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Electrical properties and stability of epoxy reinforced carbon black composites
November 2002
Materials Letters 57 (2002) 242 – 251 www.elsevier.com/locate/matlet
Electrical properties and stability of epoxy reinforced carbon black composites Farid El-Tantawy a,*, K. Kamada b, H. Ohnabe c a Department of Physics, Faculty of Science, Suez Canal University, Ismailia, Egypt Graduate Schools of Science and Technology, Niigata University, 8050, Ikarashi 2-nocho, Niigata 950-2181, Japan c Department of Biocybernetics, Faculty of Engineering, Niigata University, 8050, Ikarashi 2-nocho, Niigata 950-2181, Japan b
Received 17 November 2001; accepted 19 November 2001
Abstract The conductivity of an insulating epoxy matrix increases continuously with carbon black (CB) content and is well explained by percolation theory. The effects of CB content and sintering on the electrical conductivity (r) of epoxy composite as a function of temperature during heating and cooling cycles were discussed. The current – voltage – temperature (I – V – T) and working power – temperature ( P – T) characteristics of these composites as a function of CB content were investigated. The thermal stability was tested by means of temperature – time (T – t) curve at certain applied power on and off for one cycle. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Epoxy – carbon black; Composite; Electrical properties; Sintering; Thermal stability; Specific heat
1. Introduction Nowadays, there is great economic interest in negative and positive temperature coefficient of conductivity (NTCC and PTCC) materials because of their technological applications as heater, temperature or current sensors, antistatic coating, electromagnetic radiation shielding and others [1 –4]. Whenever such polymer composites are used as thermistor devices for electrical heater, they are subjected to repeated thermal cycles, and it becomes necessary to understand how electrical conductivity changes with loading filler, repeated thermal cycles and applied
*
Corresponding author. Fax: +20-6432-2381.
working power. The power consumption of the thermistor devices is increasing, leading to increase in the bulk temperature of the thermistor devices. It is therefore important to insure and understand the reliability rate under working power. To the best of our knowledge, no experimental work has been reported about the thermal stability of epoxy – carbon black (CB) composites under thermal cycles and working power. Consequently, the future application of these materials strongly depends on the success of improving their reliability with respect to thermal cycles and working power. With this scope, the purpose of the present contribution is to present new data on the thermal stability under thermal cycles and working power. The effect of sintering on the electrical properties of epoxy – CB composites was investigated in detail.
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 0 7 7 4 - 7
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
2. Experimental Polymer material used in this work was epoxy with a commercial type 815 and hardener type B002W produced by (Yuka Shell Epoxy Chemical, Japan). The resin/hardening ratio was stoichiometric according to the manufacturers’ data sheets. The furnace carbon black CB (Kunebo Chemical, Japan) with particle size 20 Am and surface area of 120 m2 g 1 was used as a filler component in the composite. Five batches of CB/epoxy weight ratios are: 4/6, 5/5, 6/4, 6.5/3.5, 7/3 and abbreviated as F4/6, F5/5, F6/4, F6.5/ 3.5 and F7/3, respectively. The green epoxy/hardener with different content of CB were prepared by centrifuging mixer (Matsuo, Japan); for 1 min at room temperature. Bulk samples of composite were obtained by casting the green composites on Teflon mould. Then the epoxy– CB composites were cured
243
in an oven at 80 jC for 3 h. Bulk electrical conductivity (r) was measured through two-electrode technique [2]. For sintering treatments, the samples were soaked in controlled temperature chamber at 80 jC for 1 week in dry air. For the measurement of the power-dependent temperature, the sample was placed in controlled chamber at 20 jC.
3. Results and discussion 3.1. Determination of the carbon black percolation threshold Conductivity at 25 jC as a function of CB content for epoxy composites is presented in Fig. 1a. It is clear that when CB content is lower than 4 wt.%, the r of composites changes slightly and the composites will
Fig. 1. (a) Dependence of the conductivity at 25 jC for epoxy contains different contents of CB for two batches. (b) (r – T) dependence of asprepared epoxy – CB composites measured in two cycles.
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present insulator properties. This can be explained by the fact that the conductive CB particles in the epoxy matrix are widely separated and formed a finite cluster in epoxy matrix. We presume that once the volume fraction of CB reaches critical value, namely percolation threshold Pc, the new fibrillar conductive and interpenetrating network structure will start to form. Interestingly, r increases continuously with increasing CB content and can be controlled on the molecular level for any desired application. The main reason is that CB improved the interface adhesion and quality of the conductive network structure within the epoxy matrix. The level of r for sintering batch is higher than the as-prepared batch. This supports the notion that sintering matures the conductive network density and increases shrinkability among conductive fila-
ments in epoxy matrix [3]. The packing fraction ( PF) and the effective coordination number (ECN) are given by [1]: PF=(hc/Pc), and ECN=( PF/Pc), where hc is the critical value of volume fraction after percolation, which changes sharply in r. The calculated values for PF and ECN are 0.93 and 2.12, respectively. These values indicate that the CB particles are arranged in closed packed spheres inside the epoxy matrix [4]. 3.2. Temperature dependence electrical conductivity (r –T) Fig. 1b shows (r– T) dependence for as-prepared epoxy – CB composites during heating and cooling cycles. One can see that the specimen’s r decreases
Fig. 2. (a) (r – T) dependence of epoxy sintering at 80 jC for 1 week with different CB content measured in two cycles. (b) Variation of T0, SCP and rm for epoxy with different CB content of as-prepared and sintering samples.
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
as T increases. This indicates the metal nature of the epoxy –CB composites. There are two possible reasons why r decreases with T: (1) an increase in the gap between conductive chains due to the thermal expansion of epoxy matrix may contribute to the decrease in r with T; (2) near the melting point of epoxy, the free volume increases rapidly and consequently increases the widening between conductive sites and thus carrier’s mobility transfer is poorer, and thereby r decreases. The change in r against T during temperature cycle exhibits irreversible process and the level of hysteresis decreases with increasing CB content. We speculate that the decrease of r after the heating cycle is probably due to deflocculating of conductive particles during the cycle, leading to the breakdown of conductive filaments and/or stabilizing effect of conductive particles, which reduces conduction. Fig. 2a shows the (r – T) dependence for sintering batch during heating and cooling cycles. It is clear that
245
the level and/or magnitude of r are higher than that of the as-prepared batch. This is ascribed to a size expansion of the conductive grains, and it reduces the interchain distance among these grains. In addition, we speculate that sintering introduces some texturing of the conductive grains into the epoxy matrix and thereby contribute to an increase in r. The r –T curve was analyzed by applying two different models. According to the first, namely the Mott model, r follows the relation: r(T) = rmexp (T0/T)n, where rm is a moderately temperature-dependence pre-exponential factor, T0 is a characteristic temperature, T is the absolute temperature, and n as Mott-assumed constant density of states; this gives n = 0.25 in three dimensions and n = 0.5 for the one-dimensional hopping conductivity. It is found that the value n = 0.25 fits the data better than the value n = 0.5, which give the Mott three dimensions variable range hopping law with a temperature-dependent rm. The marked increases of rm and
Fig. 3. (a) Variation of NTCC, Ea and Eh for epoxy with different CB contents of as-prepared and sintering batches. (b) NLC and ah for asprepared and sintering batches of epoxy with different contents of CB.
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decreasing T0, as shown in Fig. 2b, for two batches indicate that the conducting paths change the geometrical characteristics inside the epoxy matrix with increasing CB content. These imply that before Pc, i.e. CB V 4 wt.%, the epoxy conductive chains form a one-dimensional system. The size of conducting CB particles (SCP) in the non-conducting epoxy matrix given by: SCP=(4eE0)/(KBT0), where KB is Boltzmann constant, e is the electron charge and E0 is the intensity of the electrical field in the sample and is about 50,000 V/cm3. Examining Fig. 2b, it becomes apparent that the SCP increases for two batches with increasing CB content. These strongly support the idea that CB and sintering act as carrier reservoir and accelerate the mobilization of charge carriers into epoxy matrix. According to the second approach, the activation
energy (Ea) was estimated using the Arrhenius law: r = rpexp [Ea/(KBT)], where rp is the pre-exponential factor that depends on the type of CB and polymers. The hopping energy (Eh) can be calculated according to the following formula: rMT = Aexp [E h/(K BT)], where A is a constant. The estimated value of Ea and Eh as a function of CB content for two batches is displayed in Fig. 3. The value of Eh is quite close to the value of Ea, which means that the conduction mechanism in epoxy –CB composites is governed by small polaron hopping conduction mechanism [3]. At the end, the variations of NTCC at 70 jC versus CB content for two batches are depicted in Fig. 3a. The NTCC for both batches decreases with increasing CB content. While the level of NTCC for sintering batch is lower than that of the as-prepared batch. This indicates
Fig. 4. (a) (I – V – T) curve for as-prepared epoxy with different CB contents. (b) Electrical equivalent circuit of dispersed CB particles in epoxy matrix.
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
that both CB and the sintering process enhance the molecular structure and cross-linking density of the epoxy matrix. 3.3. Current – voltage –temperature (I –V – T) characteristics Fig. 4a shows the (I –V – T) characteristics of asprepared epoxy with different contents of CB. At a low applied voltage, the (I– V) exhibits linear resistance indicating Ohmic behavior. With an increase of the electric field, the behavior of I –V changes from Ohmic to non-Ohmic. This is attributed to the change in the percolation conductive path across the epoxy matrix and thermal fluctuations due to significant joule heating that took place and nonlinearity that set in. Increasing the electric field above a certain voltage, termed as hot voltage (Vh), depends on CB content and leads to an increase in the joule heating effect, and consequently increases the sample temperature and decreases the current—
247
i.e., showing negative resistance (dI/dV) < 0. We focus on the question why the negative resistance appears after Vh. To clarify this phenomena, let us consider the electrical operation circuit of conductive particles inside the epoxy matrix that is described by the electric equivalent circuit in Fig. 4b [4]. We speculate that, at high electric field, the whole polymer matrix is heated by joule heating and therefore polymer matrix contains link and separate conductive phases. At high electric field, the separated conductive filaments may have electrostatic capacity; therefore, the conductive filaments may charge as in the circuit in Fig. 4b. The positively charged conductive filaments may generate Coulomb attractive forces among the separated filaments and repulsive forces among the linking conductive filaments and thus resistance may decrease and/or may increase. This can be explained by the concept that charge carriers in the hot area (i.e., the area after hot voltage) move easily to the positive electrode and therefore the resistance in that side decreases. On the
Fig. 5. (I – V – T) curve for sintering epoxy with different CB contents.
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other hand, the carrier’s vacancy concentration increases at the negative potential pole, resulting in increased resistance. Therefore, we conclude that the negative resistance (i.e., resistance increases) is clearly generated by Coulomb attractive force at high applied field in epoxy composites. Fig. 5 shows the (I– V –T) characteristics of sintering batch for epoxy – CB composites. It is found that the level of current is higher compared to that of the as-prepared batch. This implies that the sintering process enhances the conductive network paths and the network structure density in epoxy matrix. However, the hopping distance (ah) of the charge carriers at high electric filed (i.e., eEHKBT) is given by: J = J0 sinh(aheE/2RT), where J is the current density, E is electric field, J0 is a constant (a/cm2), e is electronic
charge and R is the gas constant. The values ah and nonlinearity coefficient (NLC) at 50 jC versus CB content is plotted in Fig. 3b. Another clue supports the idea that CB and sintering act as carrier reservoir and pinning center effect into the epoxy matrix. 3.4. Temperature –current – time (T –I –t) dependence under applied power Fig. 6a shows the ( P – T) behavior for as-prepared samples. It is clear that the level of temperature increases by joule heating at the same applied power. This means that the insertion of CB into epoxy matrix enhances their thermodynamic stability. The (T – t) curve can serve for the estimation of the thermal stability of epoxy – CB composites, and calculate
Fig. 6. (a) ( P – T) dependence of as-prepared samples. (b) Cp, hr, sg, sd, and ti for two batches of epoxy with different contents of CB.
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
some useful thermal parameters like specific heat (Cp) and amount of heat transfer by radiation and convection (hr). The (T –I –t) dependence, when a power of about 1.5 W/cm3 is applied on and off for both batches, are displayed in Figs. 7 and 8, respectively. Comparing the two batches, it is clear that the magnitude of maximum temperature for the sintering batch is higher than that of the as-prepared batch under the same applied power. This observation clarifies that sintering improves the thermodynamic stability and ordering of epoxy matrix. In Figs. 7 and 8, the (T –t) curve can be divided into three stages: (I) the temperature growth (i.e., power on) stage; (II) the equilibrium stage (i.e., heat gain by working power = heat loss by radiation and convec-
249
tion); and (III) the temperature decay stage (i.e., power off). In stage (I), the characteristic growth time constant (sg) when power is applied, can be expressed by exponentially growth function on the form, and is an calculated as t = sg: [(T(t) Tr)/(Tm Tr)]=1 e( t/sg), where Tr and Tm are the initial and ultimate temperature, respectively. In stage (II), and according to the conservation law of energy, the amount of hr is calculated as: hr=[(IcV0)/(Tm T0)], where V0 is the initial applied voltage and Ic is the steady state current, as seen in Fig. 7b. The (I –t) curve in Fig. 7b can be described by the following empirical formula: [(I(t) I c )/ (Im Ic)] = e( t/ti), where Im is the maximum current and ti is the characteristic current constant and depends on CB content and sintering process. In stage (III), the
Fig. 7. (a) (T – t) characteristics of as-prepared epoxy with different CB contents at an applied power of 1.5 W/cm3. (b) (I – t) characteristics of asprepared epoxy with different CB contents at 1.5 W/cm3.
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Fig. 8. (T – t) characteristics of sintering epoxy with different CB contents when a power of 1.5 W/cm3 is applied.
characteristic decay time constant (sd), i.e. the working power is switched off and is expressed by the following equation: [(T(t) Tr)/(Tm Tr)] = e( t/sd). Fig. 6b presents the calculated values of sg, sd, ti and hr as a function of CB content for two batches. It is clear that sg, sd and ti decrease, while hr increases with increasing CB content for two batches. This means that the incorporation of both CB and sintering process in epoxy matrix improves the ordering and architecture microstructure core of epoxy matrix, which leads to the improvement of their thermal stability. Finally, Cp is calculated on the base of energy balance equation, by using the following equation [4]: Cp=(1/m)[AHrsd (1 e( t0/sd))], where m is the mass of the sample, A is the area of the sample, and t0 is the time required for the temperature of the sample to reach room temperature Tr. It is observed that the Cp rate for the two batches increases with increasing CB content and the
level of sintering batch is higher compared to that of the as-prepared one (see Fig. 6b). This supports the notion that both CB and sintering improve the network density and microstructure stability of epoxy matrix.
4. Conclusions (1) Conductivity of epoxy – CB composites increases continuously with increasing CB content and there it is possible to realize the electrical conductivity of epoxy composites according to desired utilization technology. The temperature dependence of conductivity strongly depends on CB concentration and can be enhanced significantly with sintering process. (2) The conduction mechanism of epoxy – CB composites is governed by the hopping conduction
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
process. NTCC depends on both carbon black and sintering process. (3) I –V characteristics are observed to non-Ohmic at high voltage and show certain kind of switching effect. The negative resistance after hot voltage is generated by Coulomb attractive force. Epoxy– CB composites show good thermal stability and they can be used as heating devices for consumer products.
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References [1] V. Svorick, Polym. Degrad. Stab. 55 (1997) 115. [2] S. Nakamura, Jpn. J. Appl. Phys. 27 (5) (1988) 830. [3] H.H. Hassan, E.M. Abdel-Bary, Appl. Phys. Commun. 9 (4) (1989 – 1990) 267. [4] Y. Fujikura, M. Kawarai, F. Ozaki, Polym. J. 21 (8) (1989) 609.
Materials Letters 57 (2002) 242 – 251 www.elsevier.com/locate/matlet
Electrical properties and stability of epoxy reinforced carbon black composites Farid El-Tantawy a,*, K. Kamada b, H. Ohnabe c a Department of Physics, Faculty of Science, Suez Canal University, Ismailia, Egypt Graduate Schools of Science and Technology, Niigata University, 8050, Ikarashi 2-nocho, Niigata 950-2181, Japan c Department of Biocybernetics, Faculty of Engineering, Niigata University, 8050, Ikarashi 2-nocho, Niigata 950-2181, Japan b
Received 17 November 2001; accepted 19 November 2001
Abstract The conductivity of an insulating epoxy matrix increases continuously with carbon black (CB) content and is well explained by percolation theory. The effects of CB content and sintering on the electrical conductivity (r) of epoxy composite as a function of temperature during heating and cooling cycles were discussed. The current – voltage – temperature (I – V – T) and working power – temperature ( P – T) characteristics of these composites as a function of CB content were investigated. The thermal stability was tested by means of temperature – time (T – t) curve at certain applied power on and off for one cycle. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Epoxy – carbon black; Composite; Electrical properties; Sintering; Thermal stability; Specific heat
1. Introduction Nowadays, there is great economic interest in negative and positive temperature coefficient of conductivity (NTCC and PTCC) materials because of their technological applications as heater, temperature or current sensors, antistatic coating, electromagnetic radiation shielding and others [1 –4]. Whenever such polymer composites are used as thermistor devices for electrical heater, they are subjected to repeated thermal cycles, and it becomes necessary to understand how electrical conductivity changes with loading filler, repeated thermal cycles and applied
*
Corresponding author. Fax: +20-6432-2381.
working power. The power consumption of the thermistor devices is increasing, leading to increase in the bulk temperature of the thermistor devices. It is therefore important to insure and understand the reliability rate under working power. To the best of our knowledge, no experimental work has been reported about the thermal stability of epoxy – carbon black (CB) composites under thermal cycles and working power. Consequently, the future application of these materials strongly depends on the success of improving their reliability with respect to thermal cycles and working power. With this scope, the purpose of the present contribution is to present new data on the thermal stability under thermal cycles and working power. The effect of sintering on the electrical properties of epoxy – CB composites was investigated in detail.
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 0 7 7 4 - 7
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
2. Experimental Polymer material used in this work was epoxy with a commercial type 815 and hardener type B002W produced by (Yuka Shell Epoxy Chemical, Japan). The resin/hardening ratio was stoichiometric according to the manufacturers’ data sheets. The furnace carbon black CB (Kunebo Chemical, Japan) with particle size 20 Am and surface area of 120 m2 g 1 was used as a filler component in the composite. Five batches of CB/epoxy weight ratios are: 4/6, 5/5, 6/4, 6.5/3.5, 7/3 and abbreviated as F4/6, F5/5, F6/4, F6.5/ 3.5 and F7/3, respectively. The green epoxy/hardener with different content of CB were prepared by centrifuging mixer (Matsuo, Japan); for 1 min at room temperature. Bulk samples of composite were obtained by casting the green composites on Teflon mould. Then the epoxy– CB composites were cured
243
in an oven at 80 jC for 3 h. Bulk electrical conductivity (r) was measured through two-electrode technique [2]. For sintering treatments, the samples were soaked in controlled temperature chamber at 80 jC for 1 week in dry air. For the measurement of the power-dependent temperature, the sample was placed in controlled chamber at 20 jC.
3. Results and discussion 3.1. Determination of the carbon black percolation threshold Conductivity at 25 jC as a function of CB content for epoxy composites is presented in Fig. 1a. It is clear that when CB content is lower than 4 wt.%, the r of composites changes slightly and the composites will
Fig. 1. (a) Dependence of the conductivity at 25 jC for epoxy contains different contents of CB for two batches. (b) (r – T) dependence of asprepared epoxy – CB composites measured in two cycles.
244
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
present insulator properties. This can be explained by the fact that the conductive CB particles in the epoxy matrix are widely separated and formed a finite cluster in epoxy matrix. We presume that once the volume fraction of CB reaches critical value, namely percolation threshold Pc, the new fibrillar conductive and interpenetrating network structure will start to form. Interestingly, r increases continuously with increasing CB content and can be controlled on the molecular level for any desired application. The main reason is that CB improved the interface adhesion and quality of the conductive network structure within the epoxy matrix. The level of r for sintering batch is higher than the as-prepared batch. This supports the notion that sintering matures the conductive network density and increases shrinkability among conductive fila-
ments in epoxy matrix [3]. The packing fraction ( PF) and the effective coordination number (ECN) are given by [1]: PF=(hc/Pc), and ECN=( PF/Pc), where hc is the critical value of volume fraction after percolation, which changes sharply in r. The calculated values for PF and ECN are 0.93 and 2.12, respectively. These values indicate that the CB particles are arranged in closed packed spheres inside the epoxy matrix [4]. 3.2. Temperature dependence electrical conductivity (r –T) Fig. 1b shows (r– T) dependence for as-prepared epoxy – CB composites during heating and cooling cycles. One can see that the specimen’s r decreases
Fig. 2. (a) (r – T) dependence of epoxy sintering at 80 jC for 1 week with different CB content measured in two cycles. (b) Variation of T0, SCP and rm for epoxy with different CB content of as-prepared and sintering samples.
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
as T increases. This indicates the metal nature of the epoxy –CB composites. There are two possible reasons why r decreases with T: (1) an increase in the gap between conductive chains due to the thermal expansion of epoxy matrix may contribute to the decrease in r with T; (2) near the melting point of epoxy, the free volume increases rapidly and consequently increases the widening between conductive sites and thus carrier’s mobility transfer is poorer, and thereby r decreases. The change in r against T during temperature cycle exhibits irreversible process and the level of hysteresis decreases with increasing CB content. We speculate that the decrease of r after the heating cycle is probably due to deflocculating of conductive particles during the cycle, leading to the breakdown of conductive filaments and/or stabilizing effect of conductive particles, which reduces conduction. Fig. 2a shows the (r – T) dependence for sintering batch during heating and cooling cycles. It is clear that
245
the level and/or magnitude of r are higher than that of the as-prepared batch. This is ascribed to a size expansion of the conductive grains, and it reduces the interchain distance among these grains. In addition, we speculate that sintering introduces some texturing of the conductive grains into the epoxy matrix and thereby contribute to an increase in r. The r –T curve was analyzed by applying two different models. According to the first, namely the Mott model, r follows the relation: r(T) = rmexp (T0/T)n, where rm is a moderately temperature-dependence pre-exponential factor, T0 is a characteristic temperature, T is the absolute temperature, and n as Mott-assumed constant density of states; this gives n = 0.25 in three dimensions and n = 0.5 for the one-dimensional hopping conductivity. It is found that the value n = 0.25 fits the data better than the value n = 0.5, which give the Mott three dimensions variable range hopping law with a temperature-dependent rm. The marked increases of rm and
Fig. 3. (a) Variation of NTCC, Ea and Eh for epoxy with different CB contents of as-prepared and sintering batches. (b) NLC and ah for asprepared and sintering batches of epoxy with different contents of CB.
246
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
decreasing T0, as shown in Fig. 2b, for two batches indicate that the conducting paths change the geometrical characteristics inside the epoxy matrix with increasing CB content. These imply that before Pc, i.e. CB V 4 wt.%, the epoxy conductive chains form a one-dimensional system. The size of conducting CB particles (SCP) in the non-conducting epoxy matrix given by: SCP=(4eE0)/(KBT0), where KB is Boltzmann constant, e is the electron charge and E0 is the intensity of the electrical field in the sample and is about 50,000 V/cm3. Examining Fig. 2b, it becomes apparent that the SCP increases for two batches with increasing CB content. These strongly support the idea that CB and sintering act as carrier reservoir and accelerate the mobilization of charge carriers into epoxy matrix. According to the second approach, the activation
energy (Ea) was estimated using the Arrhenius law: r = rpexp [Ea/(KBT)], where rp is the pre-exponential factor that depends on the type of CB and polymers. The hopping energy (Eh) can be calculated according to the following formula: rMT = Aexp [E h/(K BT)], where A is a constant. The estimated value of Ea and Eh as a function of CB content for two batches is displayed in Fig. 3. The value of Eh is quite close to the value of Ea, which means that the conduction mechanism in epoxy –CB composites is governed by small polaron hopping conduction mechanism [3]. At the end, the variations of NTCC at 70 jC versus CB content for two batches are depicted in Fig. 3a. The NTCC for both batches decreases with increasing CB content. While the level of NTCC for sintering batch is lower than that of the as-prepared batch. This indicates
Fig. 4. (a) (I – V – T) curve for as-prepared epoxy with different CB contents. (b) Electrical equivalent circuit of dispersed CB particles in epoxy matrix.
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
that both CB and the sintering process enhance the molecular structure and cross-linking density of the epoxy matrix. 3.3. Current – voltage –temperature (I –V – T) characteristics Fig. 4a shows the (I –V – T) characteristics of asprepared epoxy with different contents of CB. At a low applied voltage, the (I– V) exhibits linear resistance indicating Ohmic behavior. With an increase of the electric field, the behavior of I –V changes from Ohmic to non-Ohmic. This is attributed to the change in the percolation conductive path across the epoxy matrix and thermal fluctuations due to significant joule heating that took place and nonlinearity that set in. Increasing the electric field above a certain voltage, termed as hot voltage (Vh), depends on CB content and leads to an increase in the joule heating effect, and consequently increases the sample temperature and decreases the current—
247
i.e., showing negative resistance (dI/dV) < 0. We focus on the question why the negative resistance appears after Vh. To clarify this phenomena, let us consider the electrical operation circuit of conductive particles inside the epoxy matrix that is described by the electric equivalent circuit in Fig. 4b [4]. We speculate that, at high electric field, the whole polymer matrix is heated by joule heating and therefore polymer matrix contains link and separate conductive phases. At high electric field, the separated conductive filaments may have electrostatic capacity; therefore, the conductive filaments may charge as in the circuit in Fig. 4b. The positively charged conductive filaments may generate Coulomb attractive forces among the separated filaments and repulsive forces among the linking conductive filaments and thus resistance may decrease and/or may increase. This can be explained by the concept that charge carriers in the hot area (i.e., the area after hot voltage) move easily to the positive electrode and therefore the resistance in that side decreases. On the
Fig. 5. (I – V – T) curve for sintering epoxy with different CB contents.
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other hand, the carrier’s vacancy concentration increases at the negative potential pole, resulting in increased resistance. Therefore, we conclude that the negative resistance (i.e., resistance increases) is clearly generated by Coulomb attractive force at high applied field in epoxy composites. Fig. 5 shows the (I– V –T) characteristics of sintering batch for epoxy – CB composites. It is found that the level of current is higher compared to that of the as-prepared batch. This implies that the sintering process enhances the conductive network paths and the network structure density in epoxy matrix. However, the hopping distance (ah) of the charge carriers at high electric filed (i.e., eEHKBT) is given by: J = J0 sinh(aheE/2RT), where J is the current density, E is electric field, J0 is a constant (a/cm2), e is electronic
charge and R is the gas constant. The values ah and nonlinearity coefficient (NLC) at 50 jC versus CB content is plotted in Fig. 3b. Another clue supports the idea that CB and sintering act as carrier reservoir and pinning center effect into the epoxy matrix. 3.4. Temperature –current – time (T –I –t) dependence under applied power Fig. 6a shows the ( P – T) behavior for as-prepared samples. It is clear that the level of temperature increases by joule heating at the same applied power. This means that the insertion of CB into epoxy matrix enhances their thermodynamic stability. The (T – t) curve can serve for the estimation of the thermal stability of epoxy – CB composites, and calculate
Fig. 6. (a) ( P – T) dependence of as-prepared samples. (b) Cp, hr, sg, sd, and ti for two batches of epoxy with different contents of CB.
F. El-Tantawy et al. / Materials Letters 57 (2002) 242–251
some useful thermal parameters like specific heat (Cp) and amount of heat transfer by radiation and convection (hr). The (T –I –t) dependence, when a power of about 1.5 W/cm3 is applied on and off for both batches, are displayed in Figs. 7 and 8, respectively. Comparing the two batches, it is clear that the magnitude of maximum temperature for the sintering batch is higher than that of the as-prepared batch under the same applied power. This observation clarifies that sintering improves the thermodynamic stability and ordering of epoxy matrix. In Figs. 7 and 8, the (T –t) curve can be divided into three stages: (I) the temperature growth (i.e., power on) stage; (II) the equilibrium stage (i.e., heat gain by working power = heat loss by radiation and convec-
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tion); and (III) the temperature decay stage (i.e., power off). In stage (I), the characteristic growth time constant (sg) when power is applied, can be expressed by exponentially growth function on the form, and is an calculated as t = sg: [(T(t) Tr)/(Tm Tr)]=1 e( t/sg), where Tr and Tm are the initial and ultimate temperature, respectively. In stage (II), and according to the conservation law of energy, the amount of hr is calculated as: hr=[(IcV0)/(Tm T0)], where V0 is the initial applied voltage and Ic is the steady state current, as seen in Fig. 7b. The (I –t) curve in Fig. 7b can be described by the following empirical formula: [(I(t) I c )/ (Im Ic)] = e( t/ti), where Im is the maximum current and ti is the characteristic current constant and depends on CB content and sintering process. In stage (III), the
Fig. 7. (a) (T – t) characteristics of as-prepared epoxy with different CB contents at an applied power of 1.5 W/cm3. (b) (I – t) characteristics of asprepared epoxy with different CB contents at 1.5 W/cm3.
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Fig. 8. (T – t) characteristics of sintering epoxy with different CB contents when a power of 1.5 W/cm3 is applied.
characteristic decay time constant (sd), i.e. the working power is switched off and is expressed by the following equation: [(T(t) Tr)/(Tm Tr)] = e( t/sd). Fig. 6b presents the calculated values of sg, sd, ti and hr as a function of CB content for two batches. It is clear that sg, sd and ti decrease, while hr increases with increasing CB content for two batches. This means that the incorporation of both CB and sintering process in epoxy matrix improves the ordering and architecture microstructure core of epoxy matrix, which leads to the improvement of their thermal stability. Finally, Cp is calculated on the base of energy balance equation, by using the following equation [4]: Cp=(1/m)[AHrsd (1 e( t0/sd))], where m is the mass of the sample, A is the area of the sample, and t0 is the time required for the temperature of the sample to reach room temperature Tr. It is observed that the Cp rate for the two batches increases with increasing CB content and the
level of sintering batch is higher compared to that of the as-prepared one (see Fig. 6b). This supports the notion that both CB and sintering improve the network density and microstructure stability of epoxy matrix.
4. Conclusions (1) Conductivity of epoxy – CB composites increases continuously with increasing CB content and there it is possible to realize the electrical conductivity of epoxy composites according to desired utilization technology. The temperature dependence of conductivity strongly depends on CB concentration and can be enhanced significantly with sintering process. (2) The conduction mechanism of epoxy – CB composites is governed by the hopping conduction
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process. NTCC depends on both carbon black and sintering process. (3) I –V characteristics are observed to non-Ohmic at high voltage and show certain kind of switching effect. The negative resistance after hot voltage is generated by Coulomb attractive force. Epoxy– CB composites show good thermal stability and they can be used as heating devices for consumer products.
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