Composites: Part A 61 (2014) 108–114
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Electrical conductivity phenomena in an epoxy resin–carbon-based materials composite Castellino Micaela a,⇑, Chiolerio Alessandro a, Shahzad Muhammad Imran b, Jagdale Pravin Vitthal b, Tagliaferro Alberto b a b
Center for Space Human Robotics, Istituto Italiano di Tecnologia, Corso Trento 21, Torino 10129, Italy Applied Science and Technology Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy
a r t i c l e
i n f o
Article history: Received 16 January 2013 Received in revised form 7 February 2014 Accepted 10 February 2014 Available online 20 February 2014 Keywords: A. Polymer–matrix composites (PMCs) B. Electrical properties C. Finite element analysis (FEA) D. Physical methods of analysis
a b s t r a c t Nanocomposites (NCs) were prepared using a thermoset commercial epoxy resin and a variety of carbonbased materials (CBMs): carbon beads and powders and 13 different commercial Carbon NanoTubes (CNTs), with the aim of comparing their performance. Electrical behaviour of NCs prepared with two CBMs weight concentrations (1 and 3 wt.%) was investigated. The more promising were selected to study their conductivity behaviour more in detail (5 different concentrations in the range 0–5 wt.%). A thorough electrical characterization, performed with the support of a Finite Element Method (FEM) simulation, allowed us to estimate the resistivities and to apply physical models such as percolation and fluctuation-mediated tunnelling theories. Several conduction behaviours have been found following CBMs type used and its concentration: highly conductive NCs, non-linear diode-like trend and highly resistive. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The development of novel functional materials and of sustainable processes, that lead to products with improved performance, is an open challenge. In fact, the design of materials with new properties for specific applications is the key element in the creation of high value-added products in multidisciplinary technological areas, such as bioscience, optoelectronics, nano-electronics and nano-photonics. In this context, polymer-based composites cover applications ranging from biodegradable packaging, with reduced environmental impact, to biomedical implants [1,2]. The exploration of the nano-world has allowed the integration of nanostructures into polymer matrices with hierarchical architectures [3]. In this way either by compatibilization of nanofillers with different properties or by controlling the collective communication between particles throughout an organized network, it is possible to tailor dielectric, electrical, mechanical, thermal and magnetic properties of nanocomposites [4–9]. In fact, the nanofillers affinity with the polymeric matrices leads to the appearance of synergic structural and ⇑ Corresponding author. Tel.: +39 011 564 7344; fax: +39 011 564 7399. E-mail addresses:
[email protected] (M. Castellino), alessandro.chiolerio@ iit.it (A. Chiolerio),
[email protected] (M.I. Shahzad),
[email protected] (P.V. Jagdale),
[email protected] (A. Tagliaferro). http://dx.doi.org/10.1016/j.compositesa.2014.02.012 1359-835X/Ó 2014 Elsevier Ltd. All rights reserved.
chemical–physical phenomenon not directly attributable to the individual non-interacting components [10]. It has to be pointed out that nanofillers, which provide large interfacial areas, due to their intrinsic high surface-volume ratio, are suitable to create high density composites with a reduced percolation threshold [11]. As a result, the transfer of the properties from the nanoscale to macroscopic materials is very efficient also at low loads (10 >10
>95.0 >95.0 >95.0 >90.0 >90.0 >70.0 >70.0 >95.0 >70.0 >95.0 >60.0 >95.0 >99.0 97.0 98.5 >90.0
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Fig. 1. FESEM images of CBM #9, #10 and #11, as prepared.
Fig. 2. Composites made with epoxy resin with CBM #8 at different wt.% (from 0 to 5 wt.%). The round spot on each side is due to the silver paste, used as electrodes for the IV measurements.
by the commercial code, setting a fine quality of the elements and a progressive element growth, from a minimum element size corresponding to one hundredth of the smallest dimension (3 mm). Boundary conditions are such that a finite potential is kept on the electrodes (either zero or the positive maximum voltage provided by the DC source) and all other surfaces are kept in an ‘‘insulation’’ condition with respect to external volume, hence having no current density component parallel to the surface normal vector. Solution time for each resistivity entry is over 300 s (Intel™ CoreÒ 2 Quad Q9550 2.83 GHz 4 GB DDR3). Convergence is reached when the error (relative difference in the current values between two subsequent minimization steps of FEM code) falls below 106. 2.3. Electrical characterization Electrical measurements were performed using the so called ‘‘Two Point Probe (TPP) method’’ [41] with a Keithley-238 high current source measure unit, used as high voltage source and nanoamperometer. 3. Results and discussion FEM simulations allowed us to estimate the correction factor to be applied to the geometry in order to properly take into account
the real flow of current in the calculation of the resistivity values. An example of the simulation control volume is given in Fig. 4, where two electrodes, having a diameter of 5 mm each, have been placed at the edges of the sample, on front and on rear surface respectively. The current density is distributed almost in the whole sample, with the exception of the portions close to the electrodes, where the effective paths avoid the sample bottom and edges. Based on these simulations, the effective electrical path was estimated to be of thickness 3 mm (same as the sample), width 3 cm (same as the sample) and length 1 cm (sample length reduced due to electrodes size and dead ends). Another electrode arrangement was tested in order to verify the solidity of our approach. When the electrodes are facing one each other on top and bottom sides (see Fig. 5), the volume, in which a non-marginal current density flows, is approximately corresponding to a cylinder having a diameter twice that of the real electrode. In order to find out if the electrodes displacement could affect our results, before testing all the composites, we performed current–voltage (IV) measurements on one selected composite (epoxy + CBM #8) at 3 wt.% with both geometries, finding out that the electrodes configurations do not lead to substantial differences in the conduction behaviour. In fact we obtained similar values for resistivities (39.4 X cm and 36.1 X cm respectively, deviation within 8%). We eventually decided to use the front–back diagonal layout (Fig. 4) for the
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Fig. 3. FESEM images of epoxy composites made with (a) CBM #5 at 3 wt.%; (b) CBM #10 at 3 wt.%; (c) CBM #13 at 1 wt.% and (d) CBM #16 at 3 wt.%.
Fig. 4. Current density simulation with front–back diagonal electrodes geometry.
comparison of NCs, since (i) it involves almost the entire sample volume in the current flow and (ii) it is more easily handled during IV measurements. In Fig. 6 we have reported all the IV curves measured for each sample at 1 and 3 wt.% for all the 16 composites. Most of the samples with 1 wt.% of CBMs show a resistivity (q) value >109 X cm with very noisy signals (see black curves in Fig. 6) that can be considered as typical of insulator materials. However samples #3 and #8, with the same amount of fillers, have shown already remarkable q values in the range 102–103 X cm, with an almost but not fully linear response in the voltage range ±10 V. Increasing the amount of #3 and #8 CBMs to 3 wt.%, resulted in a perfect linear response with q values in the range 100–101 X cm (red curves), while the other NCs, with the same amount of fillers, decreased their resistivity values only down to 105–106 X cm with almost linear curves. We want to stress that #3 and #8 CBMs are the same
kind of MWCNTs (produced by the same company), the first as grown and the latter lightly functionalized with COOH groups. They differ from the others CBMs mainly because of their average length (1.5 lm), which are the shortest among all the MWCNTs (see Table 1). So it seems that the functionalization does not substantially increase or reduce the electrical conductivity of the filler, while it has been proved that the thermal properties can be affected by a functionalization process [42]. SWCNTs, independently from their lengths and functionalization, lead to worse results probably due to the presence of clustering during the dispersion procedure, (see Fig. 3a), which lowers the efficiency of the filler. CBMs #9, #10 and #11, which have been produced in our lab, show the worst behaviour among all, since their IV curves point out that their resistivity values remain almost constant and indeed high (>1010 X cm), even at 3 wt.%. This can be justified by the fact that spherical and oblate fillers (CBM #10), due to their geometry,
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Fig. 5. Current density simulation with front–back vertical electrodes geometry.
Fig. 6. IV curves for all the samples prepared with 1 (black curve) and 3 (red curve) wt.% of CBMs. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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according to this model is more accurate than the previous one, although still not fully compliant with data. So, after an exhaustive search in literature, we have found a revised tunnelling–percolation theory by Ambrosetti et al. [43,50], where they have extended the study of the conductivity dependencies by applying the low-density hopping like approach to higher densities. As it can be seen in Fig. 7 (red dots line) this time the curve fitting is approaching the experimental data in a better way, apart from the lowest measurable conductivity value (0 wt.%) which is limited by the experimental setup or by the polymer matrix intrinsic conductivity. 4. Conclusions
Fig. 7. Epoxy + CBM #8 conductivity as a function of dispersoid volume fraction fitted by percolation [46], tunnelling [49] and a revised tunnelling model [43].
are able to create percolating network if their amount (wt.%) is higher compared with cylindrical and prolate one [43]. On the other hand, CBM #9 and #11, which are made up by a mixture of highly entangled carbon structures (MWCNTs) and amorphous structures, are not suitable to be chosen as good fillers. Also CBM #2 and #12, which are the same kind of MWCNTs produced by the same company, the first one as grown and the latter graphitized, show the same behaviour, highly insulating, both at 1 and 3 wt.%. In this case these MWCNTs possess small diameters ( 109 X). The best performances have been reached by the shortest and thinner MWCNTs (both as grown and slightly functionalized with COOH groups), which can underline that small fillers with a high aspect-ratio (L/D = 158) can be better dispersed inside the composite and create a better percolating network within the matrix. Moreover, since all the CBMs have been dispersed in the same weight percentage, the smallest the dimensions the higher the concentration of fillers nanoparticles inside the composites. In fact, the relationship between the wt.% and the numbers of CNTs per unit volume is given by:
wt:% ¼
mCNT NCNTs k
ð1Þ
where k is a constant depending on the total volume of the composite and the polymer matrix density, while the mass of a single CNT (mCNT) has been calculated according to the formula:
mCNT ¼ rm p L ðNw ðDext þ dw Þ dw ðNw Þ2 Þ
ð2Þ
where L is the length of a CNT, Dext and Dint are respectively the external and internal diameters expressed in nm, Nw is the approximate number of walls for MWCNTs, considering walls spaced by a distance dw = 0.345 nm (lattice spacing of graphite [51]) and rm = 7.6 104 g/m2 is a graphene sheet mass density [52]. We have applied physical models such as the percolation theory and the fluctuation-mediated tunnelling theory to the most conductive NCs, with poor agreement between experimental data and theoretical prediction. Then we have applied a recent revised tunnelling model obtaining a good fit result. Nevertheless a new conductivity model is needed, which has to take into account for real composite characteristics like the presence of impurities, structure and spatial distribution inside the polymer matrix together with defects and agglomeration problems [53]. Acknowledgment Funding has been supported by Politecnico di Torino and Fondi Regione Piemonte (DR 360/2008) within the project ‘‘Charge transport measurements in advanced materials: novel superconductors and nanostructured semiconductors for light harvesting’’. The authors wish to thank Dr. S. Guastella and Dr. A. Virga (Politecnico di Torino) for their FESEM measurements. References [1] Koo JH. Polymer nanocomposites: processing, characterization and applications. New York: McGraw-Hill; 2006. [2] Li C, Thostenson ET, Chou TW. Sensors and actuators based on carbon nanotubes and their composites: a review. Compos Sci Tech 2008;68:1227–49.
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