Circuit elements in carbon nanotube-polymer composites

Carbon 42 (2004) 1707 1712 www.elsevier.com/locate/carbon Circuit elements in carbon nanotube-polymer composites W.K. Hsu a, *, V. Kotzeva b, P.C.P. Watts c, G.Z. Chen b a Department of Materials Science and Engineering, National Tsing-Hua University, HsinChu 300, Taiwan b Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB4 3QZ, UK c Chemistry Department, University of Sussex, Brighton BN1 9QJ, UK Received 2 December 2003; accepted 28 February 2004 Available online 8 April 2004 Abstract A simple technique has been realized for characterizing the degree of carbon nanotube dispersion in polymer matrices based on the AC impedance spectra, which reveals the nature of circuit elements in the composites, i.e. film resistance and capacitance. A model is proposed to account for nanotube migration in the polymer matrix. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: A. Carbon nanotubes 1. Introduction The degree of carbon nanotube distribution in polymer matrices, and the binding between nanotubes and matrix, determines the properties of the composite materials. Large variations in the data for electrical conductivity and tensile strength of carbon nanotubespolymers have been reported in the literature [1,2]. For example, an uneven distribution of nanotubes in polymers often causes localized conduction across the film [3], and the film mechanical properties depend largely on tube orientation [4]. The experimental outcome varies accordingly from sample to sample. Complex procedures are frequently applied to the polymer-nanotube blending in order to attain a uniform mixture of nanotube and polymer solution; e.g. the surfactant addition to the polymer-filler solution [5], lengthy stirring and ultra-sonication [6] and shear mixing [7]. Meanwhile the low viscosity of the polymer-tube solution must be maintained so that the nanotubes can move freely in order to achieve a reasonable distribution throughout the matrix. The current technique for determining the degree of nanotube dispersion in the polymer matrix is based on the electrical resistive phase and electron microscope imaging. For example when the * Corresponding author. Tel.: +886-357-1513-15399; fax: +886-357- 2236-6. E-mail address: wkhsu@mx.nthu.edu.tw (W.K. Hsu). nanotube content of the polymer reaches a percolation threshold, the composite is often regarded as being homogenous, and the tube tube network structure within the matrix is believed to be complete. In practice a nanotube-polymer film contains not only a resistive phase, but also capacitive characteristics; the former arises from the sum of the intrinsic resistance of nanotubes and tube tube contact resistance, and the localized tube/polymer/tube structure for the latter is similar to that of an electrical capacitor; i.e. metal/insulator/metal. We find that the status of nanotube dispersion in the polymer can also be determined via the capacitive phase, which is even more accurate than using resistive elements as an indication of tube distribution. Our theory is based on the following results. Fig. 1a and b represents a general situation frequently seen in carbon nanotube-polymer films. Fig. 1a indicates that the composite is not yet electrically conducting, due to insufficient nanotube content and an incomplete tube tube network structure. Fig. 1b represents the case when the tube tube network is established and the film is now conducting. The capacitance C ¼ Ake 0 =d; A the metallic plate area, k the relative permittivity of dielectric polymer, e 0 the permittivity of space and d the distance between two metallic plates. The k and e 0 of nanotube and polymer are constant. If we assume that the average value for the polymer area between two localized nanotubes is 20 nm (tube diameter) 1000 nm (tube length) (Fig. 1c) then the d 0008-6223/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2004.02.037

1708 W.K. Hsu et al. / Carbon 42 (2004) 1707 1712 Fig. 1. (a) Low concentration of carbon nanotubes dispersed in a polymer matrix. (b) High concentration of carbon nanotubes dispersed in a polymer matrix. (c) A tube/polymer/tube capacitor structure; D: tube diameter, L: tube length, d: distance between two tubes. value becomes a crucial factor in determining film capacitance. In this work, d means the distance between two localized tubes (Fig. 1c); i.e. the polymer region where electrical charges are stored. If the mean d value in the overall tube-polymer structure is considerable (e.g. Fig. 1a) the population of localized capacitive structure (i.e. tube/polymer/tube) in the composite film is significant. Accordingly, the film capacitance of Fig. 1a should be greater than that in Fig. 1b, which means that when the film resistance decreases (due to increase in tube-load) the capacitance of the composites should also decrease. This work provides a comprehensive comparison between film resistance and capacitance in order to verify the proposed theory above, i.e. the use of film capacitance as indication for nanotube dispersion is superior than using film resistance. 2. Experimental The nanotube-polymer composites were made similar to previous reports, see Refs. [1,3] for details and here we brief as follows. The films were produced as follows. Arc- and CVD-made multi-walled carbon nanotubes were individually mixed with an epoxy resin, followed by addition of a hardener. The mixture was then transferred to a petri-dish, stirred manually and subsequently ultra-sonicated for 30 min in a vacuum. The sonication device was turned off and the mixture was left in the vacuum for 48 h to remove air bubbles. As-films were then cut to equal size (15 mm 40 mm 1 mm). The film resistance and capacitance measurements were carried out using high-resolution AC impedance spectrometry with two terminal connections. 3. Results and discussion The equivalent electrical circuit corresponding to Fig. 1a and b can be expressed as resistors and capacitors connected in parallel (Fig. 2a), and the total impedance of the film can be written: ZðxÞ ¼R=ð1 þ R 2 C 2 x 2 Þ ir 2 Cx=ð1 þ R 2 C 2 x 2 Þ [8,9] where the first and second terms represent the real and imaginary impedance respectively. The complex plane impedance diagram (i.e. real vs. imaginary impedances) of a parallel RC circuit has a semicircle structure [8,9], which is briefly described here. The angular frequency ðxþ is represented by the semicircle and the maximum value for the Z 0 (real impedance) is the distance from the origin to the point intercepted by the circle at the Z 0 axis, which is also equal to the resistance R (Fig. 2a). The maximum value for the Z 00 (imaginary impedance) arises when the angular frequency x ¼ 1=RC dl (C dl : the double layer capacitance at the electrodes). The circuit element R has been detailed previously [10] and it was found that when

W.K. Hsu et al. / Carbon 42 (2004) 1707 1712 1709 Fig. 2. (a) A typical complex impedance diagram for a RC circuit in parallel connection, see Refs. [8,9] for details. (b) Multiple routes for the electrical charge diffusion from one center of the populated nanotubes to neighboring points. (c) The complex impedance plots for arc-nanotubeepoxy films. (d) The complex impedance plots for CVD-nanotube-epoxy films. the nanotube load in the film is low (Fig. 1a) the individual carbon nanotube resistors are connected in series and the total R of the film is expressed as R ¼ P R n þ R contact ( P R n : n ¼ 1; 2; 3;...; localized resistors being connected in series; R contact : the overall tube tube contact resistance). When the tube-load in the film is high (Fig. 1b) the total R of the film is 1=R ¼ P 1=R n þ R contact, which means that individual nanotube resistors in the matrix are connected in parallel [10]. The C circuits in low tube-loaded film (Fig. 1a) are always connected in parallel, because the electrical charge diffusion across the localized polymer regions, from one local tube-network center to the neighboring populated tubes, is not a single pathway, but multiple routes (Fig. 2b). Accordingly the film capacitance is expressed as C ¼ P C n þ C electrode ( P C n : n ¼ 1; 2; 3;...; localized capacitors connected in parallel; C electrode : capacitance between electrodes). Note that the alternating current (AC) can pass through a capacitor, whereas the direct current (DC) cannot. Therefore an insulating film (Fig. 1a), sandwiched between two electrodes, can also produce an electrode capacitance, i.e. C electrode ¼ C dl. When the nanotube content increases (Fig. 1b) the insulating film becomes relatively conducting, as compared with Fig. 1a. So the C electrode decreases significantly and the value of P C n increases. Once the tube tube network is established, charge storage can only occur in the local regions where tube tube contact is poor. This phenomenon can be expressed as capacitors connected in series ð1=c ¼ P 1=C n Þ. Accordingly the total capacitance of the high tube-loaded film (Fig. 1b) is 1=C ¼ P 1=C n þ C electrode. Based on the foregoing argument, circuit elements of the composite film are equivalent to the RC in parallel connections in which the R ¼ P R n þ R contact and C ¼ P C n þ C electrode for the Fig. 1a, and 1=R ¼ P 1=R n þ R contact and 1=C ¼ P 1=C n þ C electrode for the Fig. 1b. Fig. 2c shows an impedance plot of arc-nanotube films and Fig. 2d for the CVD-nanotube films. A common feature, present in Fig. 2c and d, is a semicircle slightly touching the origin, which is consistent with Fig. 2a. The impedance profiles (Fig. 2c and d) can account for our model as follows. First, if the epoxy film contains no nanotubes, the real impedance Z 0 is immeasurable (i.e. no resistive phase) and the contribution to imaginary Z 00 (capacitive reactance) arises purely from the electrode/epoxy/electrode structure, which has been observed in our experiments. Secondly, when nanotubes are incorporated into an epoxy matrix, the resistive

1710 W.K. Hsu et al. / Carbon 42 (2004) 1707 1712 phase begins to emerge and Z 0 becomes measurable, meanwhile the Z 00 rapidly decreases, which is consistent with Fig. 2c and d. The decrease in Z 00 also means that the initial electrode/epoxy/electrode texture has now been transformed into localized tube/epoxy/tube structures and the contribution to the capacitive reactance mainly arises from these localized capacitive phases. The 2 wt.% tube-loaded film exhibits lower Z 0 and Z 00 than values obtained from the films containing 1 wt.% tubes, which is seen in both types of composite film (Fig. 2c and d). This phenomenon is due to enhancement of the resistive phase in 2 wt.% tube-loaded films, accompanied by reduction of the capacitive reactance. Fig. 3a and b illustrate the film resistance and capacitance as a function of nanotube concentration for composites containing arc-tubes and CVD-tubes, respectively. In general, the film capacitance for both types of composites is small, ranging from 1 10 11 to 8 10 11 F. However, Fig. 3a reveals a consistency between resistive and capacitive profiles, i.e. both phases decrease as the nanotube content increases. Fig. 3a supports our model shown in Fig. 1b, namely when the nanotube network structure is established in the matrix, the capacitive phase (electrode/polymer/electrode) gradually becomes a resistive structure (electrode/conductor/electrode). Fig. 3b shows a similar profile for the resistive phase, whereas the capacitive curve is inconsistent with the resistive ðrþ profile; i.e. the capacitative curve fluctuates (Fig. 3b). For example the resistance, R, significantly decreases at 1.5 wt.% tube loading (Fig. 3b), accompanied by an increase in capacitance C.When the R-value reaches 2 3 wt.% the capacitance C again increases. This phenomenon is clearly indicative of poor tube dispersion across the film, which also means that the actual distribution of nanotubes in the matrix cannot be accurately reflected by the resistive profile alone. First, although CVD-made nanotube films exhibit a lower percolation threshold than the arc-films, a considerable population of discontinuous structures and incomplete network still exists in the CVD-films. Secondly, the electrical charges can be stored (i.e. charge accumulation) in the incomplete network, and discontinuous tube tube structures where poor contact and small separation between tubes are present, maintains a high profile of capacitance for the CVD-tube films over the electrical percolation threshold (1 2 wt.%, Fig. 3b). It is noteworthy that the C-value drops as nanotube load reaches the percolation threshold, which is similar to the R-profile. This phenomenon is due to the fact that the R and C constitute composite films and the relationship between both circuit elements follows the ohm s law. Experiments have been repeatedly carried out for both arc- and CVD-nanotube films and the results were always similar to Fig. 3a and b. The question remains as to why CVD-nanotubes exhibit a poor dispersion in the polymer, as compared with arc-nanotubes. Here we propose a model to account for the difference in their dispersion behavior in the polymer matrix. The CVD-nanotubes are defective and already contain functional groups on the tube surfaces (e.g. OH, CO) as recorded [10]. The arc-nanotubes are graphitic structures and, as a result, have less functional groups, due to high annealing temperatures from the arc process. These functional groups, either chemically or physically bonded to nanotube lattices, can act as strong connections with polymers chains (i.e. a stronger binding with polymer), because the interaction of polarized lattice defects and tube surface functional groups with polymer chains are strong. Accordingly, the CVD-nanotube migration within the polymer matrix, before film solidification, is limited (i.e. tubes are anchored by polymer chains) and tube dispersion in the matrix assisted via an ultra-sonication becomes insignificant. On the other hand, the weaker binding between the arc-tube structure and the epoxy significantly helps nanotube migration in the matrix. Another factor, which also assists arc-nanotube dispersion in the matrix, is the presence of gaseous O 2, which adhere to nanotube surfaces. Small O 2 bubbles attached to the nanotube surfaces can act as lubricants for assisting tube migration. (Note: a vacuum environment can only remove larger bubbles from the tube-epoxy solution.) Fig. 4 shows two images made by passing light through two thin (1 mm) films containing CVD- (a) and arc- Fig. 3. (a) The resistance capacitance vs. arc-nanotube loaded films. (b) The resistance capacitance vs. CVD-nanotube loaded films.

W.K. Hsu et al. / Carbon 42 (2004) 1707 1712 1711 Fig. 4. (a) A light microscope image taken from a CVD-nanotube film surface (insert). (b) A light microscopy image taken from an arc-nanotube film surface. Insert: void structures. (c) Low magnification SEM image of CVD-nanotube film. (d) Enlarged SEM image from Fig 4c. (e) SEM image of a CVD-nanotube coated with epoxy. (f) SEM image of a void structure from arc-nanotube film surface. (g) SEM image of protruding arc-nanotubes from a void. nanotubes (b) respectively. No significant void structures are seen in Fig. 4a, instead gray regions are present among dark areas (arrows). The gray regions are aggregated CVD-nanotubes and light can therefore pass through large gaps between nanotube aggregates (arrows, darker regions, Fig. 4a). SEM investigations show that the gray regions contain embedded and protruding tubes (Fig. 4c and d); the tubes being often coated with epoxy (Fig. 4e). In contrast, Fig. 4b shows a uniform surface from arc-tube epoxy films and no distinguishable gray-dark regions are found. However small voids (1 5 lm) are present on the film surface (insert, arrows, Fig. 4b) where nanotubes aggregate, as revealed by SEM (Fig. 4f and g). Arc-nanotubes coated with epoxy are only occasionally seen in our SEM investigations, and the number of uncoated-tubes is significant. Nanotube aggregation at bubble-like structures (Fig. 4f and g) supports our model. First, the adhered O 2 on nanotube surfaces prevents polymer coating and therefore assists tube migration in the matrix. Secondly, when tubes aggregate, small O 2 bubbles rapidly combine and become larger voids (Fig. 5a c), consistent with the Fig. 4f and g. The experiments have been repeatedly carried out and bubble structures were always found to be present in the arc-nanotube films. The absence of voids in CVD-tube films suggests that the tube migration is limited by: (a) a stronger binding force with epoxy, as consistent with epoxy coated tube structure (Fig. 4e), and (b) the lower density of O 2 bubbles adhere to CVDnanotube surfaces, because CVD-tubes strongly bond to the polymer, thus less space is available for O 2 attachment.

1712 W.K. Hsu et al. / Carbon 42 (2004) 1707 1712 Fig. 5. (a) (c) The combination of O 2 bubbles during arc-tube migration in the matrix. 4. Conclusion We have shown here that the use of composite film capacitance as an indication for nanotube dispersion in the polymer is more accurate than using film resistance data. The mechanism for the nanotube migration in the film is related to tube surface states. Acknowledgements We thank the National Tsing-Hua University and National Science Council NSC-92-2119-M-007-072 (Taiwan) and EPSRC (UK) for financial support. References [1] Watts PCP, Hsu W-K, Chen GZ, Fray DJ, Kroto HW, Walton DRM. A low resistance boron-doped carbon nanotube-polystyrene composite. J Mater Chem 2001;11(10):2482 8. [2] Schadler LS, Giannaris SC, Ajayan PM. Load transfer in carbon nanotube epoxy composites. Appl Phys Lett 1998;73(26):3842 4. [3] Watts PCP, Hsu W-K, Kroto HW, Walton DRM. Non-linear current-voltage characteristics of electrically conducting carbon nanotube-polystyrene composites. Phys Chem Chem Phys 2002;4(22):5655 62. [4] Watts PCP, Hsu W-K. Behaviours of embedded carbon nanotube during film cracking. Nanotechnology 2003;14(5):L7 L10. [5] Gong XY, Liu J, Baskaran S, Voise RD, Young JS. Surfactant assisted processing of carbon nanotubes/polymer composites. Chem Mater 2000;12(4):1049 52. [6] Sandler J, Shaffer MSP, Prasse Y, Bauhofer W, Schulte K, Windle AH. Development of a dispersion process for carbon nanotubes in an epoxy matrix and the resulting electrical properties. Polymer 1999;40(21):5967 71. [7] Andrews R, Jacques D, Minot M, Rantell T. Fabrication of carbon multiwall nanotube/polymer composites by shear mixing. Macromol Mater Eng 2002;287(6):395 403. [8] Horwood E. Southampton Electrochemistry Group. Instrumental methods in electrochemistry. London. Chapter 8. 1990:266 78 (ISBN 0-13-472093-8). [9] Macdonald RJ, editor. Impedance spectroscopy emphasizing solid materials and systems. New York: Wiley; 1987. p. 1 26 (ISBN 0-471-83122-0). [10] Watts PCP, Hsu W-K, Kroto HW, Walton DRM. Are bulk defective carbon nanotubes less electrically conducting. Nanoletters 2003;3(4):549 53.