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Alternating-current electrical properties of graphite, carbon-black and carbon-fiber polymeric composites
Composites Science and Technology 61 (2001) 903±909
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Alternating-current electrical properties of graphite, carbon-black and carbon-®ber polymeric composites T.A. Ezquerra *, M.T. Connor 1, S. Roy 2, M. Kulescza 3, J. Fernandes-Nascimento 4, F.J. BaltaÂ-Calleja Instituto de Estructura de la Materia, C.S.I.C. Serrano 119, Madrid 28006, Spain Received 12 February 1999; received in revised form 1 November 1999; accepted 20 July 2000
Abstract Electrical conductivity measurements of graphite, carbon-black and carbon-®ber polymeric composites reported over a broad frequency range covering from d.c. to 109 Hz are comparatively discussed. The d.c. electrical conductivity data from carbon-black and graphite composites exhibit a conducting additive concentration dependence which can be explained on the basis of percolation theory. In both systems, tunneling conduction among particles appears as the predominant mechanism in the concentration range investigated. A frequency-dependent conductivity is observed which is stronger the lower the additive concentration. A modi®cation of the percolation theory which includes the contribution of ®nite-size clusters is invoked to explain the frequency dependence of the conductivity. In carbon-®ber composites, the high ®ber orientation gives rise to materials with higher electrical conductivity levels than those found for particulate composites. The high anisotropic conductivity additionally exhibits an almost absence of frequency dependence. This is explained by assuming the occurrence of a highly interconnected ®ber network with almost an absence of electrical barriers. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Carbon composites; Electrical conductivity
1. Introduction Composites are a class of engineering materials consisting of a mixture of two or more components present as separated phases and combined to improve a given property of each individual component [1]. In particular, the development of conducting composites consisting of conducting particles embedded in a polymeric matrix have been pushed forward by the necessity of having light materials combining the inherent processability of polymers with the electrical conductivity of metals [2]. Carbon-black and carbon-®ber composites are two of the * Corresponding author. E-mail address: [email protected] (T.A. Ezquerra). 1 Present address: EMS-Chemie AG, CH-7013 Domat/EMS, Switzerland. 2 Present address: Datar, F-8, D Road, M.I.D.C., Ambad, Nasik422010, India. 3 Present address: Pedagogical University, Al-Zawadzkiego 13/15, 42-200 Czestochowa, Poland. 4 Present address: Escola Senai Mario Amato, CNTCQP, Av. Jose Odorizzi, 1555, 09861-000-S.B. Campo-SP, Brasil.
most actively investigated systems owing to their increasing application in the automobile and aerospace industry [3,4]. The rise of carbon-black composites as antistatic charge materials or for electromagnetic shielding addressed the interest, as far as electrical properties is concerned, towards the research of both, direct current (d.c.) and alternating current (a.c.) conductivity [5±8]. The electrical conductivity of a polymer can be increased by the addition of a conductive material in particulate or ®brillar form. For a very low content of the conducting additive, the conductivity of the composite remains at the level of the polymeric matrix. As the conductive additive loading is increased, there is a critical concentration, pc, above which a sharp increase of several orders of magnitude is observed [2]. Percolation theory has been used to describe the insulator-to-conductor transition of this kind of materials [9,10]. According to this approach, the electrical conductivity, d.c., follows a volume concentration (p) dependence of the type: d:c: / p
0266-3538/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(00)00176-7
pc t
1
904
T.A. Ezquerra et al. / Composites Science and Technology 61 (2001) 903±909
where pc is the critical concentration of the conducting additive and t is a scaling exponent ranging between 1.6 and 2 in three dimensional materials [10,11]. The frequency dependence of conductivity in composites may be originated from two main eects: (i) anomalous diusion in the conducting clusters [12,13]; and (ii) polarization of the insulating matrix between clusters [14,15]. Due to the fractal nature of the conducting clusters in a composite, the electrical conductivity exhibits a frequency (F) dependence, for F>Fc, of the type: F / Fx
2
where Fc is a critical frequency which depends on the conducting concentration and on the average length of the ®nite conducting clusters [12,13]. A value of x0.6 is expected for an anomalous diusion process [12,13] and a value x0.72 if polarization eects are present [14,15]. In real composite materials there are dierent aspects, besides concentration, which aect conductivity. Among them, the nature of the contact between conducting clusters, the degree of additive dispersion and the ®ller±matrix interaction are of crucial interest [11,16,17]. The analysis of the temperature and frequency dependence on the electrical conductivity of a composite material is a useful procedure to understand and optimize its electrical properties. In this paper, we review the a.c. electrical properties of polymeric composite materials ®lled with dierent conducting additives including carbon black (CB), graphite (G) and carbon ®bers (CF). The frequency dependence of the composites is discussed in the light of a modi®ed view of percolation theory.
CF-composites presented in this work are preimpregnated plies (``prepregs'') based on thermoplastic from Mitsui-Toatsu (TPI), Poly(ether-ether-ketone) from ICI (PEEK) and Poly(ether-ketone-ketone) from Dupont (PEKK) as polymeric matrices. The carbon ®bers, used as conducting ®ller, include T800 ®ber from Toray, AS4 continuous ®bers, and AS4-LDF long discontinuous ®bers from Hercules. Prepeg, 20 mm thick, composites of TPI/T800, PEEK/AS4 and PEKK/AS4LDFTM were used as supplied by the manufacturers with a composition of about 62% carbon ®ber [19]. 2.2. Techniques The alternating current conductivity of the composites was measured by two dierent techniques depending on the frequency range of interest. In the frequency range up to l06 Hz, a four-probe as well as a two-probe geometry was used [17,18,22]. The complex permittivity function *=0 =i00 was determined in the 102±106 Hz range using a Hewlett±Packard 4192 A Impedance Analyzer. The real part of *, related to the storage of energy, corresponds to the dielectric constant. The a.c. conductivity can be derived from the complex part of * using the equation (F)=0.2F.00 [20], where 0 is the vacuum dielectric constant, F is the exciting frequency, and 00 is related to the energy loss of the system. For the 106±109 Hz frequency range, a Novocontrol coaxial line re¯ectometer operating with a 4191 A Hewlett±Packard Analyzer was employed. The conductivity perpendicular to the free surface of the sample can be calculated by measuring the re¯ection coecient [21,22].
2. Experimental
3. Results and discussion
2.1. Materials
3.1. Carbon-black and graphite composites
The composites presented in this work can be divided into two groups: those with granular additives (carbon black (CB) and graphite (G)) and those with ®brillar additive [Carbon ®bers (CF)]. In the ®rst group the ®llers used were: (i) carbon black (grade XE2 from Phillips Petroleum Chemical) with an average particular size of 70 nm, (ii) graphite (grade T75 from Lonza), which consists of anisotropic particles with the largest average dimension in the range of 4.104 nm while the smallest dimension is ten times lower. CB-composites were prepared by mixing with high molecular weight PET (Polyclear T+6, Hoechst, Germany) [18]. G-composites were prepared by mixing with low density polyethylene (LDPE) from Repsol [17]. In both cases, composites were prepared in two consecutive steps. Firstly, by mixing the two phases in order to obtain an homogeneous compound and secondly, by compression molding of the composite plates.
3.1.1. Concentration dependence of conductivity Fig. 1 illustrates typical conductivity values taken at 102 Hz for CB and G composites as a function of the volume percent of the conducting additive. Comparison of the conductivity measured at 102 Hz with the d.c. conductivity of the composite shows similar values. Thus, the conductivity measured at 102 Hz will be considered hereafter as equivalent to the d.c. conductivity. CB-composites exhibit a dramatic stepwise increase of the electrical conductivity from 10 10 S/cm to values around 10 1 S/cm for a critical concentration of pc1.1%. For G-composites a gradual rather than stepwise increase of the conductivity is observed for pc12%. Lower values of conductivity are measured in G-composites as compared with those of CB-composites over the whole range of concentrations explored. The onset of conductivity suggests the formation of an in®nite percolative network through the sample [10,11].
T.A. Ezquerra et al. / Composites Science and Technology 61 (2001) 903±909
905
conducting regions [26]. If a random distribution of particles is assumed, then the mean average distance among particles has been shown to be proportional to p 1/3, thus providing a dependence of the conductivity as log[] /p 1/3 [27]. Such a dependence is observed for both kind of composites in Fig. 2, suggesting that tunneling conduction may be present in these samples. A steeper slope for G-composites owing to the larger particle size of G in relation to CB is expected.
Fig. 1. Plot of at 100 Hz as a function of volume additive concentration (p) for carbon-black (CB) and graphite (G) composites. Continuous lines are best ®ts to Eq. (1).
The dierent behavior followed by CB and G composites must be attributed to the dierent nature of the additive. Carbon-black is an additive characterized by a smaller particle size than graphite. Additionally CB presents a higher tendency to build up highly structured aggregates and agglomerates that increase the probability of contacts [2,5,11]. The d.c. conductivity above the percolation threshold can be analyzed in terms of Eq. (1). Continuous lines in Fig. 1 correspond to ®ttings of experimental values to Eq. (1) with pc=1.1 and t=2.17 for CB-composites and pc=12, t=6.27 for Gcomposites. The value obtained for the CB-composites is similar, although slightly higher, to the one observed in other carbon-black composites [24]. However, it is in agreement with percolation theory [10]. On the contrary the value obtained for the G-composites is higher than the expected one according to percolation theory [10,17]. This apparent disagreement can be partially corrected by shifting in Eq. (1) pc towards higher concentrations [17,23]. However for p
3.1.2. Frequency dependence of conductivity The conductivity of CB- and G-composites is plotted in Fig. 3 for dierent additive concentrations. In both cases, below a critical frequency Fc that increases with additive concentration, conductivity is frequency independent. For frequencies above Fc, the conductivity increases with frequency as predicted by Eq. (2) with a slope x0.72, practically almost independent of concentration, for GBcomposites and x0.56 for G-composites. These values are within the limits expected from percolation theory if one takes into account the fractal nature of conducting clusters [12,13] and the polarization of the polymeric matrix [14,15]. Several approaches have been suggested to explain the frequency dependence of the conductivity of composite materials [12±14,22]. According to percolation theory, the critical frequency, Fc, above which there is a frequency dependent conductivity follows a scaling law with the concentration of the type: Fc / p
pc rw
3
where rw, is a scaling exponent that in three dimensions equals 3.1 [12]. The critical frequency, Fc, for CB
Fig. 2. Dependence of log with p graphite (G) composites.
1/3
for carbon black (CB) and
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T.A. Ezquerra et al. / Composites Science and Technology 61 (2001) 903±909
Fig. 4. Critical frequency, Fc, plotted as a function of volume additive concentration (p) for carbon black (CB) and graphite (G) composites. Continuous line for CB composites is a ®t of experiments to Eq. (3).
Fig. 3. Log±log plot of vs frequency (F) for (upper) carbon black (GB) and (lower) graphite (G) composites. Dasher lines indicates the onset of the frequency dependence at Fc.
and G-composites is plotted in Fig. 4 as a function of the concentration. Experimental values for Fc, denoted in Fig. 3 by the dashed lines, have been de®ned as the frequency at which the value of conductivity is 5% higher than the value taken at 100 Hz. In both cases, one observes an increase of Fc with concentration. Smaller Fc values are measured for G-composites indicating a higher frequency dependence for these composites as compared with CB-composites in the investigated concentration range. For CB-composites a ®t of the experimental data to Eq. (3) is represented in Fig. 4 by the continuous line. However, the value of the exponent is rw=1.5, which diers considerably from the value predicted by the traditional percolation theory. A similar situation appears for G-composites where exponent values higher than expected are also found. A modi®cation of the theory [18] which considers that
above Fc, conductivity increases with frequency due to the additional contribution of ®nite-size clusters can be proposed to explain the frequency dependence of Figs. 3 and 4. The idea is that in these ®nite-size clusters charge carriers perceive an additive concentration which depends on the exciting frequency due to the fractal nature of the clusters. From the above results one can extract some conclusions which have been schematically represented in Fig. 5. For a given concentration, as the conducting particle size is decreased (left to right in Fig. 5) an increase of the overall conductivity of the composite is expected due to two main factors: (i) an improvement of the probability of cluster formation, which allows formation of interconnected particles through the material and (ii) a decrease of the mean average distance between conducting particles, d, which enhances tunneling conductivity. The eect of increasing conductivity dramatically reduces the frequency dependence of the composite by shifting to higher frequencies the critical value Fc. The extension of similar experiments to systems in which a precise control of the particle morphology is possible so that the performance of computer simulations will undoubtedly help the understanding of the above mentioned features [28]. 3.2. Carbon-®ber composites 3.2.1. Anisotropy of the electrical conductivity Due to the nature of carbon-®bers, carbon-®ber composites present a high degree of anisotropy which is re¯ected in many physical properties including thermal and electrical conductivity [29]. Fig. 6 shows the disposition of a prismatic sample in relation to the ®ber direction and to the important directions of measurements. Aniso-
T.A. Ezquerra et al. / Composites Science and Technology 61 (2001) 903±909
907
Fig. 5. Schematic model showing the eect in electrical properties of decreasing particle size for a given additive concentration.
Fig. 6. Schematic representation of the sample disposition with ®ber direction and orientation angle of the sample. WAXS and SAXS patterns obtained in the z-direction for TPI/T800.
tropy can be characterized by wide (WAXS) and small (SAXS) X-ray scattering. Typical X-ray scattering patterns of CF-composites, recorded with the X-ray beam direction along the z-direction, are included in Fig. 6 for the TPI/T800 composite. The WAXS diraction pattern reveals the existence of a sharp equatorial spot at right angles to the ®ber direction at a spacing of about 3.6 AÊ. This spacing is related to the average distance between graphite layers. The shape of this pattern oers evidence of the high degree of orientation of the carbon ®bers in the CF-composites [19]. The SAXS pattern also exhibits a high degree of micro®bril orientation (5 degrees with respect to the ®ber axis), as revealed by the sharp diuse X-ray scattering appearing at right angles to the ®ber direction. For such systems, the electrical conductivity may have dierent values and behaviour in the plane, xy, at different angles , and perpendicular to the ®lm, z. Fig. 7 represents the angular dependence of the electrical conductivity on the X±Y plane, xy d.c. for the three systems investigated. The measurements were carried out in an angular range from 0 (parallel to the ®ber direction) up
Fig. 7. Logarithm of electrical conductivity as a function of the orientation angle of the sample ( ) for TPI/T800 (~), PEEK/AS4 (^) and PEKK/AS4-LDFTM (.). Open symbols: perpendicular direction.
to 90 (perpendicular to the ®ber direction). If we de®ne xy xy the ratio A d:c: j 0 = d:c: j 90 as an indicator of the anisotropy degree in the conductivity, then our results indicate that A is dierent for the three systems investigated. The A values vary from 105 for TPI/T800 to 102 for the sample PEKK/AS4-LDFTM. The values of the electrical conductivity for the three systems in the parallel direction, xy d.c.j =0 are higher and near to each other than the corresponding ones in the perpendicular direction, xy d.c.j =90. This result suggests that for =O electrical conductivity is basically due to the contribution of the continuous carbon ®bers. All the values of zd.c. (right axis, Fig. 7) are very close to each other and their absolute value is not far from that of xy d.c.j =90 for the PEEK/AS4 material. The results of Fig. 7 indicate that, although the average ®ber orientation in the three composite materials, as revealed by X-ray scattering, is simi-
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T.A. Ezquerra et al. / Composites Science and Technology 61 (2001) 903±909
lar, the PEKK/AS4-LDFTM sample presents less anisotropy in the conductivity than the others. This result can be attributed to a higher number of contacts between ®bers occurring in this material in relation to the others, due to the shorter length of the AS4-LDFTM ®bers. 3.2.2. Frequency dependence of the electrical conductivity Fig. 8 shows the frequency dependence of the conductivity, at room temperature, xy (F) for all the investigated systems in the parallel, =0 , and in the perpendicular direction, =90 , as well as the corresponding za.c. data. Additionally, the frequency dependence of a single Toray T-800 carbon ®ber (5 mm diameter) is also shown for comparison (highest conductivity value). A clear absence of a frequency dependence in the investigated frequency range is observed for the CF-composites. This behaviour is in contrast with that of composite materials based on conducting particles like the above mentioned CB- and G-composites which exhibit a frequency dependence of the conductivity that increases as the additive concentration decreases (Fig. 3). As it was explained, the frequency dependence of the conductivity appears to be due to the existence of barriers between conducting regions. For CF-composites, the absence of frequency dependence of the conductivity must be associated with the existence of a continuous conducting network formed by the physically connected ®bers. It is noteworthy that despite of the high carbon ®ber orientation degree in the x-direction, as revealed by X-ray diffraction, there is a three-dimensional continuous network built by the conducting carbon ®bers in the investigated systems. The existence of an anisotropy of conductivity, given by A , must be attributed to a dierent degree of
carbon ®ber connection in the three directions. Due to the length of the carbon ®bers, electrical conductivity in the x-direction proceeds, mainly through the continuous single ®bers. However, in the other directions the absolute value of the conductivity depends on the average number of contacts among ®bers. 3.3. Concluding remarks Electrical conductivity measurements of Graphite (G), Carbon-black (GB) and Carbon-®ber (CF) polymeric composites have been presented in the frequency range from d.c. to 109 Hz. The d.c. electrical conductivity in particulate composites, carbon-black and graphite, exhibits a dependence on the conducting additive concentration which can be explained on the basis of the percolation theory. Lower percolation thresholds and higher conductivity values are observed upon comparing GB with G-composites due to the dierences in particle sizes. In both systems, it was shown that tunneling conduction among particles could be the predominant conduction mechanism. In both systems the conductivity exhibits a frequency dependence which becomes stronger as concentration decreases. A modi®cation of the percolation theory which includes the contribution of ®nite-size clusters can be invoked to explain the frequency dependence of the conductivity. A very dierent picture emerges when studying CF-composites. Here, the high ®ber orientation gives rise to materials with higher electrical conductivity levels than those found for particulate composites. Additionally, the high anisotropic conductivity explains the absence of a frequency dependence as expected when assuming the occurrence of a highly interconnected ®ber network with almost an absence of electrical barriers. Acknowledgements The authors are indebted to the DGICYT (grant PB 94-0049) and to Comunidad de Madrid (07N/0063/1998), Spain, for generous support of this investigation. The following agencies are acknowledged for ®nancial support and fellowships M.T.C. thanks ``Fonds National Suisse de la Recherche Scienti®que'', S.R. thanks M.E.C. (Spain), J.F.N thanks the ISASPS Ferrara (Italy) and M.K. thanks PECO (12148) from EU. We thank Prof. J. Seferis, CPL Univeristy of Washington for supplying the CF-composites. References
Fig. 8. Logarithm of electrical conductivity as a function of logarithm frequency for TPI/T800 =90 (~), PEEK/AS4 =90 (^), PEKK/ AS4-LDFTM =90 (.), TPI/T800 =0 (), PEEK/AS4 =0 (^), PEKK/AS4-LDFTM =0 (*) and Carbon ®ber T800H (&).
[1] Encyclopedia of composite materials and components. New York: Wiley, 1986 [2] Sichel EK, editor. Carbon black polymer composites. New York: Dekker, 1982.
T.A. Ezquerra et al. / Composites Science and Technology 61 (2001) 903±909 [3] Manson JA, Sperling LH. Polymer blends and composites. New York: Plenum Press, 1976. [4] Fitzer E., editor. Carbon ®bers and their composites. Berlin: Springer, 1985. [5] Probst N. Conductive compounds on the move. European Rubber Journal 1984;25±8 [6] Bledzki A, Stankowska D. Kunststoe mit schirmwirkung fuÈr elektromagnetische hochfrequenzwellen. Kunststoe 1984;74:89±96. [7] Wessling B. Elektrisch leitfaÈhige Kunststoe. Kunstoe 1986;76:930±6. [8] MoÈbius KH. FuÈllstohaltige elektrisch leitfhige kunststoe. Kunstoe 1988;78:53±8. [9] Kirkpatrick S. Percolation and conduction. Rev Modern Phys 1973;45:574±88. [10] Stauer D. Introduction to percolation theory. London: Taylor & Francis, 1984. [11] Lux F. Models proposed to explain the electrical conductivity of mixtures made of conductive and insulating materials. J Mater Sci 1993;28:285±301. [12] Gefen Y, Aharony A, Alexander S. Anomalous diusion on percolating clusters. Phys Rev Lett 1983;50:77±80. [13] Laibowitz RB, Gefen Y. Dynamic scaling near the percolation threshold in thin Au ®lms. Phys Rev Lett 1984;53:380±83 [14] Bergman DJ, Imry Y. Critical behaviour of the complex dielectric constant near the percolation threshold of a heterogeneous material. Phys Rev Lett 1977;39:1222±5. [15] Song Y, Noh TW, Lee SI, Gaines JR. Experimental study of the three-dimensional ac conductivity and dielectric constant of a conductor-insulator composite near the percolation threshold. Phys Rev B 1986;33:904±8. [16] Pierre C, Deltour R, Perenboom JAAJ, Van Bentrum PJM. Electricalconduction mechanisms in polymer-copper-particle composites. Phys Rev B 1990;42:3380±94. [17] Ezquerra TA, Kulescza M, Santa Cruz C, BaltaÂ-Calleja FJ. Charge transport in polyehtylene-graphite composite materials. Adv Mater 1990;12:597±600.
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[18] Connor MT, Roy S, Ezquerra TA, BaltaÂ-Calleja FJ. Broadband ac conductivity of conductor-polymer composites. Phys Rev B 1998;57:2286±94. [19] Fernandes-Nascimento J, Ezquerra TA, BaltaÂ-Galleja FJ, Seferis JG. Anisotropy of electrical conductivity and structure in polymer-carbon ®ber composite materials. Polymer Composites 1995;16:109±13. [20] Blythe AR. Electrical properties of polymers. Cambridge: Cambridge University Press, 1979. [21] Kremer F, Boese D, Meier G, Fischer EW. Broadband dielectric spectroscopy on the molecular dynamics in polymer model-systems. Prog Colloid & Polym Sci 1989;80:129±39. [22] Ezquerra TA, Kremer F, Wegner. Ac electrical properties of insulator-conductor composites. In: Priou A., editor. Progress in electromagnetic research PIERS6. New York: Elsevier, 1992. p. 273±301. [23] Ezquerra TA, Kulescza M, BaltaÂ-Galleja FJ. Electrical transport in polyehtylene-graphite composite materials. Synth Met 1991;41(43):915±20. [24] Balberg I. Tunneling and non-universal conductivity in composite materials, Phys. Rev. Lett. 1987;1305±8 [25] Balberg I. Limits of the continuum-percolation transport exponents. Phys Rev B 1998;57:13351±4. [26] Sheng P. Fluctuation Induced tunneling conduction in disordered materials. Phys Rev B 1980;21:2180±95. [27] Boettger H, Bryksin UV. Hopping conduction in solids. Weinheim: VCH, 1985, p. 108 and 148 [28] Flandin L, Verdier M, Boutherin B, Brechet Y, Cavaille JY. A 3D numerical simulation of AC electrical properties of short ®ber composites. J Polym Sci Part B 1999;37:805±14. [29] Bertolotti M, Ferrari A, Liakhou GL, Li Voti R, Marras A, Ezquerra TA, BaltaÂ-Calleja FJ. Thermal anisotropy of polymer carbon ®ber composites as revealed by photode¯ection methods. J AppI Phys 1995;78:5706±12.
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Alternating-current electrical properties of graphite, carbon-black and carbon-®ber polymeric composites T.A. Ezquerra *, M.T. Connor 1, S. Roy 2, M. Kulescza 3, J. Fernandes-Nascimento 4, F.J. BaltaÂ-Calleja Instituto de Estructura de la Materia, C.S.I.C. Serrano 119, Madrid 28006, Spain Received 12 February 1999; received in revised form 1 November 1999; accepted 20 July 2000
Abstract Electrical conductivity measurements of graphite, carbon-black and carbon-®ber polymeric composites reported over a broad frequency range covering from d.c. to 109 Hz are comparatively discussed. The d.c. electrical conductivity data from carbon-black and graphite composites exhibit a conducting additive concentration dependence which can be explained on the basis of percolation theory. In both systems, tunneling conduction among particles appears as the predominant mechanism in the concentration range investigated. A frequency-dependent conductivity is observed which is stronger the lower the additive concentration. A modi®cation of the percolation theory which includes the contribution of ®nite-size clusters is invoked to explain the frequency dependence of the conductivity. In carbon-®ber composites, the high ®ber orientation gives rise to materials with higher electrical conductivity levels than those found for particulate composites. The high anisotropic conductivity additionally exhibits an almost absence of frequency dependence. This is explained by assuming the occurrence of a highly interconnected ®ber network with almost an absence of electrical barriers. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Carbon composites; Electrical conductivity
1. Introduction Composites are a class of engineering materials consisting of a mixture of two or more components present as separated phases and combined to improve a given property of each individual component [1]. In particular, the development of conducting composites consisting of conducting particles embedded in a polymeric matrix have been pushed forward by the necessity of having light materials combining the inherent processability of polymers with the electrical conductivity of metals [2]. Carbon-black and carbon-®ber composites are two of the * Corresponding author. E-mail address: [email protected] (T.A. Ezquerra). 1 Present address: EMS-Chemie AG, CH-7013 Domat/EMS, Switzerland. 2 Present address: Datar, F-8, D Road, M.I.D.C., Ambad, Nasik422010, India. 3 Present address: Pedagogical University, Al-Zawadzkiego 13/15, 42-200 Czestochowa, Poland. 4 Present address: Escola Senai Mario Amato, CNTCQP, Av. Jose Odorizzi, 1555, 09861-000-S.B. Campo-SP, Brasil.
most actively investigated systems owing to their increasing application in the automobile and aerospace industry [3,4]. The rise of carbon-black composites as antistatic charge materials or for electromagnetic shielding addressed the interest, as far as electrical properties is concerned, towards the research of both, direct current (d.c.) and alternating current (a.c.) conductivity [5±8]. The electrical conductivity of a polymer can be increased by the addition of a conductive material in particulate or ®brillar form. For a very low content of the conducting additive, the conductivity of the composite remains at the level of the polymeric matrix. As the conductive additive loading is increased, there is a critical concentration, pc, above which a sharp increase of several orders of magnitude is observed [2]. Percolation theory has been used to describe the insulator-to-conductor transition of this kind of materials [9,10]. According to this approach, the electrical conductivity, d.c., follows a volume concentration (p) dependence of the type: d:c: / p
0266-3538/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(00)00176-7
pc t
1
904
T.A. Ezquerra et al. / Composites Science and Technology 61 (2001) 903±909
where pc is the critical concentration of the conducting additive and t is a scaling exponent ranging between 1.6 and 2 in three dimensional materials [10,11]. The frequency dependence of conductivity in composites may be originated from two main eects: (i) anomalous diusion in the conducting clusters [12,13]; and (ii) polarization of the insulating matrix between clusters [14,15]. Due to the fractal nature of the conducting clusters in a composite, the electrical conductivity exhibits a frequency (F) dependence, for F>Fc, of the type: F / Fx
2
where Fc is a critical frequency which depends on the conducting concentration and on the average length of the ®nite conducting clusters [12,13]. A value of x0.6 is expected for an anomalous diusion process [12,13] and a value x0.72 if polarization eects are present [14,15]. In real composite materials there are dierent aspects, besides concentration, which aect conductivity. Among them, the nature of the contact between conducting clusters, the degree of additive dispersion and the ®ller±matrix interaction are of crucial interest [11,16,17]. The analysis of the temperature and frequency dependence on the electrical conductivity of a composite material is a useful procedure to understand and optimize its electrical properties. In this paper, we review the a.c. electrical properties of polymeric composite materials ®lled with dierent conducting additives including carbon black (CB), graphite (G) and carbon ®bers (CF). The frequency dependence of the composites is discussed in the light of a modi®ed view of percolation theory.
CF-composites presented in this work are preimpregnated plies (``prepregs'') based on thermoplastic from Mitsui-Toatsu (TPI), Poly(ether-ether-ketone) from ICI (PEEK) and Poly(ether-ketone-ketone) from Dupont (PEKK) as polymeric matrices. The carbon ®bers, used as conducting ®ller, include T800 ®ber from Toray, AS4 continuous ®bers, and AS4-LDF long discontinuous ®bers from Hercules. Prepeg, 20 mm thick, composites of TPI/T800, PEEK/AS4 and PEKK/AS4LDFTM were used as supplied by the manufacturers with a composition of about 62% carbon ®ber [19]. 2.2. Techniques The alternating current conductivity of the composites was measured by two dierent techniques depending on the frequency range of interest. In the frequency range up to l06 Hz, a four-probe as well as a two-probe geometry was used [17,18,22]. The complex permittivity function *=0 =i00 was determined in the 102±106 Hz range using a Hewlett±Packard 4192 A Impedance Analyzer. The real part of *, related to the storage of energy, corresponds to the dielectric constant. The a.c. conductivity can be derived from the complex part of * using the equation (F)=0.2F.00 [20], where 0 is the vacuum dielectric constant, F is the exciting frequency, and 00 is related to the energy loss of the system. For the 106±109 Hz frequency range, a Novocontrol coaxial line re¯ectometer operating with a 4191 A Hewlett±Packard Analyzer was employed. The conductivity perpendicular to the free surface of the sample can be calculated by measuring the re¯ection coecient [21,22].
2. Experimental
3. Results and discussion
2.1. Materials
3.1. Carbon-black and graphite composites
The composites presented in this work can be divided into two groups: those with granular additives (carbon black (CB) and graphite (G)) and those with ®brillar additive [Carbon ®bers (CF)]. In the ®rst group the ®llers used were: (i) carbon black (grade XE2 from Phillips Petroleum Chemical) with an average particular size of 70 nm, (ii) graphite (grade T75 from Lonza), which consists of anisotropic particles with the largest average dimension in the range of 4.104 nm while the smallest dimension is ten times lower. CB-composites were prepared by mixing with high molecular weight PET (Polyclear T+6, Hoechst, Germany) [18]. G-composites were prepared by mixing with low density polyethylene (LDPE) from Repsol [17]. In both cases, composites were prepared in two consecutive steps. Firstly, by mixing the two phases in order to obtain an homogeneous compound and secondly, by compression molding of the composite plates.
3.1.1. Concentration dependence of conductivity Fig. 1 illustrates typical conductivity values taken at 102 Hz for CB and G composites as a function of the volume percent of the conducting additive. Comparison of the conductivity measured at 102 Hz with the d.c. conductivity of the composite shows similar values. Thus, the conductivity measured at 102 Hz will be considered hereafter as equivalent to the d.c. conductivity. CB-composites exhibit a dramatic stepwise increase of the electrical conductivity from 10 10 S/cm to values around 10 1 S/cm for a critical concentration of pc1.1%. For G-composites a gradual rather than stepwise increase of the conductivity is observed for pc12%. Lower values of conductivity are measured in G-composites as compared with those of CB-composites over the whole range of concentrations explored. The onset of conductivity suggests the formation of an in®nite percolative network through the sample [10,11].
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conducting regions [26]. If a random distribution of particles is assumed, then the mean average distance among particles has been shown to be proportional to p 1/3, thus providing a dependence of the conductivity as log[] /p 1/3 [27]. Such a dependence is observed for both kind of composites in Fig. 2, suggesting that tunneling conduction may be present in these samples. A steeper slope for G-composites owing to the larger particle size of G in relation to CB is expected.
Fig. 1. Plot of at 100 Hz as a function of volume additive concentration (p) for carbon-black (CB) and graphite (G) composites. Continuous lines are best ®ts to Eq. (1).
The dierent behavior followed by CB and G composites must be attributed to the dierent nature of the additive. Carbon-black is an additive characterized by a smaller particle size than graphite. Additionally CB presents a higher tendency to build up highly structured aggregates and agglomerates that increase the probability of contacts [2,5,11]. The d.c. conductivity above the percolation threshold can be analyzed in terms of Eq. (1). Continuous lines in Fig. 1 correspond to ®ttings of experimental values to Eq. (1) with pc=1.1 and t=2.17 for CB-composites and pc=12, t=6.27 for Gcomposites. The value obtained for the CB-composites is similar, although slightly higher, to the one observed in other carbon-black composites [24]. However, it is in agreement with percolation theory [10]. On the contrary the value obtained for the G-composites is higher than the expected one according to percolation theory [10,17]. This apparent disagreement can be partially corrected by shifting in Eq. (1) pc towards higher concentrations [17,23]. However for p
3.1.2. Frequency dependence of conductivity The conductivity of CB- and G-composites is plotted in Fig. 3 for dierent additive concentrations. In both cases, below a critical frequency Fc that increases with additive concentration, conductivity is frequency independent. For frequencies above Fc, the conductivity increases with frequency as predicted by Eq. (2) with a slope x0.72, practically almost independent of concentration, for GBcomposites and x0.56 for G-composites. These values are within the limits expected from percolation theory if one takes into account the fractal nature of conducting clusters [12,13] and the polarization of the polymeric matrix [14,15]. Several approaches have been suggested to explain the frequency dependence of the conductivity of composite materials [12±14,22]. According to percolation theory, the critical frequency, Fc, above which there is a frequency dependent conductivity follows a scaling law with the concentration of the type: Fc / p
pc rw
3
where rw, is a scaling exponent that in three dimensions equals 3.1 [12]. The critical frequency, Fc, for CB
Fig. 2. Dependence of log with p graphite (G) composites.
1/3
for carbon black (CB) and
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Fig. 4. Critical frequency, Fc, plotted as a function of volume additive concentration (p) for carbon black (CB) and graphite (G) composites. Continuous line for CB composites is a ®t of experiments to Eq. (3).
Fig. 3. Log±log plot of vs frequency (F) for (upper) carbon black (GB) and (lower) graphite (G) composites. Dasher lines indicates the onset of the frequency dependence at Fc.
and G-composites is plotted in Fig. 4 as a function of the concentration. Experimental values for Fc, denoted in Fig. 3 by the dashed lines, have been de®ned as the frequency at which the value of conductivity is 5% higher than the value taken at 100 Hz. In both cases, one observes an increase of Fc with concentration. Smaller Fc values are measured for G-composites indicating a higher frequency dependence for these composites as compared with CB-composites in the investigated concentration range. For CB-composites a ®t of the experimental data to Eq. (3) is represented in Fig. 4 by the continuous line. However, the value of the exponent is rw=1.5, which diers considerably from the value predicted by the traditional percolation theory. A similar situation appears for G-composites where exponent values higher than expected are also found. A modi®cation of the theory [18] which considers that
above Fc, conductivity increases with frequency due to the additional contribution of ®nite-size clusters can be proposed to explain the frequency dependence of Figs. 3 and 4. The idea is that in these ®nite-size clusters charge carriers perceive an additive concentration which depends on the exciting frequency due to the fractal nature of the clusters. From the above results one can extract some conclusions which have been schematically represented in Fig. 5. For a given concentration, as the conducting particle size is decreased (left to right in Fig. 5) an increase of the overall conductivity of the composite is expected due to two main factors: (i) an improvement of the probability of cluster formation, which allows formation of interconnected particles through the material and (ii) a decrease of the mean average distance between conducting particles, d, which enhances tunneling conductivity. The eect of increasing conductivity dramatically reduces the frequency dependence of the composite by shifting to higher frequencies the critical value Fc. The extension of similar experiments to systems in which a precise control of the particle morphology is possible so that the performance of computer simulations will undoubtedly help the understanding of the above mentioned features [28]. 3.2. Carbon-®ber composites 3.2.1. Anisotropy of the electrical conductivity Due to the nature of carbon-®bers, carbon-®ber composites present a high degree of anisotropy which is re¯ected in many physical properties including thermal and electrical conductivity [29]. Fig. 6 shows the disposition of a prismatic sample in relation to the ®ber direction and to the important directions of measurements. Aniso-
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Fig. 5. Schematic model showing the eect in electrical properties of decreasing particle size for a given additive concentration.
Fig. 6. Schematic representation of the sample disposition with ®ber direction and orientation angle of the sample. WAXS and SAXS patterns obtained in the z-direction for TPI/T800.
tropy can be characterized by wide (WAXS) and small (SAXS) X-ray scattering. Typical X-ray scattering patterns of CF-composites, recorded with the X-ray beam direction along the z-direction, are included in Fig. 6 for the TPI/T800 composite. The WAXS diraction pattern reveals the existence of a sharp equatorial spot at right angles to the ®ber direction at a spacing of about 3.6 AÊ. This spacing is related to the average distance between graphite layers. The shape of this pattern oers evidence of the high degree of orientation of the carbon ®bers in the CF-composites [19]. The SAXS pattern also exhibits a high degree of micro®bril orientation (5 degrees with respect to the ®ber axis), as revealed by the sharp diuse X-ray scattering appearing at right angles to the ®ber direction. For such systems, the electrical conductivity may have dierent values and behaviour in the plane, xy, at different angles , and perpendicular to the ®lm, z. Fig. 7 represents the angular dependence of the electrical conductivity on the X±Y plane, xy d.c. for the three systems investigated. The measurements were carried out in an angular range from 0 (parallel to the ®ber direction) up
Fig. 7. Logarithm of electrical conductivity as a function of the orientation angle of the sample ( ) for TPI/T800 (~), PEEK/AS4 (^) and PEKK/AS4-LDFTM (.). Open symbols: perpendicular direction.
to 90 (perpendicular to the ®ber direction). If we de®ne xy xy the ratio A d:c: j 0 = d:c: j 90 as an indicator of the anisotropy degree in the conductivity, then our results indicate that A is dierent for the three systems investigated. The A values vary from 105 for TPI/T800 to 102 for the sample PEKK/AS4-LDFTM. The values of the electrical conductivity for the three systems in the parallel direction, xy d.c.j =0 are higher and near to each other than the corresponding ones in the perpendicular direction, xy d.c.j =90. This result suggests that for =O electrical conductivity is basically due to the contribution of the continuous carbon ®bers. All the values of zd.c. (right axis, Fig. 7) are very close to each other and their absolute value is not far from that of xy d.c.j =90 for the PEEK/AS4 material. The results of Fig. 7 indicate that, although the average ®ber orientation in the three composite materials, as revealed by X-ray scattering, is simi-
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lar, the PEKK/AS4-LDFTM sample presents less anisotropy in the conductivity than the others. This result can be attributed to a higher number of contacts between ®bers occurring in this material in relation to the others, due to the shorter length of the AS4-LDFTM ®bers. 3.2.2. Frequency dependence of the electrical conductivity Fig. 8 shows the frequency dependence of the conductivity, at room temperature, xy (F) for all the investigated systems in the parallel, =0 , and in the perpendicular direction, =90 , as well as the corresponding za.c. data. Additionally, the frequency dependence of a single Toray T-800 carbon ®ber (5 mm diameter) is also shown for comparison (highest conductivity value). A clear absence of a frequency dependence in the investigated frequency range is observed for the CF-composites. This behaviour is in contrast with that of composite materials based on conducting particles like the above mentioned CB- and G-composites which exhibit a frequency dependence of the conductivity that increases as the additive concentration decreases (Fig. 3). As it was explained, the frequency dependence of the conductivity appears to be due to the existence of barriers between conducting regions. For CF-composites, the absence of frequency dependence of the conductivity must be associated with the existence of a continuous conducting network formed by the physically connected ®bers. It is noteworthy that despite of the high carbon ®ber orientation degree in the x-direction, as revealed by X-ray diffraction, there is a three-dimensional continuous network built by the conducting carbon ®bers in the investigated systems. The existence of an anisotropy of conductivity, given by A , must be attributed to a dierent degree of
carbon ®ber connection in the three directions. Due to the length of the carbon ®bers, electrical conductivity in the x-direction proceeds, mainly through the continuous single ®bers. However, in the other directions the absolute value of the conductivity depends on the average number of contacts among ®bers. 3.3. Concluding remarks Electrical conductivity measurements of Graphite (G), Carbon-black (GB) and Carbon-®ber (CF) polymeric composites have been presented in the frequency range from d.c. to 109 Hz. The d.c. electrical conductivity in particulate composites, carbon-black and graphite, exhibits a dependence on the conducting additive concentration which can be explained on the basis of the percolation theory. Lower percolation thresholds and higher conductivity values are observed upon comparing GB with G-composites due to the dierences in particle sizes. In both systems, it was shown that tunneling conduction among particles could be the predominant conduction mechanism. In both systems the conductivity exhibits a frequency dependence which becomes stronger as concentration decreases. A modi®cation of the percolation theory which includes the contribution of ®nite-size clusters can be invoked to explain the frequency dependence of the conductivity. A very dierent picture emerges when studying CF-composites. Here, the high ®ber orientation gives rise to materials with higher electrical conductivity levels than those found for particulate composites. Additionally, the high anisotropic conductivity explains the absence of a frequency dependence as expected when assuming the occurrence of a highly interconnected ®ber network with almost an absence of electrical barriers. Acknowledgements The authors are indebted to the DGICYT (grant PB 94-0049) and to Comunidad de Madrid (07N/0063/1998), Spain, for generous support of this investigation. The following agencies are acknowledged for ®nancial support and fellowships M.T.C. thanks ``Fonds National Suisse de la Recherche Scienti®que'', S.R. thanks M.E.C. (Spain), J.F.N thanks the ISASPS Ferrara (Italy) and M.K. thanks PECO (12148) from EU. We thank Prof. J. Seferis, CPL Univeristy of Washington for supplying the CF-composites. References
Fig. 8. Logarithm of electrical conductivity as a function of logarithm frequency for TPI/T800 =90 (~), PEEK/AS4 =90 (^), PEKK/ AS4-LDFTM =90 (.), TPI/T800 =0 (), PEEK/AS4 =0 (^), PEKK/AS4-LDFTM =0 (*) and Carbon ®ber T800H (&).
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