Introduction to Carbon Nanotubes
Since their discovery in 1991, carbon nanotubes have generated huge activity in most areas of science and engineering due to their unprecedented physical and chemical properties. No previous material has displayed the combination of superlative mechanical, thermal and electronic properties attributed to them. These properties make nanotubes ideal, not only for a wide range of applications1 but as a test bed for fundamental science2.
In particular, this combination of properties makes them ideal candidates as advanced filler materials in composites. Researchers have envisaged taking advantage of their conductivity and high aspect ratio to produce conductive plastics with exceedingly low percolation thresholds3. In another area, it is thought that their massive thermal conductivity can be exploited to make thermally conductive composites4. However, probably the most promising area of composites research involves the mechanical enhancement of plastics using carbon nanotubes as reinforcing fillers.
The idea of using pseudo one-dimensional fillers as a reinforcing agent is nothing new: straw has been used to reinforce mud bricks since about 4000 BC. In more recent times, fibres made from materials such as alumina, glass, boron, silicon carbide and especially carbon have been used as fillers in composites. However, these conventional fibres have dimensions on the meso-scale with diameters of tens of microns and lengths of order of millimetres. Their mechanical properties are impressive with carbon fibres typically displaying stiffness and strength in the ranges 230-725 GPa and 1.5-4.8 GPa respectively 5. In recent years carbon nano-fibres have been grown from the vapour phase with diameters of order of 100 nm and lengths between 20 and 100 microns. These small dimensions mean they have much higher surface area per unit mass than conventional carbon fibres allowing much greater interaction with composite matrices. They also tend to have impressive mechanical properties with Young’s modulus in the range 100-1000 GPa and strengths between 2.5 and 3.5 GPa6.
However the ultimate mechanical filler material must be carbon nanotubes. Nanotubes can have diameters ranging from 1-100 nm and lengths of up to millimetres7. Their densities can be as low as ~1.3 g/cm3 and their Young’s moduli are superior to all carbon fibres with values greater than 1 TPa8. However, their strength is what really sets them apart. The highest measured strength for a carbon nanotube was 63 GPa9. This is an order of magnitude stronger than high strength carbon fibres. Even the weakest type of carbon nanotubes have strengths of several GPa 10.
There are two main types of nanotubes available today. Single walled nanotubes (SWNT)11,12 consist of a single sheet of graphene rolled seamlessly to form a cylinder with diameter of order of one nanometre and length of up to centimetres. Multi walled nanotubes (MWNT) consist of an array of such cylinders formed concentrically and separated by 0.35 nm, similar to the basal plane separation in graphite13. MWNTs can have diameters from 2-100 nm and lengths of tens of microns.
Single walled nanotubes can be fabricated in a variety of ways. Early fabrication relied on a modified version of arc-discharge generators used for Fullerene synthesis11,12. However, today the most common synthetic methods are based on laser ablation14 and chemical vapour deposition15,16, in particular, decomposition of CO17. It should be noted that, while high quality SWNTs can be produced, some level of defects are always present. These may significantly affect the physical and chemical properties of the nanotubes.
A graphene sheet may be rolled up in many ways to form a single walled nanotube. The rolling action breaks the symmetry of the planar system and imposes a distinct direction with respect to the hexagonal lattice, the axial direction. Depending on the relationship between this axial direction and the unit vectors describing the hexagonal lattice, the tube can be metallic, semi-metallic or semiconducting. Semi-conducting nanotubes have bandgaps that scale inversely with diameter, ranging from approximately 1.8 eV for very small diameter tubes to 0.18 eV for the widest possible stable SWNT18
Pristine carbon nanotubes are extremely conductive. Due to their one-dimensional nature, charge carriers can travel through nanotubes without scattering resulting in ballistic transport. The absence of scattering means that Joule heating is minimised so that nanotubes can carry massive current densities of up to 100 MA/cm2 19 . In addition, carrier mobilities as high as 105 cm2/Vs have been observed in semi-conducting nanotubes20. Superconductivity has also been observed in SWNT, albeit with transition temperatures of 5 K21 .
Nanotubes are also very conductive for phonons. Theory predicts a room temperature thermal conductivity of up to 6000 W/mK22-24. While this has not yet been attained, values around 200 W/mK have been measured25.
However, it should be pointed out that pristine, isolated SWNT are rarely available to experimentalists. Due to their great flexibility and high surface energy, SWNT tend to aggregate into large bundles. Bundles contain huge numbers of both metallic and semiconducting SWNT in a random mixture. Bundle properties are generally inferior to those of isolated SWNT. It is extremely difficult to separate SWNT from bundles making this issue a serious hurdle in the way of real applications.
Well graphitised, relatively defect free MWNT can be produced by the arc discharge method26. In some ways, these materials are rather similar to those of perfect SWNT as the interwall coupling is relatively weak. Electronically, they act as either metals or very small bandgap semiconductors. Ballistic conduction has been observed by a number of groups27 and thermal conductivities as high as 3000 W/mK have been measured28.
However, the most common production mechanism for MWNT is undoubtedly chemical vapour deposition (CVD). Nanotubes made from this method generally have very large quantities of defects. This means their structure is very far from the ideal rolled up hexagonal lattice. Their physical properties suffer due to the presence of defects with thermal, electronic and mechanical properties deviating significantly from those expected for pristine nanotubes. However CVD produced MWNT are important because they can be produced in very large quantities relatively cheaply. If nanotubes are ever to be useful at an industrial level it is likely that they will be produced by some type of CVD process.
From virtually the moment nanotubes were discovered it was expected that they would display superlative mechanical properties by analogy with graphite. It had long been known that graphite had an in-plane modulus of 1.06 TPa29 and nanotubes were expected to display similar stiffness. While the tensile strength of graphite was not accurately known, Perepelkin had estimated it to be as high as 130 GPa from the properties of C-C bonds30. In addition Bacon had fabricated graphite whiskers in 1960 with a yield strength of 20 GPa31. Thus, it was expected that carbon nanotubes would be in a class of their own in terms of high strength and stiffness.
Long before sufficient quantities of nanotubes were produced to allow mechanical measurements, a number of studies had used computer simulation to study their properties. As early as 1993, Overney et al.32 calculated the rigidity of short SWNT using ab initio local density calculations to determine the parameters in a Keating potential. The calculated Young’s modulus was 1500 GPa, similar to that of graphite. This was followed by a range of papers predicting that the Young’s modulus of nanotubes was close to 1 TPa independent of nanotube type and diameter 33.
The first actual mechanical measurements were made on multi walled nanotubes produced by the arc discharge process. As only small amounts were available, early measurements were carried out in a transmission electron microscope. Treacy et al.34 measured the amplitude of intrinsic thermal vibrations observed in the TEM. They used this to calculate moduli of 0.41 to 4.15 TPa for a number of tubes. Three years later Poncheral induced electromechanical resonant vibrations, giving moduli values between 0.7 and 1.3 TPa35. In addition, Falvo et al. observed the reversible bending of MWNT with radii of curvature as low as ~25nm indicating unprecedented flexibility36.
The first direct measurement was made by Wong et al. in 19978. They used an atomic force microscope (AFM) to measure the stiffness constant of arc-MWNTs pinned at one end. This gave an average value for Young’s modulus of 1.28 TPa. More importantly they also managed to make the first strength measurements, obtaining an average bending strength of 14 GPa. Salvetat et al. used an AFM to bend an arc-MWNT that had been pinned at each end over a hole37 obtaining an average modulus value of 810 GPa.
However, the ultimate measurements were carried out by Yu et al. in 2000 when they managed to do stress-strain measurements on individual arc-MWNTs inside an electron microscope9. For a range of tubes they obtained modulus values of 0.27-0.95 TPa. More interestingly they showed fracture of MWNT at strains of up to 12% and with strengths in the range 11-63 GPa. This allows the estimation of nanotube toughness at ~1240 J/g. In addition, failure was observed at the outer tube with the inner walls telescoping out in a “sword and sheath” mechanism.
Figure1. Stress strain curves for individual MWNT. Reproduced from 9.
Measurements on SWNT took longer due to the difficulties in handling them. The first measurements were carried out by Salvetat et al. using their AFM method38. They observed a tensile modulus of ~1 TPa for small diameter SWNT bundles by bending methods. However, the properties of larger diameter bundles were dominated by shear slippage of individual nanotubes within the bundle. Yu et al. were able to measure the tensile properties of bundles by the same method they used for their MWNT study. They saw moduli in the range 0.32-1.47 TPa and strengths between 10 and 52 GPa. Failure occurred at a maximum strain of 5.3% giving a toughness of approximately 770 J/g. In addition they observed that failure occurred for the nanotubes on the perimeter of the bundle only with the rest of the tubes slipping apart39.
Figure 2. TEM images of A) an arc-MWNT B) a CVD-MWNT. AFM images of C) arc-MWNT and D) CVD-MWNT lying across a pore. Reproduced from 37.
Intertube slippage within bundles presents a serious limitation to their mechanical properties. The low shear modulus means that effective moduli and strengths for bundles are far below those expected for individual SWNT. As mentioned previously, it is extremely difficult to de-bundle SWNT. Forro and co-workers showed that SWNT could be fused together in bundles by electron irradiation40,41. By fine-tuning the dose and irradiation energy they found that they could increase the bundle bending modulus to 750 GPa, close to that of an individual SWNT.
The relatively high values of modulus and strength values of ~1 TPa and tens of GPa have been measured on high quality SWNT and arc discharge MWNT. However as discussed previously, CVD MWNT are expected to display significantly reduced values. The first measurements on CVD MWNT were carried out by Salvetat et al. using the AFM technique. They measured Young’s modulus values between 12 and 50 GPa37. Shortly afterwards Xie et al. made stress-strain measurements on bundles of CVD-MWNT10. They measured a modulus of 0.45 TPa and values of tensile strength of ~4 GPa. The much larger variation in modulus for CVD-MWNT compared to arc-MWNT strongly suggests that the modulus is very sensitive to defect concentration and type.
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