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Investigation into the deformation of carbon nanotubes and their composites through the use of Raman spectroscopy
Composites: Part A 32 (2001) 401–411 www.elsevier.com/locate/compositesa
Investigation into the deformation of carbon nanotubes and their composites through the use of Raman spectroscopy C.A. Cooper a, R.J. Young a,*, M. Halsall b a
Manchester Materials Science Centre, UMIST/University of Manchester, Grosvenor Street, Manchester M1 7HS, UK b Department of Physics, UMIST, Manchester M60 1QD, UK
Abstract The deformation micromechanics of single-walled carbon nanotube (SWNT) and multi-walled carbon nanotube (MWNT) particulate nanocomposites has been studied using Raman spectroscopy. SWNTs prepared by two different methods (pulsed-laser and arc-discharge) and MWNTs have been used as reinforcement for a polymer matrix nanocomposite. The carbon nanotubes exhibit well-defined Raman peaks and Raman spectroscopy has been used to follow their deformation. SWNTs have been deformed with hydrostatic pressure in a diamond anvil pressure cell and has been found that the G 0 peak position shifts to a higher wavenumber with hydrostatic compression. It has been found that for all nanocomposites samples deformed, the G 0 Raman band shifts to a lower wavenumber upon application of a tensile stress indicating stress transfer from the matrix to the nanotubes and hence reinforcement by the nanotubes. The behaviour has been compared with that of high-modulus carbon fibres and has been modelled using orientation factors suggested initially by Cox. In this way it has been possible to demonstrate that the effective modulus of SWNTs dispersed in a composite could be over 1 TPa and that of the MWNTs about 0.3 TPa. 䉷 2001 Elsevier Science Ltd. All rights reserved. Keyword: Carbon nanotubes
1. Introduction In general it is found that the highest levels of reinforcement for composites are obtained through the use of continuous fibres although such composites are often difficult to fabricate [1]. This article considers the extension of the Raman technique to composite systems where the reinforcing phase is in the form of particles (i.e. nanotubes) rather than fibres, which would make the composites easier to fabricate. Carbon nanotubes were first observed in 1991 by Iijima [2] and it is now possible to synthesise carbon nanotubes and nested concentric carbon nanotube [3]. A nanotube can be considered as a hexagonal arrangement of carbon atoms arranged in sheet form, which has been rolled up to form a tube. The tubes can either be open ended or have caps formed from half a C60 molecule at either end. Carbon nanotubes are thought to have remarkable mechanical properties with theoretical Young’s modulus values being quoted in the past as high as 5 TPa [4] and the calculated theoretical tensile strength of carbon nanotubes as high as 200 GPa [5]. * Corresponding author. Tel.: ⫹44-161-200-3551; fax: ⫹44-161-2008877. E-mail addresses: [email protected] (R.J. Young), [email protected] (M. Halsall).
The mechanical properties of carbon nanotubes has been measured recently in various tests such as atomic force microscopy of a single-walled carbon nanotube (SWNT) laid on a special holey membrane [6] where a load is applied on the nanotube. The elastic moduli of SWNT ropes were found to be in the order of 1 TPa. Another method used was the electrically induced mechanical deflections of MWNTs in a transmission electron microscope [7]. The elastic bending modulus was found to depend strongly on the nanotube diameter from 0.1 to 1 TPa with increasing diameter. These high values of mechanical properties make them ideal as reinforcements in nanocomposites. In this present study, Raman spectroscopy has been used to characterise reinforcement by SWNTs and multi-walled carbon nanotube (MWNTs) by following nanotube deformation from stress-induced Raman band shifts. 2. Experimental 2.1. Materials and preparation of specimens The SWNTs were supplied by Rice University, USA (prepared by pulsed laser vaporisation process) [8] (SWNT-P) and Sussex University, UK (arc-discharge prepared with Ni/Y catalyst) [8] (SWNT-A). The Rice
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Table 1 Tensile modulus values for the carbon fibres Fibres
Tensile modulus (GPa)
T50 (PAN-based) P55 (Pitch-based) P75 (Pitch based) P100 (Pitch-based) P120 (Pitch-based)
393 379 520 724 823
University SWNTs were supplied suspended in a basic (NaOH, pH 10) non-ionic surfactant/water solution which were then re-suspended in ethanol by diluting and centrifuging several times; the Sussex University SWNTs were supplied in a powder form. The MWNTs were supplied in the form of a powder by Sussex University, UK (prepared using the arc-discharge method). High modulus carbon fibres were employed to provide an analogy with the deformation of carbon nanotubes. The carbon fibres were supplied by Amoco and their tensile modulus values (as quoted by the manufacturer) are given in Table 1. A two-part cold-curing epoxy resin consisting of 100 parts by weight of Araldite LY5052 resin to 38 parts by weight of HY5052 hardener was employed both as the composite matrix and substrate for the beam specimens. To form the substrate, the resin was cured at room temperature for 7 days in a square ‘picture frame’ mould then cut into beams measuring 3 × 10 × 60 ^ 0:2 mm2 : A carbon nanotube/ethanol mixture was added to uncured epoxy resin and sonicated for 2 h before leaving in a vacuum oven overnight to evaporate the solvent. The hardener was added and the mixture stirred well to distribute the nanotubes and again placed in a vacuum oven for about 30 min to remove any air bubbles. The composite was formed by applying the epoxy resin/nanotube mix to the surface of the epoxy beam to give a layer ⬃0.1 mm thick and was cured at room temperature for 7 days before testing. For the carbon fibre specimens, a single carbon fibre was bonded onto the surface of a poly(methyl methacrylate) (PMMA) beam 3 × 10 × 60 ^ 0:2 mm2 using an application of a thin layer of PMMA in chloroform solution.
Fig. 2. Diagram of diamond anvil pressure cell.
of a 25 mW He–Ne laser with the laser beam focussed to a spot size of the order of 2 mm. The peak values were derived by using Lorentzian routines fitted to the raw data obtained from the spectrometer.
2.3. Tensile deformation The beam specimens were inserted into a self-made four-point bending rig and placed on the Raman microscope stage. The configuration of the beams under tensile loading can be seen in Fig. 1. The surface strain was measured using a resistance strain gauge, of gauge factor 2.09, bonded to the surface of the specimens using a cyanoacrylate adhesive. The beam was deformed step-wise and several Raman spectra were acquired at 0.25% strain intervals with the polarisation of the laser beam parallel to the direction of tensile strain, unless otherwise stated.
2.2. Raman spectroscopy The spectra for the carbon nanotubes were obtained using a Renishaw 1000 Raman system using the 633 nm red line
Fig. 1. Composite beam under four-point bending to give tensile loading on the top surface.
2.4. Diamond anvil pressure cell The pressure cell used in this study was the Mao–Bell type [9] as shown schematically in Fig. 2. The pressure was generated by compressing a metal gasket containing the specimen between the flat faces of two diamonds. Very high pressures can be generated in the gasket hole which also usually contains a pressure medium such as 4:1 methanol/ethanol mix or water. A ruby chip was also pressured along with the specimen to determine the pressure within the cell using a known calibration for the R2 fluorescence line of 7.53 cm ⫺1/GPa [9].
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Fig. 3. Raman spectra in the range 1000–3000 cm ⫺1 (a) SWNT-A, (b) SWNT-P.
3. Deformation of the nanotubes and nanocomposites 3.1. Single-walled nanotubes Raman spectroscopy was used both to characterise and follow the deformation behaviour of the SWNTs obtained from each source. Fig. 3(a) shows the Raman spectrum of SWNT-A in the range 1000–3000 cm ⫺1. The strong Raman bands at 1532 and 1569 cm ⫺1 (G band) are a combination of the Ag1, Eg1 and Eg2 vibrational modes [10]. The band at 1308 cm ⫺1 (D band) arises from the disorder-induced mode Ag1, and the band at 2610 cm ⫺1 (G 0 band) is an overtone of the D band. Fig. 3(b) shows the Raman spectrum of SWNT-P in the range 1000–3000 cm ⫺1 which is similar to that obtained from SWNT-A although it can be seen that all of the Raman band peak positions for SWNT-P are upshifted to higher wavenumber. The G 0 Raman band position was upshifted for the SWNT-P by almost 30–2639 cm ⫺1. The reason for this is unclear but may be a result of the different
production methods used or because of the SWNTs resuspension in a solvent. Wood et al. [11] have followed the response of the SWNT G 0 Raman band when the nanotubes are immersed in different liquids. They found that the G 0 band shifted to a higher wavenumber; the amount depending on the liquid employed.
3.2. Pressure dependence of SWNT-P The SWNT-P material was pressurised in a diamond anvil pressure cell to determine to what extent the G 0 Raman band shifted when subjected to compressive stress. It can be seen in Fig. 4 that the G 0 Raman band shifts to a higher wavenumber with increasing pressure. The pressureinduced initial Raman shift was 23 cm ⫺1/GPa. Lourie and Wagner [12] also found that the Raman bands shift to a higher wavenumber when embedded in a thermally cured epoxy resin and cooled to room temperature due to thermal contraction of the resin.
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Fig. 4. Pressure dependence of the SWNT-P (2639 cm ⫺1) G 0 Raman peak.
3.3. Four-point bending of SWNT reinforced composite The SWNTs were distributed dilutely into an epoxy matrix resulting in a low volume fraction (⬍0.1 wt%) nanocomposite. The nanocomposites were subjected to tensile deformation in the four-point bending rig. The variation of the G 0 Raman peak position with strain for the SWNT-A composite can be seen in Fig. 5(a). The G 0 Raman peak position moves to a lower wavenumber with tensile strain indicating that the macroscopic stress on the composite deforms the SWNTs. This is in agreement with the deformation behaviour of other carbon materials and in particular, carbon fibres [13]. Fig. 5(b) shows the strain-induced Raman band shift for the SWNT-P reinforced composite. It can be seen that the peak position of the 2640 cm ⫺1 Raman band shifts significantly (average initial slope ⫺13 cm ⫺1/ % strain) to a lower wavenumber on application of a tensile stress. This demonstrates the reinforcement of the epoxy resin with the SWNTs that is comparable with the behaviour of carbon fibre reinforced composites [14–18]. 3.4. Multi-walled nanotubes Fig. 6 shows the Raman spectrum of the MWNTs in the range 1000–3000 cm ⫺1 and it should be noted that the Raman spectrum for MWNTs differs from that for the SWNTs. The spectrum of MWNTs resembles closely that of carbon fibres [13], and graphite [19]. A sharp peak is seen at 1582 cm ⫺1 that corresponds to one of the E2g modes [10]. A band is seen at 1334 cm ⫺1 (D band), which has been attributed to the breakdown of translational symmetry produced by the microcrystalline structure [19]. The Raman band at 2663 cm ⫺1 (G 0 band) is the overtone of the D band. Fig. 7
shows the stress-induced Raman band shift for the MWNTreinforced particulate composite (low volume fraction nanocomposite as with the SWNTs). It can be seen that the peak position of the 2663 cm ⫺1 Raman band shifts to a lower wavenumber on application of a tensile stress. The Raman band shift rate for the MWNTs is lower than that obtained for SWNT-P but higher than that obtained for SWNT-A. 3.5. The effect of random orientation of carbon nanotubes It was observed that the second-order Raman band broadened with increasing strain. This can be seen in Fig. 8 for the 2640 cm ⫺1 Raman peak for SWNT-P. Broadening of this peak shows that in the 2 mm region probed there are contributions to the Raman band shift from nanotubes oriented at all angles to the deformation axis. Nanotubes oriented at 90⬚ to the deformation axis will shift to a higher wavenumber with strain due to Poisson’s contraction of the matrix; compression on the nanotubes will result in a positive shift of the 2640 cm ⫺1 Raman band. This effect can be seen from the pressure-induced Raman band shift (Fig. 4) where the G 0 band moves to a higher wavenumber with compressive stress. 4. Deformation of high modulus carbon fibre composites The nanotube reinforced composites can be thought of as fibre-reinforced composites within which the fibres are distributed randomly. The measured Raman band shifts can give an indication of the mechanical properties of the carbon nanotubes, in particular effective Young’s modulus of the nanotubes in the composites which can be estimated using the analogy of carbon fibre-reinforced composites.
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Fig. 5. Variation of the G 0 Raman peak position with tensile strain for (a) SWNT-Adispersed in epoxy resin, (b) SWNT-P dispersed in epoxy resin.
The following issues need to be addressed in the consideration of Raman band shifts for composites with randomlyoriented fibres. • What would be the Raman band shift rate (per unit strain) for a fibre not parallel to the deformation axis? • What would be the Raman band shift rate (per unit strain) for a fibre not parallel to the axis of laser polarisation? • How can the Raman band shift be related to the stress on the nanotubes?
In order to investigate the effective Raman band shifts of the carbon nanotubes, an investigation has been made into the effect of off-axis loading of high modulus carbon fibres and the effect of changing laser polarisation direction with effect to the deformation axis of the fibres. In addition, the effect of carbon fibre modulus on the Raman band shift rate was determined to enable a comparison with the deformation of carbon nanotubes to be made so that their effective modulus could be estimated and so the stress on the nanotubes determined.
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Fig. 6. Raman spectrum of MWNTs in the range 1000–3000 cm ⫺1.
4.1. Off-axis deformation of carbon fibres Single carbon fibre specimens were prepared using T50 fibres embedded in a PMMA matrix and deformed using the four-point bend technique described earlier. The carbon fibre was placed near the top surface of the four-point bend specimen so that the fibres were located in the centre of the test region as shown in Fig. 9. The direction of laser polarisation was maintained parallel to the fibre axis. Fig. 10 shows the dependence of the peak shift of the 2660 cm ⫺1 Raman band on fibre angle for fibres oriented at an angle, u , to the tensile axis. Fibres at angles greater than 58⬚ result in compression of the fibre, indicated by a
positive shift of the 2660 cm ⫺1 Raman band. The relationship between fibre strain, eu , and the fibre angle, u , can be represented by an equation of the form: eu A cos2 u ⫺ B sin2 u
1
An equation of the form of Eq. (1) can also be derived to give the dependence of fibre strain on u by assuming that the fibre and matrix strains are equal in the centre of a fibre aligned parallel to the tensile axis [20]. This gives: e eo cos2 u ⫺ n sin2 u
2
where e eu ; A eo and B n (Poisson’s ratio of the
Fig. 7. Variation of the 2663 cm ⫺1 Raman peak position for MWNT with tensile strain.
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Fig. 8. Variation of the 2640 cm ⫺1 Raman peak width (FWHM — full width at half maximum height) for SWNT-P with tensile strain.
matrix). The dashed curve on Fig. 10 was calculated from Eq. (2) by assuming n ⬇ 1=3; a typical value for PMMA [21]. It can be seen that the experimental data fall close to the theoretical curve.
the nanotubes would be independent of the direction of laser polarisation and the spectra obtained from the nanocomposites would have contributions from nanotubes in all directions.
4.2. Effect of laser polarisation on Raman band shift of carbon fibres
4.3. Effect of carbon fibre modulus on Raman band shift rate
Single T50 carbon fibre specimens were prepared by embedding the fibres in a PMMA matrix such that the fibres were aligned parallel to the deformation axis. The specimens were deformed using the four-point bend technique described earlier but with the Raman laser polarised at 0, 30, 60 and 90⬚ to the fibre axis. Fig. 11 shows the dependence of the peak shift of the 2660 cm ⫺1 G 0 Raman band on laser polarisation angle for T50 fibres oriented at these angles to the tensile axis. It can be seen from Fig. 11 that there is little difference between the rates of band shift for the four laser polarisation angles and so the Raman band shift rate appears to be independent of angle between the fibre axis and laser polarisation direction. This is presumably a consequence of the two-dimensional turbostratic sheet-like structure of the carbon fibres. It would therefore be expected that, using this analogy, the appearance of the Raman spectra obtained from
Fig. 9. Schematic representation of an off-axis carbon fibre at an angle, u , to the tensile axis in a PMMA matrix.
Huang and Young [13] showed that the shift rate per unit strain for the 1580 cm ⫺1 Raman band of both PAN- and pitch-based carbon fibres increased as the fibre modulus increased. In fact the Raman band shift rate of carbon fibres was found to be proportional to the fibre modulus although lines of different slope were obtained for the two different types of fibres. They attributed this behaviour to the different microstructure of the fibres with the pitch-based fibres having a uniform structure and the PAN-based fibres having different levels of orientation in the fibre skin and core. Hence, in order to obtain a fundamental band shift calibration for the nanotubes, the deformation of a number of pitchbased carbon fibres of different modulus (Table 1) was investigated. A set of pitch-based fibres, P55, P75, P100 and P120, were tested in single fibre composites and deformed by the four-point bending method described earlier (Fig. 1). It can be seen from Fig. 12 that the rate of shift per unit strain of the 2660 cm ⫺1 Raman band is higher for the highmodulus fibres and from the limited data available it confirms that the shift rate for this band is also proportional to the fibre modulus. The slope of the line in Fig. 12 corresponds to ⫺5 cm ⫺1/GPa and this was chosen to calibrate the Raman band shift of carbon nanotubes.
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Fig. 10. Dependence of the peak shift of the 2660 cm ⫺1 Raman band on fibre angle for T50 fibres oriented at an angle, u , to the tensile axis.
5. Nanotube deformation in the nanocomposites 5.1. Reinforcement of epoxy resin with carbon nanotubes The results of this study show that the maximum initial Raman band shift rate of the SWNT-P with strain in the epoxy resin matrix is ⫺13 cm ⫺1/% (mean shift rate for five specimens of SWNT-P). Stress transfer from the epoxy resin to the nanotubes has been demonstrated from the stress-induced band shift; therefore, the carbon nanotubes must provide some reinforcement of the resin. The band shift rate for SWNT-P of ⫺13 cm ⫺1/% implies that
the nanotube modulus is at least 260 GPa, using the calibration of ⫺5 cm ⫺1/GPa. The carbon nanotubes however, have a random distribution within the epoxy matrix which contrasts with the unidirectional alignment of the carbon fibres used in the calibration. An orientation efficiency factor, h 0 has been proposed by Cox [1,22], to take into account fibre orientation distributions for fibre reinforcement by assuming that the matrix and fibre deform elastically. Values for h 0 have been calculated by Krenchel [23], for different fibre orientation distributions. The parameter h 0 can be determined by dividing fibre reinforcement into groups of uniaxially aligned fibres
Fig. 11. Dependence of the peak shift of the 2660 cm ⫺1 Raman band on laser polarisation angle for T50 fibres oriented at 0⬚ to the tensile axis.
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Fig. 12. Dependence of Raman band shift rate upon tensile modulus for P55, P75, P100 and P120 carbon fibres.
such that: X h0 an cos4 un n
where:
P
3
an 1: The parameter, an is the proportion of
n
those fibres making an angle u n with respect to the axis of the applied load. For the case of fibres lying in parallel planes but uniformly distributed over all directions in that plane intersecting an arbitrary point in the material (random-in-plane), the efficiency factor must be determined by an integration: 1 Zp=2 h0 cos4 u du 9=8p 4 p ⫺ p=2 The relationship between fibre strain, e and fibre orientation angle, u , is taken into account by substituting cos2 u ⫺ n 2 u from Eq. (2) for cos 4 u . The measured Raman band shift is proportional to the strain on in the fibre [1,15] therefore 1 Zp=2 cos2 u ⫺ n sin2 udu 5 S 2 S0 p ⫺ p=2 where S2 the measured band shift at 1% strain (i.e. the band shift rate) for fibres arranged random-in-plane (twodimensional arrangement) and S0 is the band shift at 1% strain for fibres aligned parallel to the deformation direction u 0: If n 1=3; then integration of Eq. (5) gives: S2 =S0 1=3
6
For the case of fibres arranged three-dimensionally (3-D) and uniformly distributed in all directions (which also needs to be considered for the carbon nanotube reinforced composite), an integration is again used. The fibres can be envi-
sioned as running through an arbitrary point in the centre of a sphere and the intersections of the radial fibres with the sphere are distributed uniformly over its surface. Therefore the proportion au is equal to the ratio between the area of the zone of the sphere (u to u ⫹ du and the area of the hemisphere such that: au sin u du
7
Hence: Zp=2 h0 sin u cos4 u du 1=5
8
0
If the measured Raman band shift, S, is proportional to the strain on in the fibre, then: S3 S0 cos2 u ⫺ n sin2 u
9
where S3 the measured band shift at 1% strain for fibres arranged three-dimensionally. This can be related to Eq. (2) such that: X an cos2 u ⫺ n sin2 u 10 S3 S0 n
Hence: Zp=2 sin u cos2 u ⫺ n sin2 udu S 3 S0 0
11
And again when n 1=3 S3 =S0 1=9
12
5.2. Estimation of carbon nanotube moduli The parameters S2 =S0 ( 1/3) and S3 =S0 ( 1/9) imply
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Table 2 Calculated effective moduli for SWNT-A, SWNT-P and MWNT nanotubes (^ standard deviation)
SWNT-A SWNT-P MWNT
Average initial Raman band shift at 1% strain (cm ⫺1/%)
Calculated modulus (2-D distribution) S2 =S0 1=3 GPa
Calculated modulus (3-D distribution) S3 =S0 1=9 GPa
⫺1:3 ^ 0:3 ⫺13 ^ 3:8 ⫺3:4 ^ 1:5
78 ^ 17 780 ^ 210 204 ^ 83
234 ^ 50 2340 ^ 629 612 ^ 248
that the equivalent band shift rates for nanotubes aligned unidirectionally would be between 3 and 9 times those measured for nanotubes in random orientations (2-D and 3-D, respectively). These factors and the universal band shift calibration of ⫺5 cm ⫺1/GPa allow the effective modulus of the nanotubes to be determined from the measured band shifts and the results are shown in Table 2. The values for effective modulus estimated using the 3-D efficiency factor (1/9) may be too high since a random distribution of the carbon nanotubes within the matrix is unlikely to be fully 3-D as there will be some collapse towards a 2-D distribution when the solvent evaporates and the resin matrix cures. The random packing of fibres in 3-D has been investigated previously by various workers [24] who found that the arrangement of fibres within space will be less than fully 3-D because of the interference from fibres crossing each over each other and touching. The effective modulus for the nanotubes will therefore lie somewhere between the 2-D and 3-D estimates. The effective modulus values for the SWNT-P nanotubes is within the range of the values of 1–3 TPa found by other workers [6,25,26]. The most recent estimates [6] suggest a value closer to 1 TPa, similar to the modulus value of 1.06 TPa for deformation along the basal plane of graphite [27]. A modulus of 1 TPa suggests that the arrangement of nanotubes in the composite is closer to 2-D than 3-D. The modulus for MWNTs has been measured as between 0.1 and 1 TPa [6,28] depending upon the diameter of the nanotubes. The estimated effective modulus value for MWNTs listed in Table 2 is within this range. Assuming that the reinforcement is again between 2-D and 3-D the modulus of the MWNTs investigated in this study is estimates to be in the order of 0.3 TPa. It is of interest to consider why the rates of band shift for the SWNT-A are lower than for the SWNT-P material. There are a number of possibilities. They may have lower modulus values or poorer dispersion in the resin. It was found that the SWNT-A were more difficult to disperse in the epoxy resin that would result in a less efficient reinforcement. The adhesion to the epoxy matrix may be worse than for the SWNT-P material and the aspect ratio of the nanotubes may be different. The production method for the nanotubes could also have a significant effect. The arcdischarge production method produces larger bundles than the pulsed laser method resulting in lower aspect ratio for the ‘particles’ [29].
5.3. Predicted properties of carbon-nanotube reinforced composites The advantage of the use of Raman spectroscopy to follow the deformation of carbon nanotube composites is that it can be undertaken with very low volume fraction of the reinforcement. Once the reinforcement has been demonstrated, however, the modulus of high-volume fraction nanocomposites can be estimated using the Krenchel [23] efficiency factors, h 0. If it assumed that the reinforcement is 2-D h0 9=8p in view of the present findings and the difficulties of aligning fibres in 3-D [23,24], then a 50% volume fraction in 2-D of 1 TPa modulus SWNT-P nanotubes in epoxy resin would give a composite with an inplane modulus of about 200 GPa. Similarly a 50% volume fraction of a 2-D distribution of 0.3 TPa modulus MWNTs would give a composite with a modulus of about 60 GPa. In both cases unidirectional alignment of the tubes would increase the modulus significantly. 6. Conclusions It has been demonstrated that Raman spectroscopy can be used to characterise and follow the tensile deformation of a dilute dispersion of SWNTs and MWNTs in a particulate composite system. Well-defined Raman spectra have been obtained from the dispersed phase and stress transfer between the different phases has been demonstrated from stress-induced Raman band shifts. Using this method, and comparison with the stress-induced Raman band shift of high-modulus carbon fibres, the effective modulus of the nanotubes in the composite can be determined. The experimental measurements of band shift have been shown to be consistent with the SWNTs having a modulus of the order of 1 TPa and the MWNTs having a modulus of about 0.3 TPa. The analysis developed has also allowed the mechanical properties of high volume fraction composites reinforced with carbon nanotubes to be predicted. Acknowledgements This work is part of a larger programme supported by the EPSRC and one author, (C.A.C) is grateful to the EPSRC for support in the form of a studentship. The authors are thankful to the Defence Evaluation and Research Agency (DERA) for providing financial support and the SWNT-A
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Investigation into the deformation of carbon nanotubes and their composites through the use of Raman spectroscopy C.A. Cooper a, R.J. Young a,*, M. Halsall b a
Manchester Materials Science Centre, UMIST/University of Manchester, Grosvenor Street, Manchester M1 7HS, UK b Department of Physics, UMIST, Manchester M60 1QD, UK
Abstract The deformation micromechanics of single-walled carbon nanotube (SWNT) and multi-walled carbon nanotube (MWNT) particulate nanocomposites has been studied using Raman spectroscopy. SWNTs prepared by two different methods (pulsed-laser and arc-discharge) and MWNTs have been used as reinforcement for a polymer matrix nanocomposite. The carbon nanotubes exhibit well-defined Raman peaks and Raman spectroscopy has been used to follow their deformation. SWNTs have been deformed with hydrostatic pressure in a diamond anvil pressure cell and has been found that the G 0 peak position shifts to a higher wavenumber with hydrostatic compression. It has been found that for all nanocomposites samples deformed, the G 0 Raman band shifts to a lower wavenumber upon application of a tensile stress indicating stress transfer from the matrix to the nanotubes and hence reinforcement by the nanotubes. The behaviour has been compared with that of high-modulus carbon fibres and has been modelled using orientation factors suggested initially by Cox. In this way it has been possible to demonstrate that the effective modulus of SWNTs dispersed in a composite could be over 1 TPa and that of the MWNTs about 0.3 TPa. 䉷 2001 Elsevier Science Ltd. All rights reserved. Keyword: Carbon nanotubes
1. Introduction In general it is found that the highest levels of reinforcement for composites are obtained through the use of continuous fibres although such composites are often difficult to fabricate [1]. This article considers the extension of the Raman technique to composite systems where the reinforcing phase is in the form of particles (i.e. nanotubes) rather than fibres, which would make the composites easier to fabricate. Carbon nanotubes were first observed in 1991 by Iijima [2] and it is now possible to synthesise carbon nanotubes and nested concentric carbon nanotube [3]. A nanotube can be considered as a hexagonal arrangement of carbon atoms arranged in sheet form, which has been rolled up to form a tube. The tubes can either be open ended or have caps formed from half a C60 molecule at either end. Carbon nanotubes are thought to have remarkable mechanical properties with theoretical Young’s modulus values being quoted in the past as high as 5 TPa [4] and the calculated theoretical tensile strength of carbon nanotubes as high as 200 GPa [5]. * Corresponding author. Tel.: ⫹44-161-200-3551; fax: ⫹44-161-2008877. E-mail addresses: [email protected] (R.J. Young), [email protected] (M. Halsall).
The mechanical properties of carbon nanotubes has been measured recently in various tests such as atomic force microscopy of a single-walled carbon nanotube (SWNT) laid on a special holey membrane [6] where a load is applied on the nanotube. The elastic moduli of SWNT ropes were found to be in the order of 1 TPa. Another method used was the electrically induced mechanical deflections of MWNTs in a transmission electron microscope [7]. The elastic bending modulus was found to depend strongly on the nanotube diameter from 0.1 to 1 TPa with increasing diameter. These high values of mechanical properties make them ideal as reinforcements in nanocomposites. In this present study, Raman spectroscopy has been used to characterise reinforcement by SWNTs and multi-walled carbon nanotube (MWNTs) by following nanotube deformation from stress-induced Raman band shifts. 2. Experimental 2.1. Materials and preparation of specimens The SWNTs were supplied by Rice University, USA (prepared by pulsed laser vaporisation process) [8] (SWNT-P) and Sussex University, UK (arc-discharge prepared with Ni/Y catalyst) [8] (SWNT-A). The Rice
1359-835X/01/$ - see front matter 䉷 2001 Elsevier Science Ltd. All rights reserved. PII: S1359-835 X( 00)00 107-X
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Table 1 Tensile modulus values for the carbon fibres Fibres
Tensile modulus (GPa)
T50 (PAN-based) P55 (Pitch-based) P75 (Pitch based) P100 (Pitch-based) P120 (Pitch-based)
393 379 520 724 823
University SWNTs were supplied suspended in a basic (NaOH, pH 10) non-ionic surfactant/water solution which were then re-suspended in ethanol by diluting and centrifuging several times; the Sussex University SWNTs were supplied in a powder form. The MWNTs were supplied in the form of a powder by Sussex University, UK (prepared using the arc-discharge method). High modulus carbon fibres were employed to provide an analogy with the deformation of carbon nanotubes. The carbon fibres were supplied by Amoco and their tensile modulus values (as quoted by the manufacturer) are given in Table 1. A two-part cold-curing epoxy resin consisting of 100 parts by weight of Araldite LY5052 resin to 38 parts by weight of HY5052 hardener was employed both as the composite matrix and substrate for the beam specimens. To form the substrate, the resin was cured at room temperature for 7 days in a square ‘picture frame’ mould then cut into beams measuring 3 × 10 × 60 ^ 0:2 mm2 : A carbon nanotube/ethanol mixture was added to uncured epoxy resin and sonicated for 2 h before leaving in a vacuum oven overnight to evaporate the solvent. The hardener was added and the mixture stirred well to distribute the nanotubes and again placed in a vacuum oven for about 30 min to remove any air bubbles. The composite was formed by applying the epoxy resin/nanotube mix to the surface of the epoxy beam to give a layer ⬃0.1 mm thick and was cured at room temperature for 7 days before testing. For the carbon fibre specimens, a single carbon fibre was bonded onto the surface of a poly(methyl methacrylate) (PMMA) beam 3 × 10 × 60 ^ 0:2 mm2 using an application of a thin layer of PMMA in chloroform solution.
Fig. 2. Diagram of diamond anvil pressure cell.
of a 25 mW He–Ne laser with the laser beam focussed to a spot size of the order of 2 mm. The peak values were derived by using Lorentzian routines fitted to the raw data obtained from the spectrometer.
2.3. Tensile deformation The beam specimens were inserted into a self-made four-point bending rig and placed on the Raman microscope stage. The configuration of the beams under tensile loading can be seen in Fig. 1. The surface strain was measured using a resistance strain gauge, of gauge factor 2.09, bonded to the surface of the specimens using a cyanoacrylate adhesive. The beam was deformed step-wise and several Raman spectra were acquired at 0.25% strain intervals with the polarisation of the laser beam parallel to the direction of tensile strain, unless otherwise stated.
2.2. Raman spectroscopy The spectra for the carbon nanotubes were obtained using a Renishaw 1000 Raman system using the 633 nm red line
Fig. 1. Composite beam under four-point bending to give tensile loading on the top surface.
2.4. Diamond anvil pressure cell The pressure cell used in this study was the Mao–Bell type [9] as shown schematically in Fig. 2. The pressure was generated by compressing a metal gasket containing the specimen between the flat faces of two diamonds. Very high pressures can be generated in the gasket hole which also usually contains a pressure medium such as 4:1 methanol/ethanol mix or water. A ruby chip was also pressured along with the specimen to determine the pressure within the cell using a known calibration for the R2 fluorescence line of 7.53 cm ⫺1/GPa [9].
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Fig. 3. Raman spectra in the range 1000–3000 cm ⫺1 (a) SWNT-A, (b) SWNT-P.
3. Deformation of the nanotubes and nanocomposites 3.1. Single-walled nanotubes Raman spectroscopy was used both to characterise and follow the deformation behaviour of the SWNTs obtained from each source. Fig. 3(a) shows the Raman spectrum of SWNT-A in the range 1000–3000 cm ⫺1. The strong Raman bands at 1532 and 1569 cm ⫺1 (G band) are a combination of the Ag1, Eg1 and Eg2 vibrational modes [10]. The band at 1308 cm ⫺1 (D band) arises from the disorder-induced mode Ag1, and the band at 2610 cm ⫺1 (G 0 band) is an overtone of the D band. Fig. 3(b) shows the Raman spectrum of SWNT-P in the range 1000–3000 cm ⫺1 which is similar to that obtained from SWNT-A although it can be seen that all of the Raman band peak positions for SWNT-P are upshifted to higher wavenumber. The G 0 Raman band position was upshifted for the SWNT-P by almost 30–2639 cm ⫺1. The reason for this is unclear but may be a result of the different
production methods used or because of the SWNTs resuspension in a solvent. Wood et al. [11] have followed the response of the SWNT G 0 Raman band when the nanotubes are immersed in different liquids. They found that the G 0 band shifted to a higher wavenumber; the amount depending on the liquid employed.
3.2. Pressure dependence of SWNT-P The SWNT-P material was pressurised in a diamond anvil pressure cell to determine to what extent the G 0 Raman band shifted when subjected to compressive stress. It can be seen in Fig. 4 that the G 0 Raman band shifts to a higher wavenumber with increasing pressure. The pressureinduced initial Raman shift was 23 cm ⫺1/GPa. Lourie and Wagner [12] also found that the Raman bands shift to a higher wavenumber when embedded in a thermally cured epoxy resin and cooled to room temperature due to thermal contraction of the resin.
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Fig. 4. Pressure dependence of the SWNT-P (2639 cm ⫺1) G 0 Raman peak.
3.3. Four-point bending of SWNT reinforced composite The SWNTs were distributed dilutely into an epoxy matrix resulting in a low volume fraction (⬍0.1 wt%) nanocomposite. The nanocomposites were subjected to tensile deformation in the four-point bending rig. The variation of the G 0 Raman peak position with strain for the SWNT-A composite can be seen in Fig. 5(a). The G 0 Raman peak position moves to a lower wavenumber with tensile strain indicating that the macroscopic stress on the composite deforms the SWNTs. This is in agreement with the deformation behaviour of other carbon materials and in particular, carbon fibres [13]. Fig. 5(b) shows the strain-induced Raman band shift for the SWNT-P reinforced composite. It can be seen that the peak position of the 2640 cm ⫺1 Raman band shifts significantly (average initial slope ⫺13 cm ⫺1/ % strain) to a lower wavenumber on application of a tensile stress. This demonstrates the reinforcement of the epoxy resin with the SWNTs that is comparable with the behaviour of carbon fibre reinforced composites [14–18]. 3.4. Multi-walled nanotubes Fig. 6 shows the Raman spectrum of the MWNTs in the range 1000–3000 cm ⫺1 and it should be noted that the Raman spectrum for MWNTs differs from that for the SWNTs. The spectrum of MWNTs resembles closely that of carbon fibres [13], and graphite [19]. A sharp peak is seen at 1582 cm ⫺1 that corresponds to one of the E2g modes [10]. A band is seen at 1334 cm ⫺1 (D band), which has been attributed to the breakdown of translational symmetry produced by the microcrystalline structure [19]. The Raman band at 2663 cm ⫺1 (G 0 band) is the overtone of the D band. Fig. 7
shows the stress-induced Raman band shift for the MWNTreinforced particulate composite (low volume fraction nanocomposite as with the SWNTs). It can be seen that the peak position of the 2663 cm ⫺1 Raman band shifts to a lower wavenumber on application of a tensile stress. The Raman band shift rate for the MWNTs is lower than that obtained for SWNT-P but higher than that obtained for SWNT-A. 3.5. The effect of random orientation of carbon nanotubes It was observed that the second-order Raman band broadened with increasing strain. This can be seen in Fig. 8 for the 2640 cm ⫺1 Raman peak for SWNT-P. Broadening of this peak shows that in the 2 mm region probed there are contributions to the Raman band shift from nanotubes oriented at all angles to the deformation axis. Nanotubes oriented at 90⬚ to the deformation axis will shift to a higher wavenumber with strain due to Poisson’s contraction of the matrix; compression on the nanotubes will result in a positive shift of the 2640 cm ⫺1 Raman band. This effect can be seen from the pressure-induced Raman band shift (Fig. 4) where the G 0 band moves to a higher wavenumber with compressive stress. 4. Deformation of high modulus carbon fibre composites The nanotube reinforced composites can be thought of as fibre-reinforced composites within which the fibres are distributed randomly. The measured Raman band shifts can give an indication of the mechanical properties of the carbon nanotubes, in particular effective Young’s modulus of the nanotubes in the composites which can be estimated using the analogy of carbon fibre-reinforced composites.
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Fig. 5. Variation of the G 0 Raman peak position with tensile strain for (a) SWNT-Adispersed in epoxy resin, (b) SWNT-P dispersed in epoxy resin.
The following issues need to be addressed in the consideration of Raman band shifts for composites with randomlyoriented fibres. • What would be the Raman band shift rate (per unit strain) for a fibre not parallel to the deformation axis? • What would be the Raman band shift rate (per unit strain) for a fibre not parallel to the axis of laser polarisation? • How can the Raman band shift be related to the stress on the nanotubes?
In order to investigate the effective Raman band shifts of the carbon nanotubes, an investigation has been made into the effect of off-axis loading of high modulus carbon fibres and the effect of changing laser polarisation direction with effect to the deformation axis of the fibres. In addition, the effect of carbon fibre modulus on the Raman band shift rate was determined to enable a comparison with the deformation of carbon nanotubes to be made so that their effective modulus could be estimated and so the stress on the nanotubes determined.
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Fig. 6. Raman spectrum of MWNTs in the range 1000–3000 cm ⫺1.
4.1. Off-axis deformation of carbon fibres Single carbon fibre specimens were prepared using T50 fibres embedded in a PMMA matrix and deformed using the four-point bend technique described earlier. The carbon fibre was placed near the top surface of the four-point bend specimen so that the fibres were located in the centre of the test region as shown in Fig. 9. The direction of laser polarisation was maintained parallel to the fibre axis. Fig. 10 shows the dependence of the peak shift of the 2660 cm ⫺1 Raman band on fibre angle for fibres oriented at an angle, u , to the tensile axis. Fibres at angles greater than 58⬚ result in compression of the fibre, indicated by a
positive shift of the 2660 cm ⫺1 Raman band. The relationship between fibre strain, eu , and the fibre angle, u , can be represented by an equation of the form: eu A cos2 u ⫺ B sin2 u
1
An equation of the form of Eq. (1) can also be derived to give the dependence of fibre strain on u by assuming that the fibre and matrix strains are equal in the centre of a fibre aligned parallel to the tensile axis [20]. This gives: e eo cos2 u ⫺ n sin2 u
2
where e eu ; A eo and B n (Poisson’s ratio of the
Fig. 7. Variation of the 2663 cm ⫺1 Raman peak position for MWNT with tensile strain.
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Fig. 8. Variation of the 2640 cm ⫺1 Raman peak width (FWHM — full width at half maximum height) for SWNT-P with tensile strain.
matrix). The dashed curve on Fig. 10 was calculated from Eq. (2) by assuming n ⬇ 1=3; a typical value for PMMA [21]. It can be seen that the experimental data fall close to the theoretical curve.
the nanotubes would be independent of the direction of laser polarisation and the spectra obtained from the nanocomposites would have contributions from nanotubes in all directions.
4.2. Effect of laser polarisation on Raman band shift of carbon fibres
4.3. Effect of carbon fibre modulus on Raman band shift rate
Single T50 carbon fibre specimens were prepared by embedding the fibres in a PMMA matrix such that the fibres were aligned parallel to the deformation axis. The specimens were deformed using the four-point bend technique described earlier but with the Raman laser polarised at 0, 30, 60 and 90⬚ to the fibre axis. Fig. 11 shows the dependence of the peak shift of the 2660 cm ⫺1 G 0 Raman band on laser polarisation angle for T50 fibres oriented at these angles to the tensile axis. It can be seen from Fig. 11 that there is little difference between the rates of band shift for the four laser polarisation angles and so the Raman band shift rate appears to be independent of angle between the fibre axis and laser polarisation direction. This is presumably a consequence of the two-dimensional turbostratic sheet-like structure of the carbon fibres. It would therefore be expected that, using this analogy, the appearance of the Raman spectra obtained from
Fig. 9. Schematic representation of an off-axis carbon fibre at an angle, u , to the tensile axis in a PMMA matrix.
Huang and Young [13] showed that the shift rate per unit strain for the 1580 cm ⫺1 Raman band of both PAN- and pitch-based carbon fibres increased as the fibre modulus increased. In fact the Raman band shift rate of carbon fibres was found to be proportional to the fibre modulus although lines of different slope were obtained for the two different types of fibres. They attributed this behaviour to the different microstructure of the fibres with the pitch-based fibres having a uniform structure and the PAN-based fibres having different levels of orientation in the fibre skin and core. Hence, in order to obtain a fundamental band shift calibration for the nanotubes, the deformation of a number of pitchbased carbon fibres of different modulus (Table 1) was investigated. A set of pitch-based fibres, P55, P75, P100 and P120, were tested in single fibre composites and deformed by the four-point bending method described earlier (Fig. 1). It can be seen from Fig. 12 that the rate of shift per unit strain of the 2660 cm ⫺1 Raman band is higher for the highmodulus fibres and from the limited data available it confirms that the shift rate for this band is also proportional to the fibre modulus. The slope of the line in Fig. 12 corresponds to ⫺5 cm ⫺1/GPa and this was chosen to calibrate the Raman band shift of carbon nanotubes.
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Fig. 10. Dependence of the peak shift of the 2660 cm ⫺1 Raman band on fibre angle for T50 fibres oriented at an angle, u , to the tensile axis.
5. Nanotube deformation in the nanocomposites 5.1. Reinforcement of epoxy resin with carbon nanotubes The results of this study show that the maximum initial Raman band shift rate of the SWNT-P with strain in the epoxy resin matrix is ⫺13 cm ⫺1/% (mean shift rate for five specimens of SWNT-P). Stress transfer from the epoxy resin to the nanotubes has been demonstrated from the stress-induced band shift; therefore, the carbon nanotubes must provide some reinforcement of the resin. The band shift rate for SWNT-P of ⫺13 cm ⫺1/% implies that
the nanotube modulus is at least 260 GPa, using the calibration of ⫺5 cm ⫺1/GPa. The carbon nanotubes however, have a random distribution within the epoxy matrix which contrasts with the unidirectional alignment of the carbon fibres used in the calibration. An orientation efficiency factor, h 0 has been proposed by Cox [1,22], to take into account fibre orientation distributions for fibre reinforcement by assuming that the matrix and fibre deform elastically. Values for h 0 have been calculated by Krenchel [23], for different fibre orientation distributions. The parameter h 0 can be determined by dividing fibre reinforcement into groups of uniaxially aligned fibres
Fig. 11. Dependence of the peak shift of the 2660 cm ⫺1 Raman band on laser polarisation angle for T50 fibres oriented at 0⬚ to the tensile axis.
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Fig. 12. Dependence of Raman band shift rate upon tensile modulus for P55, P75, P100 and P120 carbon fibres.
such that: X h0 an cos4 un n
where:
P
3
an 1: The parameter, an is the proportion of
n
those fibres making an angle u n with respect to the axis of the applied load. For the case of fibres lying in parallel planes but uniformly distributed over all directions in that plane intersecting an arbitrary point in the material (random-in-plane), the efficiency factor must be determined by an integration: 1 Zp=2 h0 cos4 u du 9=8p 4 p ⫺ p=2 The relationship between fibre strain, e and fibre orientation angle, u , is taken into account by substituting cos2 u ⫺ n 2 u from Eq. (2) for cos 4 u . The measured Raman band shift is proportional to the strain on in the fibre [1,15] therefore 1 Zp=2 cos2 u ⫺ n sin2 udu 5 S 2 S0 p ⫺ p=2 where S2 the measured band shift at 1% strain (i.e. the band shift rate) for fibres arranged random-in-plane (twodimensional arrangement) and S0 is the band shift at 1% strain for fibres aligned parallel to the deformation direction u 0: If n 1=3; then integration of Eq. (5) gives: S2 =S0 1=3
6
For the case of fibres arranged three-dimensionally (3-D) and uniformly distributed in all directions (which also needs to be considered for the carbon nanotube reinforced composite), an integration is again used. The fibres can be envi-
sioned as running through an arbitrary point in the centre of a sphere and the intersections of the radial fibres with the sphere are distributed uniformly over its surface. Therefore the proportion au is equal to the ratio between the area of the zone of the sphere (u to u ⫹ du and the area of the hemisphere such that: au sin u du
7
Hence: Zp=2 h0 sin u cos4 u du 1=5
8
0
If the measured Raman band shift, S, is proportional to the strain on in the fibre, then: S3 S0 cos2 u ⫺ n sin2 u
9
where S3 the measured band shift at 1% strain for fibres arranged three-dimensionally. This can be related to Eq. (2) such that: X an cos2 u ⫺ n sin2 u 10 S3 S0 n
Hence: Zp=2 sin u cos2 u ⫺ n sin2 udu S 3 S0 0
11
And again when n 1=3 S3 =S0 1=9
12
5.2. Estimation of carbon nanotube moduli The parameters S2 =S0 ( 1/3) and S3 =S0 ( 1/9) imply
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Table 2 Calculated effective moduli for SWNT-A, SWNT-P and MWNT nanotubes (^ standard deviation)
SWNT-A SWNT-P MWNT
Average initial Raman band shift at 1% strain (cm ⫺1/%)
Calculated modulus (2-D distribution) S2 =S0 1=3 GPa
Calculated modulus (3-D distribution) S3 =S0 1=9 GPa
⫺1:3 ^ 0:3 ⫺13 ^ 3:8 ⫺3:4 ^ 1:5
78 ^ 17 780 ^ 210 204 ^ 83
234 ^ 50 2340 ^ 629 612 ^ 248
that the equivalent band shift rates for nanotubes aligned unidirectionally would be between 3 and 9 times those measured for nanotubes in random orientations (2-D and 3-D, respectively). These factors and the universal band shift calibration of ⫺5 cm ⫺1/GPa allow the effective modulus of the nanotubes to be determined from the measured band shifts and the results are shown in Table 2. The values for effective modulus estimated using the 3-D efficiency factor (1/9) may be too high since a random distribution of the carbon nanotubes within the matrix is unlikely to be fully 3-D as there will be some collapse towards a 2-D distribution when the solvent evaporates and the resin matrix cures. The random packing of fibres in 3-D has been investigated previously by various workers [24] who found that the arrangement of fibres within space will be less than fully 3-D because of the interference from fibres crossing each over each other and touching. The effective modulus for the nanotubes will therefore lie somewhere between the 2-D and 3-D estimates. The effective modulus values for the SWNT-P nanotubes is within the range of the values of 1–3 TPa found by other workers [6,25,26]. The most recent estimates [6] suggest a value closer to 1 TPa, similar to the modulus value of 1.06 TPa for deformation along the basal plane of graphite [27]. A modulus of 1 TPa suggests that the arrangement of nanotubes in the composite is closer to 2-D than 3-D. The modulus for MWNTs has been measured as between 0.1 and 1 TPa [6,28] depending upon the diameter of the nanotubes. The estimated effective modulus value for MWNTs listed in Table 2 is within this range. Assuming that the reinforcement is again between 2-D and 3-D the modulus of the MWNTs investigated in this study is estimates to be in the order of 0.3 TPa. It is of interest to consider why the rates of band shift for the SWNT-A are lower than for the SWNT-P material. There are a number of possibilities. They may have lower modulus values or poorer dispersion in the resin. It was found that the SWNT-A were more difficult to disperse in the epoxy resin that would result in a less efficient reinforcement. The adhesion to the epoxy matrix may be worse than for the SWNT-P material and the aspect ratio of the nanotubes may be different. The production method for the nanotubes could also have a significant effect. The arcdischarge production method produces larger bundles than the pulsed laser method resulting in lower aspect ratio for the ‘particles’ [29].
5.3. Predicted properties of carbon-nanotube reinforced composites The advantage of the use of Raman spectroscopy to follow the deformation of carbon nanotube composites is that it can be undertaken with very low volume fraction of the reinforcement. Once the reinforcement has been demonstrated, however, the modulus of high-volume fraction nanocomposites can be estimated using the Krenchel [23] efficiency factors, h 0. If it assumed that the reinforcement is 2-D h0 9=8p in view of the present findings and the difficulties of aligning fibres in 3-D [23,24], then a 50% volume fraction in 2-D of 1 TPa modulus SWNT-P nanotubes in epoxy resin would give a composite with an inplane modulus of about 200 GPa. Similarly a 50% volume fraction of a 2-D distribution of 0.3 TPa modulus MWNTs would give a composite with a modulus of about 60 GPa. In both cases unidirectional alignment of the tubes would increase the modulus significantly. 6. Conclusions It has been demonstrated that Raman spectroscopy can be used to characterise and follow the tensile deformation of a dilute dispersion of SWNTs and MWNTs in a particulate composite system. Well-defined Raman spectra have been obtained from the dispersed phase and stress transfer between the different phases has been demonstrated from stress-induced Raman band shifts. Using this method, and comparison with the stress-induced Raman band shift of high-modulus carbon fibres, the effective modulus of the nanotubes in the composite can be determined. The experimental measurements of band shift have been shown to be consistent with the SWNTs having a modulus of the order of 1 TPa and the MWNTs having a modulus of about 0.3 TPa. The analysis developed has also allowed the mechanical properties of high volume fraction composites reinforced with carbon nanotubes to be predicted. Acknowledgements This work is part of a larger programme supported by the EPSRC and one author, (C.A.C) is grateful to the EPSRC for support in the form of a studentship. The authors are thankful to the Defence Evaluation and Research Agency (DERA) for providing financial support and the SWNT-A
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