperature Figs. 5 and 6 show the temperature dependence of the dielectric constant (ε′) at various frequencies. Dielectric constant (ε′) increases with increase of temperature from 35 to 100 °C (approximate) for all the series of prepared room temperature cured and thermally cured samples. This increase in ε′ is due to the incorporation of carbon black in the epoxy matrix. It was also observed that the ε′ values after 100 °C starts decreasing up to 130 °C and after that it remains almost constant. At lower temperatures, the electrical conductivity is governed by electron tunneling and hopping. The electrical conductivity of CB–EP composites at higher temperatures (above the glass transition temperature Tg of epoxy resin matrix), is governed by the electrical transport in polymer matrix and tunneling from carbon black clusters to the polymer matrix. At higher temperature above 100 °C there is a decrease in dielectric
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Fig. 7. (a, b, c) Shows the variation of dielectric dissipation factor (tan δ) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP room temperature cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
constant of both the samples. There may be two possible reasons for this decrement. Firstly, an increase in the gap between conductive chains due to the thermal expansion of the epoxy matrix. Secondly, near the heat distortion temperature of epoxy, the free volume increases rapidly which result to an increase in the widening between conductive sites which in turn causes the carrier's mobility transfer to be poorer [31]. The reason for conductivity is primarily tunneling, where the carbon particles are not in direct physical contact and the electrons tunnel through the insulating polymer gap between them. As the temperature is increased after 100 °C, the gap between particles also widens and tunneling becomes less probable [10].
4.3. Dielectric dissipation factor (tan δ) 4.3.1. Effect of volume fraction (Vf) Figs. 7 (a, b, c) and 8 (a, b, c) show the variation of dielectric dissipation factor (tan δ) with temperature for different filler concentrations at three different frequencies 0.5 kHz, 5 kHz and 10 kHz for room temperature cured and thermally cured sample respectively. Dissipation factor (tan δ) is the ratio of the electrical power dissipated in a material to the total power circulating in the circuit. In polymers or their composites, tan δ is a function of the electrical conductivity (which depends on the charge carrier mobility) and the applied excitation frequency. There
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Fig. 8. (a, b, c) Shows the variation of dielectric dissipation factor (tan δ) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP thermally cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
are two different interaction processes, which might influence tan δ behaviour in composites. The first one is the number of charge carriers available for electrical conduction and the other is the number of interfaces as well as a polymer chain entanglements present in the bulk [32]. As shown in Fig. 7 there is a trend of continuous decrease of tan δ values at 5 kHz and 10 kHz with increasing filler concentration. However, for the concentration of 1 w/v % of filler concentration tan δ value is comparably high, which may be due to the agglomeration of the CB in the matrix. Inset curves of Fig. 7 show that at 85 °C values of tan δ decrease with an increasing CB concentration in epoxy.
samples. At lower temperatures the values of tan δ are approximately the same. The most likely reason for this observation is a decrease in electrical conductivity in the epoxy composites with increasing frequency, which may be caused by the inability of the charge carriers to traverse the thickness of the material at higher frequencies. At high frequencies, the motion of charge carriers contributing to the conductivity primarily occurs along polymer chains [33]. A barrier to the charge transport in polymers (causing reduction in electrical conductivity) can occur due to defects, inter-chain charge transport and transport through interfaces.
4.3.2. Effect of frequency The plots of Figs. 7 (a, b, c) and 8 (a, b, c) show that in all the composite samples, there is a continuous decrease in tan δ values with increasing frequency for all filler concentrations for both the batches of cured
4.3.3. Effect of temperature Fig. 7 (a, b, c) represents the variation of dissipation factor tan δ with temperature for room temperature cured and thermally cured samples. It is seen from the curves that there is a continuous increase in tan δ
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Fig. 9. (a, b, c) Shows the variation of AC conductivity (σac) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP room temperature cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
values as temperature increases. The inset curves show a sudden increase in tan δ values at 50 °C for room temperature cured samples. The influence of temperature on conductivity has been explained by considering the mobility of charge carriers responsible for hopping. As the temperature increases, the mobility of hopping ions also increases thereby increasing conductivity. The electrons that are involved in hopping are responsible for electronic polarization in these composites. The conductivity increases up to a temperature and further increase of temperature reduces the conductivity. This decrease in conductivity at higher temperature is based on the thermal expansion of polymer. At higher temperatures, the polymer density, reduced by thermal expansion, reduces the conductivity [30]. Probably, in composites, the presence of a large number of interfaces and polymer chain entanglements inhibits the motion of charges in the system, which in turn causes
a reduction in the electrical conductivity thus rendering a lower tan δ value. 4.4. AC conductivity (σac) 4.4.1. Effect of volume fraction (Vf) Figs. 9 (a, b, c) and 10 (a, b, c) show the effect of filler concentration on the AC conductivity (σac) with different frequencies for both the batches of prepared samples. The inset graph of these plots shows that, AC conductivity increases with increasing filler concentration and temperature. The increase in σac is more for the higher filler concentration as compared to the pure epoxy. This increase in σac starts from 50 °C for different filler concentrations. Before this temperature the σac value remains almost the same for all the filler concentration samples.
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Fig. 10. (a, b, c) Shows the variation of AC conductivity (σac) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP thermally cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
4.4.2. Effect of frequency Figs. 9 and 10 show the dependency of the AC conductivity (σac) on the frequency for different w/v % fillers. The increase in conductivity by increasing the frequency and temperature is a common response for polymeric and semiconductor samples [34]. The reason for this increase in AC conductivity (σac) is tremendous increase of the mobility of charge carriers in the polymer composite. It is observed from the inset graph of Figs. 9 and 10 that AC conductivity (σac) suddenly increases after 80 °C (approximately) for room temperature and thermally cured pure epoxy samples at 0.5 kHz. This is because Tg (glass transition temperature) of epoxy is around 75 °C, and below that temperature the
AC conductivity increases gradually but the increase is not appreciable. Above Tg, epoxy comes in amorphous phase, and sudden changes are observed in conductivity. For higher frequencies, (i.e., 5 kHz and 10 kHz) σac values are suddenly increasing after 50 °C for both batches of prepared samples. 4.4.3. Effect of temperature Figs. 9 and 10 show the changes in AC conductivity (σac) with temperature. At high temperature (above glass transition of epoxy resin matrix), electrical conductivity is possible via transport through the conductive epoxy resin (σEP), tunneling between carbon clusters (σCB)
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Fig. 11. (a, b) Shows the variation of dielectric constant (ε′) versus log (f) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP composite samples at 100 °C temperature for room temperature curing and thermally curing respectively.
Fig. 12. (a, b) Shows the variation of dielectric dissipation factor (tan δ) versus log (f) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP composite samples at 100 °C temperature for room temperature curing and thermally curing respectively.
and carbon clusters–epoxy resin series transport (σEP–CB). Thus, the total conductivity of composite is the sum of all three conductivities and represented as:
4.5. Dielectric constant (ε′), tan δ, AC conductivity (σac) with log frequency (f)
σ tot ¼ σ EP þ σ CB þ σ EP−CB :
ð5Þ
It is found that the tunneling conductivity (σCB) occurs also at lower temperatures; however, its temperature dependence is much lower in comparison to that of (σEP). Therefore, this conductivity cannot change remarkably the activation energy of the total conductivity at higher temperatures. The main mechanism responsible for conductivity changes at higher temperatures is the carbon clusters–epoxy resin series transport, where important support comes from electron tunneling through Schottky contact between carbon black and epoxy resin. A simple analysis of such a barrier shows that this potential barrier is inversely proportional to the carrier concentration in completely depleted areas. This phenomenon can explain the decrease of conductivity activation energy with CB concentration. Besides, when the CB concentration increases in CB–EP composite, the contribution of σCB to the total conductivity σtot increases, and therefore the conductivity is minimized (denoting the crossover from electrical conductivity inside and between CB clusters to the CB–epoxy resin serial conductivity) as observed at higher temperatures [35].
The variation of dielectric constant (ε′) values with log frequency (f) for different filler concentrations at 100 °C is shown in Fig. 11 (a, b). It is clear from the figure that ε′ values decrease with the increase in the log (f) for all prepared filler concentrations. The ε′ values are approximately the same for 2.25 and 2.5 w/v % of filler concentration for both the prepared batches. The change of ε′ at lower frequency region is higher than that of at high frequency. The atomic and electronic polarizations are instantaneous polarization components, the effect of which is seen only at high frequencies. The dipole or orientation polarization occurs due to the presence of polar groups in the material. The interfacial polarization arises due to heterogeneity, which is higher at lower frequency. Hence, the higher values of ε′ at low frequency can be explained in terms of interfacial polarization. Fig. 12 (a, b) shows the variation of tan δ with log (f) with different filler concentrations at 100 °C. It is observed that tan δ values decrease with increasing frequency. The behaviour of tan δ with frequency is very much similar to ε′, i.e., with the increase in frequency tan δ value also decreases. The value of tan δ in both the batches of prepared samples at low frequency region becomes high due to free motion of dipoles within the material. It was observed that the ε′ and tan δ decreased with increasing frequency.
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constant as compared to the other concentrations. The dielectric constant increases with increase of temperature and decreases with the increase of frequency from 0.5 kHz to 10 kHz. The peak height at the transition temperature decreases with increasing frequency. The tan δ values continuously increase with increasing frequency for all filler concentrations and remain approximately the same at lower temperatures. Acknowledgment The author is thankful to the Director, Dr. Appu Kuttan K.K., Maulana Azad National Institute of Technology (MANIT) Bhopal-462003 (M.P.) India for providing basic facilities in the institute and acknowledges the support of Dr. Rajnish Kurchania (HOD), Department of Physics, MANIT, Bhopal-462003 (M.P.) India. Special thanks go to Dr. Manish Manoria Director, Truba Groups of Institute, Bhopal-462038 (M.P.) India. References
Fig. 13. (a, b) Shows the variation of AC conductivity (σac) versus log (f) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP composite samples at 100 °C temperature for room temperature curing and thermally curing respectively.
Fig. 13 (a, b) shows the graph between AC conductivity (σac) and log frequency at different filler concentrations at 100 °C. As observed the σac value increases with increase in log (f). With all filler concentrations, the increase of frequency increases AC conductivity, which is due to increase in the hopping of conducting electrons present in filler. At higher frequencies this hopping frequency could not match the applied field frequency. Increase in σac values observed to be sharp for room temperature cured samples as compared to thermally cured samples. 5. Conclusions Both the curing effects on the activation energy and dielectric properties of the CB–EP composites have been investigated in the present work. Thermal curing of the CB–EP composite reduces the activation energy. Room temperature cured CB–EP composites have higher activation energy when compared with thermally cured specimens. Incorporation of carbon black in epoxy composite significantly enhances the dielectric properties of the cured samples as compared to uncured. The conduction mechanisms of the CB–EP composites are governed by hopping conduction process. The dielectric relaxation phenomenon observed, for all volume concentrations, which may be due to dipolar groups of epoxy polymer as well as interfacial polarization. Sample having 2.25 w/v % of filler concentration exhibited higher value of dielectric
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Effect of curing on activation energy and dielectric properties of carbon black–epoxy composites at different temperatures Manindra Trihotri a,b,⁎, U.K. Dwivedi c, Fozia Haque Khan a, M.M. Malik a, M.S. Qureshi a a b c
Department of Physics and Nanotechnology, Maulana Azad National Institute of Technology, Bhopal 462003, M.P. India Department of Physics, Truba Institute of Engineering & Information Technology, Bhopal 462038, M.P., India Department of Physics, Amity University, Jaipur 302006, Rajasthan, India
a r t i c l e
i n f o
Article history: Received 18 December 2014 Received in revised form 8 April 2015 Accepted 10 April 2015 Available online xxxx Keywords: Activation energy; Electron tunneling; Polymer Matrix Composite (PMC); Dielectric properties; Curing effect
a b s t r a c t The effect of curing on activation energy and dielectric properties of carbon black–epoxy (CB–EP) composites has been reported at different temperatures and frequencies. The activation energy was found to be higher for the room temperature cured CB–EP samples as compared with the thermally cured CB–EP samples. Curing behavior of epoxy nanocomposites prove that epoxide molecules contribute to the curing reaction and reacted with them to form a cross-linked network. Dielectric constants of thermally cured CB–EP samples were higher than the room temperature cured samples. The results showed that activation energy, decreased with an increase in the concentration of carbon black in the composite, which may be due to an increase of polarization energy and/or charge carrier density leading to a decrease of the domain boundary potential of carbon black aggregates into the epoxy matrix. At room temperature, the electrical conductivity is due to electron tunneling and hopping. Dielectric constant of the CB–EP composite increase with increase in temperature and decreases with an increase in frequency from 0.5 kHz to 10 kHz for both room temperature cured and thermally cured specimens. The peak height of the dielectric constant curve of both cured samples decreases with increasing frequency. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Development of nanocomposites is a fast growing field owing to the excellent properties at low concentration of filler. Epoxy based nanocomposites have attracted much interest, as there is an enhancement in the physical properties of epoxy composites due to dispersion of conducting particles within an insulating matrix [1–6]. Epoxy resin a thermosetting material is widely used in advanced structures of composite materials. This is because of the attractive physical and chemical properties. It contains two or more oxirane rings or epoxy groups in their molecular structure. The performance of an epoxy-based nanocomposite significantly depends on its curing circumstance. Studies on curing behavior of epoxy based nanocomposites conclude that epoxide molecules contribute to the curing reaction and react with themselves to form a cross linked network and/or with other reactive molecules whether a catalyst is used or not [7]. Curing of epoxy plays a vital role in its composite properties. The electrical, mechanical, and chemical properties possessed by the epoxy-based composites are due to the curing reaction. Curing refers to an irreversible exothermic chemical reaction by which the composite is transformed from a soft, multi-layered mixture of resin to a hard structural component [8]. During curing low ⁎ Corresponding author at: Department of Physics and Nanotechnology, Maulana Azad National Institute of Technology, Bhopal 462003, M.P., India. E-mail address: [email protected] (M. Trihotri).
http://dx.doi.org/10.1016/j.jnoncrysol.2015.04.020 0022-3093/© 2015 Elsevier B.V. All rights reserved.
molecular weight, resin is converted to an infinite molecular weight polymer with a three-dimensional network structure through chemical reaction or physical interlocking or both. Hence, the study of cure behavior of epoxy composites is significant for the design and analysis of processing parameters [9]. The electrical properties of such systems are dependent on various factors like the curing of composites, the degree of dispersion, the interaction between components, the volume fraction of the filler and percolation [10–14]. Electrical conductivity of polymer nanocomposites strongly depends on the filler content and can be explained in terms of the percolation theory. Below the percolation threshold, the electrically conducting composite materials behave either as insulators or semiconductors, whereas the raise in conductivity with increase of temperature is determined by thermally assisted hopping or, possibly, charge tunneling between the conducting particles [15]. Among the available fillers, carbon black (CB) has been widely used because of its ability to give high electrical conductivity to an insulating polymer at relatively low filler content. Conductivity of an insulating polymeric material using CB as filler is enhanced by free electron transport through a continuous network in the polymer matrix. Carbon black as filler is used to reduce the tunneling distance and increase the number of tunneling contacts, which have to be overcome by charge carriers, determining the overall conductivity [16–18]. The dependence of conductivity σ on temperature can be explained by Arrhenius equation. It expresses the dependence of the conductivity
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σ over a wide range of temperatures in terms of two parameters, first is the preexponential factor A depending on mobilities of charge carriers and second is the experimental activation energy Ea in joules [19]. The equation is given by −Ea σ ¼ A exp KBT
ð1Þ
where KB is the Boltzmann's constant; and T is the temperature in Kelvin. Recent investigation has shown that epoxy/nanocomposites exhibit some advantages for both mechanical and dielectric properties when compared with pure resin system [10,20–22]. An enhancement in the electrical properties of the epoxy nanocomposites can be attributed to the relaxation processes. The relaxation processes correlate to dipolar orientation effects or space charge migration [23,24]. The dielectric effect of the epoxy nanocomposites is due to the charge mobility and interfacial polarization. At lower temperatures, polar side groups enhance the electrical performance of the system. Interfacial polarization is the result of the heterogeneity of the system e.g., mobile charges assembled at the polymer–filler interface form large dipoles. The volume concentrations of the conductive charges are proved crucial parameter governing the electrical behaviour of the polymer composites [25]. When the filler content is low, the mean distance between charge particles or clusters is large and conductance is limited due to the presence of the dielectric polymer matrix. At a critical volume fraction (or percolating threshold) of the filler, a physical path is formed in a way that the current can flow, percolating the whole system [26]. The effect of CB on the network structure of epoxy composites, like volume fraction of the network, the extent of CB reinforcing, and the interparticle distance between conductive particles, has been investigated in detail for thermally cured and as prepared samples. It is found that the conductivity of an insulating epoxy matrix increases continuously with CB content and is well explained by percolation theory. The temperature dependence of the dielectric response has been analyzed below and at near the epoxy glass transition temperature for various CB concentrations. The aim of the present study is to obtain new information on the curing effect on the activation energy and dielectric properties of CB–epoxy composite under different conditions of different temperatures and frequencies. In addition, we attempt to give extensive experimental results that may lead to a better understanding of network structure and electrical properties of carbon black–epoxy (CB–EP) composites for practical applications as heating devices and/or conducting composites. 2. Experimental details 2.1. Materials The carbon black used in this study was Ketjenblack EC-600 JD (Supplied by Akzonoble) with a total surface area, BET 1400 m2/g, diameter 36 nm, apparent bulk density 0.12 g/cm3, iodine absorption 1000–1100 mg/g, pore volume DBP 480–510 ml/100 g and ash content b 0.1 (as specified). The thermosetting matrix used in this study was unmodified epoxy resin provided by Atul Pvt. Ltd. Valsad, India. Fig. 1 (a, b) shows the structure of unmodified epoxy prepolymer resin and structure of a hardener. The density of the resin, cured at room temperature was 1.15 g/cm3.
Fig. 1. (a) Structure of unmodified epoxy pre-polymer resin. (b) Structure of a hardener.
reducing the viscosity of resin and then the weighed amount of CB was mixed with the resin. The mixture was then sonicated for 30 min using an ultrasonic bath sonicator. The mixture was again heated for 15 min and sonicated for another 30 min. This dispersed mixture of CB and epoxy resin was then stirred for 1 h with 50 °C temperature using a hot plate stirrer. After cooling, hardener was added to the mixture in the abovementioned ratio and then stirred for complete mixing. For preventing air entrapment in the prepared mixture, vacuum mixing was used and the mixture was then poured in the mould for making the sheets. The sample sheet was cured at room temperature for 7 days and another set of samples having a same w/v % was cured at 125 °C for 1 h. 2.3. Preparation of test sample Sample sheets of 0.5, 1, 1.5, 2, 2.25, and 2.5 w/v % of CB–EP composite cured at room temperature and at 125 °C were prepared. Test samples, are then cut from the sheets in a square, having the each side of 9 mm and with 2 mm thickness. Uniformity of surface was obtained by polishing the sample. Both surfaces of the sample were coated by airdrying conducting paint in such a way that both the surfaces should not connect electrically with each other. The test samples were then heated at 60 °C for 10 min, to remove the solvent of the silver conducting paste. 3. Characterization 3.1. Activation energy The Arrhenius equation plays a dominant role in classical studies of chemical kinetics. Ea is in practice taken as the slope of an Arrhenius plot of ln (σ) versus 1/T in Kelvin [27,28]. The term (− Ea/KBT) is the slope and Eq. (1) can be rewritten as 1 ln ðσ Þ ¼ ln ðAÞSlope : T
ð2Þ
Now the value of the slope can be computed from the linear graph of ln (σ) V/s 1/T in Kelvin as follows [15]: Slope ¼
Δ ln ðσ Þ . :
Δ
1
ð3Þ
T
The activation energy (Ea) is now calculated as Ea ¼ −K B slope:
ð4Þ
2.2. Composite preparation The slope being negative, a positive value of Ea is obtained [19]. Composite was prepared using a resin/hardener ratio of 10:1. Carbon black was first heated to 60 °C for 30 min in order to remove the moisture. The carbon black–epoxy (CB–EP) composite samples of 0.5, 1, 1.5, 2, 2.25, and 2.5 w/v % respectively were prepared. For the proper dispersion of the CB, initially the resin was heated at 60 °C for 30 min for
3.2. Dielectric measurements Dielectric constant (ε′) refers to the measure of the reduction of coulomb interaction between the ion pairs in polymer electrolytes.
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Fig. 2. (a, b) Shows the Arrhenius plot between log (σ) versus 1/T in K−1 for room temperature cured and thermally cured CB–EP 0.5 w/v % samples at 0.5 kHz, 5 kHz And 10 kHz frequency respectively.
Fig. 3. (a, b) Shows the Arrhenius plot between log (σ) versus 1/T in K−1 for room temperature cured and thermally cured CB–EP 2.5 wt.% samples at 0.5 kHz, 5 kHz And 10 kHz frequency respectively.
Thus the dielectric property of any material/composites provides valuable information such as characteristics of the ionic/molecular interaction of the polymer electrolyte and the understanding of ion transport behavior as well. In all cases, the increase in dielectric constant implies the increase in the number of ions [29]. The method of measuring the dielectric properties of the epoxy composite is explained elsewhere [30].
molecule, the higher is the dielectric constant [30]. Therefore, the polarizability decreases with increase in volume of filler.
4. Results and discussions Thermal curing significantly affects the activation energy and dielectric properties of polymer composites. The dielectric constant of polymeric materials depends on the contribution of interfacial, dipole, electronic and atomic polarizations. The interfacial polarization can explain the behaviour at low frequencies. This type of polarization is due to the heterogeneity present as an impurity in the composite material. Interfacial relaxation occurs when charge carriers are trapped at the interfaces of heterogeneous systems. It decreases with increasing frequency and influences the low frequency dielectric properties. The dielectric constant of the material directly depends upon the polarizability in such a manner that the greater the polarizability of the
4.1. Activation energy Figs. 2 (a, b) and 3 (a, b) indicate the variation of AC conductivity as a function of temperature for 0.5 and 2.5 w/v % prepared CB–EP composite samples respectively at three different frequencies. Resins have a thermally activated character of conductivity. A change of the slope in curve is observed at the temperature above Tg and can be formally connected with the changes of activation energy. With the help of these Arrhenius plots, the corresponding parts of ln (σ) versus 1/T plots were interpolated and from the slope and intercept, the activation energies were estimated. The slope of the linear curve was calculated using Eq. (3) and Ea is calculated using Eq. (4). It is clear that, as the temperature increases the conductivity decreases. The increase in frequency decreases the slope of the straight line. Comparing the room temperature cured samples and thermally cured samples; it was found that the slope decreases as the sample is thermally cured. This behaviour of decrease in slope may be due to the reduction of activation energy Ea. The linear curves called Arrhenius plots shown as a straight line are obtained using curve fitting.
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Table 1 (a, b, c): Activation energies of room temperature and thermally cured samples at 0.5 kHz, 5 kHz and 10 kHz Frequency. Sample
Room temp. cured
Thermally cured
Activation energy Ea at 0.5 kHz EP-00 0.667 EP-0.5 0.686 EP-1 0.705 EP-1.5 0.690 EP-2 0.707 EP-2.25 0.480 EP-2.5 0.580
0.685 0.615 0.685 0.678 0.650 0.575 0.707
Activation energy Ea at 5 kHz EP-00 0.482 EP-0.5 0.436 EP-1 0.465 EP-1.5 0.490 EP-2 0.466 EP-2.25 0.317 EP-2.5 0.448
0.438 0.253 0.420 0.485 0.404 0.386 0.453
Activation energy Ea at 10 kHz EP-00 0.387 EP-0.5 0.370 EP-1 0.405 EP-1.5 0.433 EP-2 0.377 EP-2.25 0.320 EP-2.5 0.361
0.374 0.151 0.347 0.469 0.368 0.292 0.413
The above graphs show that there is a decrease in the activation energy as the filler concentration increases. This may be due to saturation of the dangling bonds; i.e., there is reduction in the density of state. Table 1 (a, b, c) shows the values of activation energies at three different frequencies (0.5 kHz, 5 kHz and 10 kHz) for room temperature cured and thermally cured samples. From these data, we can conclude that the activation energy value is less for room temperature cured samples as compared to the thermally cured samples. It was also observed that the activation energy decreases as the frequency increases. The Ea values for 2.25 w/v % and 2.5 w/v % CB–EP samples were found to be almost the same for both the room temperature cured and thermally cured samples. Fig. 4 (a, b, c) shows the variation of Ea values with respect to filler concentration at three different frequencies (0.5 kHz, 5 kHz and 10 kHz). As seen in Fig. 4 (a, b, c) the values of Ea for room temperature cured and thermally cured samples decrease with increasing CB content and frequency. Decrease in Ea values with CB content may be due to an increase of polarization energy and/or charge carrier density leading to a decrease of the domain boundary potential of CB aggregates into the epoxy matrix [31]. The Ea value shows almost constancy at 2.25 and 2.5 w/v % samples. 4.2. Dielectric constant (ε′) 4.2.1. Effect of volume concentration (Vf) The volume concentration of the fillers in composites has been proved to be a crucial parameter governing the dielectric behaviour of the polymer composites. Figs. 5 (a, b, c) and 6 (a, b, c) show the effect of volume concentration, frequency and temperature on the dielectric constant (ε′) of the prepared CB–EP composites at room temperature cured and thermally cured composites respectively. When the content of filler in polymer matrix is low the dielectric constant (ε′) of the EP– CB composite changes slightly in both types of cured samples at all frequencies (Figs. 5 and 6). The composites exhibit insulating properties due to the large mean distance between charged particles (carbon black as filler) or clusters and limited conductance due to the presence of the filler in polymer matrix. This effect is shown in Fig. 5 (a, b, c) for room temperature cured samples and in Fig. 6 (a, b, c) for thermally cured samples. The conductive CB particles form a finite cluster in the
Fig. 4. (a, b, c) shows the curve of CB concentration versus Ea for room temperature cured and thermally cured samples at 0.5 kHz, 5 kHz, and 10 kHz frequency respectively.
epoxy matrix hence the conductive network paths cannot form in the matrix due to the physical barriers between the gaps. These gaps hinder the flow of charge carriers through the epoxy matrix. A small increase in
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Fig. 5. (a, b, c) Shows the variation of dielectric constant (ε′) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP room temperature cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
conductivity of polymer composite may be attributed to the transportation of the small number of charged particles through the polymer matrix without having any continuous conductive path [10,31]. At a critical volume concentration (or percolating threshold) of the filler, a physical path percolating the whole system is formed within the matrix in a way that the current can flow [26]. It is evident from the three graphs of Figs. 5 and 6 that the volume fraction of the filler affects the dielectric constant (ε′) of the polymer composite considerably. In Fig. 5(a) the value of ε′ with 0.5 w/v% of filler concentration starts increasing from 3.5 and attains a maximum value of 6 at 95 °C and 0.5 kHz frequency, after that it starts decreasing up to 5.2 at 180 °C. The same trend was followed by another w/v % of filler concentration. The effect of postcuring of the sample on ε′ is also clear from Fig. 6 (a, b, c). As the weight percent of the filler increases in both types of room temperature cured and thermally cured samples, dielectric constant (ε′) increases. For thermally cured sample as shown in the curves of Fig. 6(a), ε′ with
0.5 w/v % of filler concentration starts increasing from 5.6 for 0.5 kHz frequency to a maximum value of 8.43 at 95 °C, after that it starts decreasing up to 7.23 at 180 °C. The level of dielectric constant (ε′) for thermally cured samples is higher which supports that the thermal curing maturates the conductive network density and increases the shrinkability among conductive filaments in the epoxy matrix. Comparing the thermally cured to room temperature cured samples, it reflects that the thermal curing acts as an additional cross-linking agent and/ or charge carriers reservoir into the epoxy matrix [31]. The value of the dielectric constant (ε′) of room temperature cured sample raises up to 2.25 w/v % of filler concentration, after that the (ε′) value is almost constant. 4.2.2. Effect of frequency The three graphs (a, b, c) of Figs. 5 and 6 show that dielectric constant decreases with increase in frequency from 0.5 to 10 kHz for both
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Fig. 6. (a, b, c) Shows the variation of dielectric constant (ε′) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP thermally cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
room temperature and thermally cured batches respectively. The peak height at the transition temperature decreases with increasing frequency as shown in Figs. 5 (a, b, c) and 6 (a, b, c). At low frequencies the mobile ions accumulate at the interface which gives a high value of dielectric constant as it is a measure of stored charge directly related to charge carriers. Also, all the dipole groups in the epoxy molecular chains can orient themselves at low frequencies again resulting in higher dielectric constant (ε′). With an increase in the frequency of ac voltage, the polarization fails to settle completely and the values of dielectric constant of epoxy resin begin to drop at the higher frequencies. At high frequencies, periodic reversal of the electric field occurs so fast that there is no room for excess ion diffusion in the direction of the field and polarization due to charge accumulation decreases, leading to the decrease in dielectric constant.
4.2.3. Effect of temperature Figs. 5 and 6 show the temperature dependence of the dielectric constant (ε′) at various frequencies. Dielectric constant (ε′) increases with increase of temperature from 35 to 100 °C (approximate) for all the series of prepared room temperature cured and thermally cured samples. This increase in ε′ is due to the incorporation of carbon black in the epoxy matrix. It was also observed that the ε′ values after 100 °C starts decreasing up to 130 °C and after that it remains almost constant. At lower temperatures, the electrical conductivity is governed by electron tunneling and hopping. The electrical conductivity of CB–EP composites at higher temperatures (above the glass transition temperature Tg of epoxy resin matrix), is governed by the electrical transport in polymer matrix and tunneling from carbon black clusters to the polymer matrix. At higher temperature above 100 °C there is a decrease in dielectric
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Fig. 7. (a, b, c) Shows the variation of dielectric dissipation factor (tan δ) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP room temperature cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
constant of both the samples. There may be two possible reasons for this decrement. Firstly, an increase in the gap between conductive chains due to the thermal expansion of the epoxy matrix. Secondly, near the heat distortion temperature of epoxy, the free volume increases rapidly which result to an increase in the widening between conductive sites which in turn causes the carrier's mobility transfer to be poorer [31]. The reason for conductivity is primarily tunneling, where the carbon particles are not in direct physical contact and the electrons tunnel through the insulating polymer gap between them. As the temperature is increased after 100 °C, the gap between particles also widens and tunneling becomes less probable [10].
4.3. Dielectric dissipation factor (tan δ) 4.3.1. Effect of volume fraction (Vf) Figs. 7 (a, b, c) and 8 (a, b, c) show the variation of dielectric dissipation factor (tan δ) with temperature for different filler concentrations at three different frequencies 0.5 kHz, 5 kHz and 10 kHz for room temperature cured and thermally cured sample respectively. Dissipation factor (tan δ) is the ratio of the electrical power dissipated in a material to the total power circulating in the circuit. In polymers or their composites, tan δ is a function of the electrical conductivity (which depends on the charge carrier mobility) and the applied excitation frequency. There
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Fig. 8. (a, b, c) Shows the variation of dielectric dissipation factor (tan δ) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP thermally cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
are two different interaction processes, which might influence tan δ behaviour in composites. The first one is the number of charge carriers available for electrical conduction and the other is the number of interfaces as well as a polymer chain entanglements present in the bulk [32]. As shown in Fig. 7 there is a trend of continuous decrease of tan δ values at 5 kHz and 10 kHz with increasing filler concentration. However, for the concentration of 1 w/v % of filler concentration tan δ value is comparably high, which may be due to the agglomeration of the CB in the matrix. Inset curves of Fig. 7 show that at 85 °C values of tan δ decrease with an increasing CB concentration in epoxy.
samples. At lower temperatures the values of tan δ are approximately the same. The most likely reason for this observation is a decrease in electrical conductivity in the epoxy composites with increasing frequency, which may be caused by the inability of the charge carriers to traverse the thickness of the material at higher frequencies. At high frequencies, the motion of charge carriers contributing to the conductivity primarily occurs along polymer chains [33]. A barrier to the charge transport in polymers (causing reduction in electrical conductivity) can occur due to defects, inter-chain charge transport and transport through interfaces.
4.3.2. Effect of frequency The plots of Figs. 7 (a, b, c) and 8 (a, b, c) show that in all the composite samples, there is a continuous decrease in tan δ values with increasing frequency for all filler concentrations for both the batches of cured
4.3.3. Effect of temperature Fig. 7 (a, b, c) represents the variation of dissipation factor tan δ with temperature for room temperature cured and thermally cured samples. It is seen from the curves that there is a continuous increase in tan δ
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Fig. 9. (a, b, c) Shows the variation of AC conductivity (σac) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP room temperature cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
values as temperature increases. The inset curves show a sudden increase in tan δ values at 50 °C for room temperature cured samples. The influence of temperature on conductivity has been explained by considering the mobility of charge carriers responsible for hopping. As the temperature increases, the mobility of hopping ions also increases thereby increasing conductivity. The electrons that are involved in hopping are responsible for electronic polarization in these composites. The conductivity increases up to a temperature and further increase of temperature reduces the conductivity. This decrease in conductivity at higher temperature is based on the thermal expansion of polymer. At higher temperatures, the polymer density, reduced by thermal expansion, reduces the conductivity [30]. Probably, in composites, the presence of a large number of interfaces and polymer chain entanglements inhibits the motion of charges in the system, which in turn causes
a reduction in the electrical conductivity thus rendering a lower tan δ value. 4.4. AC conductivity (σac) 4.4.1. Effect of volume fraction (Vf) Figs. 9 (a, b, c) and 10 (a, b, c) show the effect of filler concentration on the AC conductivity (σac) with different frequencies for both the batches of prepared samples. The inset graph of these plots shows that, AC conductivity increases with increasing filler concentration and temperature. The increase in σac is more for the higher filler concentration as compared to the pure epoxy. This increase in σac starts from 50 °C for different filler concentrations. Before this temperature the σac value remains almost the same for all the filler concentration samples.
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Fig. 10. (a, b, c) Shows the variation of AC conductivity (σac) versus temperature (T) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP thermally cured composite samples at three different frequencies 0.5 kHz, 5 kHz and 10 kHz.
4.4.2. Effect of frequency Figs. 9 and 10 show the dependency of the AC conductivity (σac) on the frequency for different w/v % fillers. The increase in conductivity by increasing the frequency and temperature is a common response for polymeric and semiconductor samples [34]. The reason for this increase in AC conductivity (σac) is tremendous increase of the mobility of charge carriers in the polymer composite. It is observed from the inset graph of Figs. 9 and 10 that AC conductivity (σac) suddenly increases after 80 °C (approximately) for room temperature and thermally cured pure epoxy samples at 0.5 kHz. This is because Tg (glass transition temperature) of epoxy is around 75 °C, and below that temperature the
AC conductivity increases gradually but the increase is not appreciable. Above Tg, epoxy comes in amorphous phase, and sudden changes are observed in conductivity. For higher frequencies, (i.e., 5 kHz and 10 kHz) σac values are suddenly increasing after 50 °C for both batches of prepared samples. 4.4.3. Effect of temperature Figs. 9 and 10 show the changes in AC conductivity (σac) with temperature. At high temperature (above glass transition of epoxy resin matrix), electrical conductivity is possible via transport through the conductive epoxy resin (σEP), tunneling between carbon clusters (σCB)
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Fig. 11. (a, b) Shows the variation of dielectric constant (ε′) versus log (f) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP composite samples at 100 °C temperature for room temperature curing and thermally curing respectively.
Fig. 12. (a, b) Shows the variation of dielectric dissipation factor (tan δ) versus log (f) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP composite samples at 100 °C temperature for room temperature curing and thermally curing respectively.
and carbon clusters–epoxy resin series transport (σEP–CB). Thus, the total conductivity of composite is the sum of all three conductivities and represented as:
4.5. Dielectric constant (ε′), tan δ, AC conductivity (σac) with log frequency (f)
σ tot ¼ σ EP þ σ CB þ σ EP−CB :
ð5Þ
It is found that the tunneling conductivity (σCB) occurs also at lower temperatures; however, its temperature dependence is much lower in comparison to that of (σEP). Therefore, this conductivity cannot change remarkably the activation energy of the total conductivity at higher temperatures. The main mechanism responsible for conductivity changes at higher temperatures is the carbon clusters–epoxy resin series transport, where important support comes from electron tunneling through Schottky contact between carbon black and epoxy resin. A simple analysis of such a barrier shows that this potential barrier is inversely proportional to the carrier concentration in completely depleted areas. This phenomenon can explain the decrease of conductivity activation energy with CB concentration. Besides, when the CB concentration increases in CB–EP composite, the contribution of σCB to the total conductivity σtot increases, and therefore the conductivity is minimized (denoting the crossover from electrical conductivity inside and between CB clusters to the CB–epoxy resin serial conductivity) as observed at higher temperatures [35].
The variation of dielectric constant (ε′) values with log frequency (f) for different filler concentrations at 100 °C is shown in Fig. 11 (a, b). It is clear from the figure that ε′ values decrease with the increase in the log (f) for all prepared filler concentrations. The ε′ values are approximately the same for 2.25 and 2.5 w/v % of filler concentration for both the prepared batches. The change of ε′ at lower frequency region is higher than that of at high frequency. The atomic and electronic polarizations are instantaneous polarization components, the effect of which is seen only at high frequencies. The dipole or orientation polarization occurs due to the presence of polar groups in the material. The interfacial polarization arises due to heterogeneity, which is higher at lower frequency. Hence, the higher values of ε′ at low frequency can be explained in terms of interfacial polarization. Fig. 12 (a, b) shows the variation of tan δ with log (f) with different filler concentrations at 100 °C. It is observed that tan δ values decrease with increasing frequency. The behaviour of tan δ with frequency is very much similar to ε′, i.e., with the increase in frequency tan δ value also decreases. The value of tan δ in both the batches of prepared samples at low frequency region becomes high due to free motion of dipoles within the material. It was observed that the ε′ and tan δ decreased with increasing frequency.
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constant as compared to the other concentrations. The dielectric constant increases with increase of temperature and decreases with the increase of frequency from 0.5 kHz to 10 kHz. The peak height at the transition temperature decreases with increasing frequency. The tan δ values continuously increase with increasing frequency for all filler concentrations and remain approximately the same at lower temperatures. Acknowledgment The author is thankful to the Director, Dr. Appu Kuttan K.K., Maulana Azad National Institute of Technology (MANIT) Bhopal-462003 (M.P.) India for providing basic facilities in the institute and acknowledges the support of Dr. Rajnish Kurchania (HOD), Department of Physics, MANIT, Bhopal-462003 (M.P.) India. Special thanks go to Dr. Manish Manoria Director, Truba Groups of Institute, Bhopal-462038 (M.P.) India. References
Fig. 13. (a, b) Shows the variation of AC conductivity (σac) versus log (f) for 0.5, 1, 1.5, 2, 2.25 and 2.5 w/v % filler content in CB–EP composite samples at 100 °C temperature for room temperature curing and thermally curing respectively.
Fig. 13 (a, b) shows the graph between AC conductivity (σac) and log frequency at different filler concentrations at 100 °C. As observed the σac value increases with increase in log (f). With all filler concentrations, the increase of frequency increases AC conductivity, which is due to increase in the hopping of conducting electrons present in filler. At higher frequencies this hopping frequency could not match the applied field frequency. Increase in σac values observed to be sharp for room temperature cured samples as compared to thermally cured samples. 5. Conclusions Both the curing effects on the activation energy and dielectric properties of the CB–EP composites have been investigated in the present work. Thermal curing of the CB–EP composite reduces the activation energy. Room temperature cured CB–EP composites have higher activation energy when compared with thermally cured specimens. Incorporation of carbon black in epoxy composite significantly enhances the dielectric properties of the cured samples as compared to uncured. The conduction mechanisms of the CB–EP composites are governed by hopping conduction process. The dielectric relaxation phenomenon observed, for all volume concentrations, which may be due to dipolar groups of epoxy polymer as well as interfacial polarization. Sample having 2.25 w/v % of filler concentration exhibited higher value of dielectric
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