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Electrical transport in carbon nanotube fibres
SMM-11377; No of Pages 7 Scripta Materialia xxx (2016) xxx–xxx
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Electrical transport in carbon nanotube fibres Agnieszka Lekawa-Raus a,b,⁎, Tomasz Gizewski a,c, Jeff Patmore d, Lukasz Kurzepa a, Krzysztof K. Koziol a,⁎ a
Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, CB3 0FS, Cambridge, UK Institute of Metrology and Biomedical Engineering, Faculty of Mechatronics, Warsaw University of Technology, ul. sw. A. Boboli 8, 02 525 Warsaw, Poland c Faculty of Electrical Engineering and Computer Science, ul. Nadbystrzycka 38A, Lublin, Poland d Pembroke College, CB2 1RF Cambridge, UK b
a r t i c l e
i n f o
Article history: Received 13 September 2016 Received in revised form 20 November 2016 Accepted 21 November 2016 Available online xxxx Keywords: Carbon nanotubes Carbon nanotube fibres Electrical properties Electrical resistivity/conductivity Nanostructured materials
a b s t r a c t Individual carbon nanotubes are highly interesting electrical conductors which could well complete with superconductors. Yet, the possibility of production of top-performance carbon nanotube electrical conductors beyond nanoscale, is the question currently challenging scientists. This study discusses theoretical potential of macroscopic fibres made purely of carbon nanotubes, in charge transport and electrical applications. It also examines various aspects of their electrical conductivity including both direct and alternating current transport, weight-conductivity ratios, current density and doping issues. The reasons for the constraints in electrical transport in fibres manufactured today are explained, as are possible routes to achieving significant improvements in the performance. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction At the UK's Royal Society Science Summer Exhibition in London (2013), our research team demonstrated to the public that properly engineered carbon nanotubes (CNTs) may work as macroscopic electrical conductors in many electrical machines by replacing their copper windings with CNT wires (Fig. 1) [1,2]. This proper engineering starts with the spinning of CNT fibres, that is forming yarn-like assemblies of longitudinally aligned CNTs [3], combining many yarns together to form CNT cords and then coating the cords with standard insulating polymers [4]. Further steps of the process include cutting the wires to desired length, winding the chosen machine design and connecting electrically using a newly-developed carbon solder [5]. The device, which attracted the most attention at the Royal Society event, was a small DC generator in which the copper windings were fully replaced by CNT windings. Images of all parts of this generator are presented in Fig. 2 a). While Fig. 2 b) shows a magnified image of the rotor fully wound with CNT wires of approximately 0.5 mm diameter (with insulation). Each winding had 33 turns and a resistance of approximately 90 Ω. The operation of this device is presented in online Supplementary Materials (Video 1). In testing the CNT wound generator it was found that it performed, in terms of the voltage generated at a specific angular velocity, as is predicted by conventional theories. Fig. 3, below, shows the experimental ⁎ Corresponding authors. E-mail addresses: [email protected] (A. Lekawa-Raus), [email protected] (K.K. Koziol).
results recorded, in no-load conditions, of the maximum voltage produced at the output of the CNT wound generator, against increasing rotational velocity. In accordance with classical theory, the graph is linear and increasing. Further tests showed that the power generated at the output of the tested device was enough to light a red diode (1.5 V, 2 mA). It was lit at approximately 3000 RPM (see also online Supplementary Video 1). However, this was close to the limit of operation for the device, which had a very poor performance in comparison to a copper wound version. Recently an independent group reported building an almost identical machine wound using fibres spun using a different fibre manufacturing process [6]. Elegant extensive modelling and experimental testing yielded exactly the same result. The reason for the poor performance of both devices was the high resistance of the CNT fibre based windings. Therefore, the key question is; Will CNT fibres ever be able to reach a sufficient conductivity to compete with copper?
2. DC electrical transport within the fibre As theorized by Xu et al. fibres could in principle transport electricity almost like one, long, ballistic conductor [7]. “Almost” comes from the fact that they could be a true ballistic conductor only if the CNT fibres were made exclusively of long, single-walled CNTs of one armchair chirality, which would contact each other with a chirality dependent overlap of a precise length. As a precise length of overlap would seem to be technologically impractical to achieve, the authors calculated that it would be sufficient just to have a very long overlap. In this case, it is
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Fig. 1. The manufacture of carbon nanotube wires, which are then used as windings in electrical machines, such as transformers, generators and motors.
calculated, that a voltage of 0.04 V applied to the whole fibre would be sufficient to drive electrons freely [7]. However, when considering the conductivity of CNTs, it is important to remember that a ballistic conductor is not fully resistanceless. Each CNT connected to standard metal contact will theoretically experience a resistance of at least 6.5 kΩ, which equals half of a quantum resistance predicted for very narrow conductors [8]. So when considering a practical fibre of, for example, 10 μm diameter and made only of single walled armchair nanotubes of (10.10) chirality, we may calculate a theoretical limit of conductivity. Assuming a dense hexagonal packing of (10.10) nanotubes in a round cross-sectional area of 5 μm radius, the fibre will have approximately 31 million nanotubes that should be in direct contact with a metal contact pad. Hence the conductance of the fibre due to connections cannot be higher than approximately 4600 S which, in turn translates to theoretical values of 5.9 × 1011 S/m, 5.9 × 1013 S/m and 5.9 × 1016 S/m for a 1 cm, 1 m and 1 km long fibre, respectively (see online Supplementary Materials for calculation details). Obviously for other chiralities these values will change as the number of nanotubes in a given cross-section depends on the diameter of the nanotubes. Calculations of conductivity performed for one length
and dimeter of the wire but various armchair nanotubes show that the conductivity scales inversely proportionally to CNT diameter (Fig. 4 a)). Considering the fact, that not all armchair nanotubes will be practically useful as the (2.2) and (3.3) nanotubes were found stable only as inner walls of multi-walled CNTs [9,10] and nanotubes beyond (15.15) are prone to collapsing [11], we may show that e.g. for a 1 m long wire of 10 μm diameter the conductivities will vary from as much as 2.1 × 1014 S/m for (4.4) nanotubes to 3 × 1013 S/m for (15.15). Thus, summing up all the energy losses expected from an ideal theoretical CNT fibre, we might expect it to be significantly better than any conventional metallic conductor. However, this is conditional on the fibres having the ideal structure explained above. In our recent extensive review paper, we recognized a set of research challenges to overcome in current fibre manufacturing processes, so as to obtain these ultimate CNT conductors [3]. These include the simultaneous elimination of multi-walled CNTs and synthesis/use of longer nanotubes, the precise control of chirality, removal of impurities and defects and finally the ensuring of perfect alignment and densification of the fibres. However, it is just as important to consider the very practical aspects such as the length and diameter of
Fig. 2. a) Three main parts of the generator: stator (left) with two permanent magnets which accommodates the rotor (middle) with CNT windings and a plastic cap (right) with metal brushes and electrical terminals to connect the generator to external circuitry. b) A close up of the generator rotor with carbon nanotube windings.
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Fig. 3. a) A schematic diagram of the generator tested in no load conditions excited by an external motor with a varying rotational speed. b) The relationship between the maximum voltage produced by the generator and the angular velocity in revolutions per minute. The red line presents the linear fit to the data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
produced fibres, speed of manufacture, continuity of processes, costs involved, industrial viability etc. Based on our examination of the current literature we have recognized the potential of the existing spinning method dependent techniques which may be used to improve certain areas of the fibre morphology as well as the processes that are the most likely to succeed in reaching all the above listed goals, simultaneously [3]. Yet, with all this, it is still difficult to predict when the successful structure of the fibres may be achieved.
3. Specific conductivity It is quite probable that gradual structural advancements will lead first to improvements in specific conductivity i.e. the conductivity over density parameter. This is due to the extremely low theoretical density of nanotubes. For example, for a (10.10) nanotube density will amount to 1.4 g/cm3 and for the fibre considered in a section above, made solely of such (10.10) nanotubes the density would amount to approximately 1.3 g/cm3 ((see online Supplementary Materials for calculation details). Thus, we may expect a specific conductivity of 4.5 × 105 S/m/g/m3, 4.5 × 107 S/m/g/m3 and 4.5 × 1010 S/m/g/m3 for 1 cm, 1 m and 1 km long fibre samples, respectively. Obviously, similarly to the section above we may show that both density and specific conductivity depend on exact chirality. However, analogous calculations performed for all practically useful armchair chiralities and 1 m long wire of 10 μm diameter show that the specific conductivity although decreases with increasing dimeter, remains very
high (Fig. 4 b)). In comparison, the specific conductivity of copper and aluminium amounts to 6.52 S/m/g/m3 and 14.15 S/m/g/m3 respectively. These orders of magnitude differences between traditional conductors and CNT wires seem very exciting as any decrease in the weight of wires may be of paramount importance in, for example, aeroplanes where any decrease in the weight of wiring may significantly cut the use of fuel and running costs. Another example is the electric motor where lowering of the weight of windings will decrease the moment of inertia and thus increase the rotational speed of the machine. However, it is also a very tricky parameter in the case of non-ideal CNT fibres, as there are windows of specific conductivity values which may be higher than for copper and aluminium due to the very low density, but of not sufficiently high real conductivity. Such conductors would produce increased losses and in case of traditional machines both lower efficiency and a compromise on the performance. The performance here may include e.g. lowering of rotational speed of a motor due to smaller acceptable current density of windings or an increase in the volume of wires, so as to maintain a comparable current density, which entails the use of larger cores and thus an increase of the overall volume and weight of the machine. Still, there may be some applications where the volume or efficiency maybe traded for weight such as in power cables or novel machine designs for space or medical applications. Nevertheless, the ultimate solution for all DC applications is to reach an ideal structure of the fibre and thus an improvement in both conductivity and weight [3,7]. There is however an additional concern and
Fig. 4. a) Conductivity and b) specific conductivity values for theoretical 1 m long fibres of 10 μm diameter made of armchair nanotubes with a chirality shown as a label of each data point.
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question; Will the ideal morphology of the fibre presented in the previous section be optimal for every application? 4. AC electrical transport within the fibre Examining the example of copper, its very good DC conductivity does not ensure its performance at high frequencies, causing issues in telecommunications, power grids, electrical machines and many other applications. The major problems here are skin and proximity effects i.e. the phenomena of AC current displacement in the conductor crosssection that increases with frequency. In the case of currently produced CNT wires the AC losses are largely due to undesired resistances and capacitances within the fibre [12–14]. Getting rid of all poorly conducting nanotubes and resistive connections from the fibre would significantly reduce these issues, and would leave us with only some minor capacitive losses on the CNT metal contacts and inductances within the fibre. But what of the skin effect? Theoretically, an individual nanotube due to its tubular structure should be devoid of skin effect as it conducts current only through its circumference at any frequency. However, the CNT fibre cross-section comprises millions of these little tubules, which in an ideal sample should form a practically resistanceless network. To the best of our knowledge, up to now no theoretical studies exist that show quantum transport in the frequency domain between carbon nanotubes of various chiralities. Therefore, it is not unexpected that, the ideal structure of a CNT fibre proposed by Xu et al. has not been considered yet [7]. However, even without going into the complex quantum transport calculations we may draw some very interesting conclusions from the standard classical calculations which consider the role of the specific geometry of the fibres. To portray the frequency dependent current distribution in a nanotubular conductor we first modelled a copper wire of 12.5 nm diameter with a cross-section made of 111 tubules of 1.4 nm diameter and 0.34 nm wall thickness i.e. emulating (10.10) carbon nanotubes (Fig. 5) and for comparison, a solid copper wire of the same 12.5 nm diameter and a copper tubes of 12.5 nm and 9.5 nm of external and internal diameter, respectively. The simulations were performed in COMSOL Multiphysics® Modelling Software, using classical Maxwell equation (Eq. 1) in a complex number domain, where magnetic field potential A was defined in the formula (Eq. 2) and current density distribution (Eq. 3) was used for conductive and non-conductive (Eq. 4a and b) regions respectively. ∇H¼ J
ð1Þ
B¼∇A
ð2Þ
J ¼ γE þ jωD þ Je
ð3Þ
E ¼ jωA
ð4aÞ
J ¼ jωD
ð4bÞ
Where, J is a current density vector, E – electric field vector, D – electric flux vector, γ – conductivity, ω – pulsation of the AC field, j – imaginary unit, Je – is an external current density and A stands for magnetic potential vector. As shown in Fig. 5 a) and b) at 500 THz the solid wire suffers most from the skin effect and the tube is practically unaffected (Fig. 5 b), d)). The nanotube fibre-like cross-section significantly suppresses the onset of current dislocation yet it does not eradicate it fully (Fig. 5 e), f)). The extremely high frequency used in this modelling is related to the extremely small diameter of the wires and relatively high conductivity of copper. Further simulations showed that the dependency of the skin effect on the diameter of the potentially useful nanotubes, such as armchair (6.6), (9.9), (10.10), (12.12), is negligible (Fig. 6) [7,15,16]. However, a
Fig. 5. a) Geometry and b) current distribution in a solid conductor, c), d) tube and a e), f) tubular conductor made of copper at frequency of 500 THz.
notable result is that the fibre like geometry causes locally an increase in surface magnetic flux density, which may be an important and helpful property in electric machine designs.
Fig. 6. Comparison of skin effect for fibres made fully of armchair nanotubes of one chirality or copper of analogous geometry. The current density is calculated over the blue envelope of the fibre (inset of the figure).
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All of the above indicates that the ideal structure of fibre, as predicted for DC current, although decreases the skin effect in comparison to a solid conductor of the same conductivity, does not ensure full mitigation of the AC related issues. Therefore, in the case of AC it would be worth considering some alternative CNT wire structures, such as the production of concentric wires of armchair nanotubes and semiconducting nanotubes which could ensure better use of the full volume of the conductor (Fig. 7 a)). Another solution could be combination of several fibres each one with nanotubes of different indices e.g. one fibre with only (6.6), one with (9.9) and one with (12.12) nanotubes, which will ensure a slightly resistive electron transport between such fibres (Fig. 7 b)) or perhaps a traditional method of insulation as used in copper Litz wires (Fig. 7 c)). Finally, it should be noted that in comparing geometrically similar conductors composed of copper nanotubules, non-armchair CNTs and armchair CNTs, the latter ones show skin effect at the lowest frequencies (Fig. 6). This is an expected result predicted by classical skin effect theory related simply to the conductivity of the material. Yet it has to be taken into account that a limiting factor for copper is its current carrying capacity, which may not be the case for CNT fibres. 5. Current transport The maximum current density of individual nanotubes in vacuum is several orders of magnitude higher than that of copper or aluminium and even higher than the critical current density of superconductors and amounts to 109–1010 A cm−2 (experimental values) [17–19]. However, up until now calculations have not been made on how this number translates into the theoretically acceptable current density of an ideal CNT fibre operating under specific ambient conditions including vacuum, air, polymeric insulation etc. and how this will change for AC and DC. Estimation of the maximum current density of a CNT fibre has to take account of two critical factors, these are heat and electric field induced failure. The latter one could for example play a significant role in a perfectly cooled fibre in which the connections between its nanotubes are resistive, thus allowing the electric field induced discharge between CNTs. However, considering the earlier described ideal fibre with negligible resistances present we may expect that the maximum current observed for individual CNTs should not be significantly influenced by electric field induced effects. However, the situation is quite different in case of thermal phenomena. It will probably not come as any great surprise that the heat removal efficiency of a CNT fibre made of many tightly packed nanotubes would be slightly lower than that of a single free-standing nanotube. Although a ballistic heat conduction phenomenon along the nanotube has been found, the currently reported length scales, at room temperature, were not excessive, yet there is still a debate about the theoretical limits of ballistic transport in long nanotubes [20]. Similarly debatable, is the dependence of thermal conductivity on chirality [20]. This is probably
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why, to the best of our knowledge, up to now there exist no studies regarding the conduction of heat between CNTs of same armchair chirality which would aid the calculation of the overall heat transport in an ideal fibre proposed by Xu et al. [7]. These quantum transport calculations will point at any potential constraints on the heat flow through the fibre which influences the heat removal efficiency and thus the thermal failure defined maximum current density. However, even if the maximum current density of an ideal fibre will be slightly lower than for a free-standing individual CNT, we may expect that,the characteristic features of CNT fibres may ensure a higher current transport than in the case of copper or aluminium. Classical theory states that heat generated in a body by the electric current flow may be removed via radiation, convection and conduction. Thus, we have: P ¼ ε σ Srad T 4 þ αSconv ðT−T 0 Þ þ
λAcond ðT−T 0 Þ d
ð5Þ
where, P stands for electric power, ε - emissivity, σ – StefanBoltzmann constant, Srad – radiation area, T - temperature, T0 – room temperature, α - convection heat transfer coefficient, Srad – convection area, λ - thermal conductivity, Acond – cross-section area. Comparing all the above parameters we may show that CNT fibres should remove heat much more efficiently than metallic conductors. Firstly, we may expect that emissivity of CNT fibre will be high and constant [21,22]. It is well known that in case of bare aluminium and copper wires operating in ambient conditions, the emissivity changes over time due to oxidation of their surface area. Over many years of service this emissivity can increase from an initial value of approximately 0.2 to a value as high as 0.9 (average value used for most calculations - 0.5) [23,24]. This indicates that it takes many years for the wire to reach the level of emissivity which may be easily expected from the CNT fibres. The emissivity of currently produced CNT fibres, which are not very well condensed and pure, amounts to 0.85 [22]. An ideal fibre should easily increase this value to the 0.9 range, although it is difficult to predict an exact number, due to the fact, that the surface of any fibre will be always wavy and bent. Yet, a good approximation of the number could be potentially obtained using classical differential equations. It is finally worth mentioning that the interaction of CNT fibres with ambient conditions should not influence their emissivity, keeping it constant over years. Considering further the parameters of Equation 5 we may observe that the CNT fibres will have a larger lateral surface area for convective and radiative heat removal as compared to a round-shaped metal wire. For R = 5 μm radius fibre made of (10.10) nanotubes, the lateral surface will be approximately 60% larger than for a smooth round wire (see online Supplementary Materials for more details). The amount of convective heat removed per unit of time is also determined by a heat transfer coefficient α, which is dependent on many factors including the type of material, dimensions, and structure of a body, surrounding medium and its temperature/pressure etc.
Fig. 7. Theoretical structures of CNT fibres that could decrease skin effect. a) concentric rings of armchair and semiconducting nanotubes b) Litz-like wire with strands made of various types of armchair chiralities, c) or with insulated strands.
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Therefore, the calculations of this parameter are quite complicated. However, based on the experimental values found for CNT materials we may draw some initial conclusions. Coefficients measured for currently produced CNT fibres amounted to approx. 103 W /mK for fibre of approximately 40 μm diameter and 25–190 W /mK for 150–800 μm diameter [22,25]. The scaling with the diameter is well-expected and observed also for other materials. The convective heat coefficient observed for macro-scale copper amounts to 2–25 W /mK while for micro-wire of 40 μm diameter increases to 450 W /mK [22,26]. These values indicate that α could be larger than for copper. However, finding the theoretical values for ideally structured fibres will require further studies and calculations, as the internal structure of the fibre such as packing density was found to be a very important parameter in the experimental studies. Heat removal via conduction will need to be strongly based on the results of quantum transport calculations, as these will determine the ballistic length scales and potential limits of heat transfer between nanotubes which will define an overall thermal conductivity λ. Up to now the measurements of thermal conductivity of practical CNT fibres were not satisfactory, yet the values for doped fibres reached 635 W / mK [27]. Taking into account, that thermal conductivity of individual nanotubes was calculated to be even as high as 6600 W /mK we may expect that λ of an ideal fibre may be well above copper or aluminium [28]. Therefore, even the fact that cross-sectional area used for conduction will be decreased due to voids present in the fibre (e.g. for (10.10) fibre the share of pores will amount to approx. 40%), and the whole fibre will be a very porous material thanks to the efficient heat transport between nanotubes the overall heat removal should not suffer significantly. To summarize, we may well expect that the heat removal from CNT fibre should be much better than in case of copper or aluminium, which should ensure much higher current carrying capacity. Considering these electrically related thermal phenomena in the fibre, it is also worth mentioning that the temperature coefficient of resistivity of an ideal CNT fibre may differ from conventional metals, but its exact theoretical value, which for current fibres changes with morphology, would have to be calculated [29]. Finally, when considering the media surrounding the fibres it may be necessary to remember that the mechanism of carbon nanotube assembly thermal failure in air, is based on the rapid oxidation and does not involve any melting as in the case of metal, which may influence future current ratings for this material [30,31].
however, taking into account that the operation of copper in acidic environment is mostly impossible, a small permanent offset of conductivity in case of CNT fibres should be quite acceptable [36]. It is worth mentioning that at the current stage of fibre development, the doping of semiconducting or semi-metallic and defected nanotubes as well as their contacts in the fibre, can produce unexpectedly good results in terms of conductivity and specific conductivity [37–39]. It is possible that for the time being such an approach may suffice for practical applications, therefore is definitely worth exploring. Even more interesting may be a combination of carbon nanotube fibres with metals [40,41]. Unfortunately, these topics go well beyond the scope of this paper.
6. Doping
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Last but not the least to consider is the influence of environment on the electrical transport in CNT fibres. It is well known that copper and aluminium left in contact with oxygen undergo an oxidation of their surface layers. The oxides are fully insulating but passivate the surface thus preventing further in-depth oxidation. Unfortunately, when the metals are in contact with more harmful chemicals they may even fully dissolve such as in case of dipping in strong acids. Carbon, in contrast, is not structurally damaged by any of these factors at standard ambient conditions. Yet, it is a well-known adsorbent of many species such as oxygen, water vapour or acids that may, in turn, change the electronic properties by various mechanisms of doping [32–34]. In most cases these adsorbates were reported to p-dope nanotubes and increase their conductivity. However, as indicated by the simulations, armchair nanotubes should be the least prone to doping, therefore an ideal structure of fibre is one made fully of armchair SWNTs and this should ensure a lower fluctuation of conductivity upon contact with oxygen [35]. Also the ideal packing of nanotubes, described above, should decrease porosity, which normally facilitates adsorption. If needed additional protection could be provided by a simple insulation of the CNT wire. In the case of acids, it may be difficult to fully prevent doping,
7. Summary The discussion presented above is intended to capture the ultimate goals of research on carbon nanotube fibres, for use as electrical conductors. An in-depth analysis of the current issues indicates that, firstly, there may not be one ideal structure for the fibre, but it may depend on the application. Secondly, the performance of an ideal CNT fibre will differ from that of an individual nanotube considerably and so to predict it, an account needs to be taken of number of assembly-related phenomena. Moreover, the research on currently produced CNT fibres does not include enough about the performance which we should expect from these ultimate CNT fibres and a vast amount of theoretical work is still needed to predict their properties. Finally, the behaviour of even ideal CNT fibres will almost certainly differ considerably from any metallic conductors, therefore new standards will need to be introduced in order to operate them in existing or future electrical circuits. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.scriptamat.2016.11.027. Acknowledgements A.L.- R. T. G., L. K. and K.K.K. thank the European Research Council (under the Seventh Framework Program FP7/2007–2013, grant agreement 259061) for funding. K.K. is also grateful to the Royal Society for further financial support and A.L.-R. to National Centre for Research and Development, Poland for grant Lider VI (agreement number LIDER/220/L-6/14/NCBR/2015). References
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Viewpoint Article
Electrical transport in carbon nanotube fibres Agnieszka Lekawa-Raus a,b,⁎, Tomasz Gizewski a,c, Jeff Patmore d, Lukasz Kurzepa a, Krzysztof K. Koziol a,⁎ a
Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, CB3 0FS, Cambridge, UK Institute of Metrology and Biomedical Engineering, Faculty of Mechatronics, Warsaw University of Technology, ul. sw. A. Boboli 8, 02 525 Warsaw, Poland c Faculty of Electrical Engineering and Computer Science, ul. Nadbystrzycka 38A, Lublin, Poland d Pembroke College, CB2 1RF Cambridge, UK b
a r t i c l e
i n f o
Article history: Received 13 September 2016 Received in revised form 20 November 2016 Accepted 21 November 2016 Available online xxxx Keywords: Carbon nanotubes Carbon nanotube fibres Electrical properties Electrical resistivity/conductivity Nanostructured materials
a b s t r a c t Individual carbon nanotubes are highly interesting electrical conductors which could well complete with superconductors. Yet, the possibility of production of top-performance carbon nanotube electrical conductors beyond nanoscale, is the question currently challenging scientists. This study discusses theoretical potential of macroscopic fibres made purely of carbon nanotubes, in charge transport and electrical applications. It also examines various aspects of their electrical conductivity including both direct and alternating current transport, weight-conductivity ratios, current density and doping issues. The reasons for the constraints in electrical transport in fibres manufactured today are explained, as are possible routes to achieving significant improvements in the performance. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction At the UK's Royal Society Science Summer Exhibition in London (2013), our research team demonstrated to the public that properly engineered carbon nanotubes (CNTs) may work as macroscopic electrical conductors in many electrical machines by replacing their copper windings with CNT wires (Fig. 1) [1,2]. This proper engineering starts with the spinning of CNT fibres, that is forming yarn-like assemblies of longitudinally aligned CNTs [3], combining many yarns together to form CNT cords and then coating the cords with standard insulating polymers [4]. Further steps of the process include cutting the wires to desired length, winding the chosen machine design and connecting electrically using a newly-developed carbon solder [5]. The device, which attracted the most attention at the Royal Society event, was a small DC generator in which the copper windings were fully replaced by CNT windings. Images of all parts of this generator are presented in Fig. 2 a). While Fig. 2 b) shows a magnified image of the rotor fully wound with CNT wires of approximately 0.5 mm diameter (with insulation). Each winding had 33 turns and a resistance of approximately 90 Ω. The operation of this device is presented in online Supplementary Materials (Video 1). In testing the CNT wound generator it was found that it performed, in terms of the voltage generated at a specific angular velocity, as is predicted by conventional theories. Fig. 3, below, shows the experimental ⁎ Corresponding authors. E-mail addresses: [email protected] (A. Lekawa-Raus), [email protected] (K.K. Koziol).
results recorded, in no-load conditions, of the maximum voltage produced at the output of the CNT wound generator, against increasing rotational velocity. In accordance with classical theory, the graph is linear and increasing. Further tests showed that the power generated at the output of the tested device was enough to light a red diode (1.5 V, 2 mA). It was lit at approximately 3000 RPM (see also online Supplementary Video 1). However, this was close to the limit of operation for the device, which had a very poor performance in comparison to a copper wound version. Recently an independent group reported building an almost identical machine wound using fibres spun using a different fibre manufacturing process [6]. Elegant extensive modelling and experimental testing yielded exactly the same result. The reason for the poor performance of both devices was the high resistance of the CNT fibre based windings. Therefore, the key question is; Will CNT fibres ever be able to reach a sufficient conductivity to compete with copper?
2. DC electrical transport within the fibre As theorized by Xu et al. fibres could in principle transport electricity almost like one, long, ballistic conductor [7]. “Almost” comes from the fact that they could be a true ballistic conductor only if the CNT fibres were made exclusively of long, single-walled CNTs of one armchair chirality, which would contact each other with a chirality dependent overlap of a precise length. As a precise length of overlap would seem to be technologically impractical to achieve, the authors calculated that it would be sufficient just to have a very long overlap. In this case, it is
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Fig. 1. The manufacture of carbon nanotube wires, which are then used as windings in electrical machines, such as transformers, generators and motors.
calculated, that a voltage of 0.04 V applied to the whole fibre would be sufficient to drive electrons freely [7]. However, when considering the conductivity of CNTs, it is important to remember that a ballistic conductor is not fully resistanceless. Each CNT connected to standard metal contact will theoretically experience a resistance of at least 6.5 kΩ, which equals half of a quantum resistance predicted for very narrow conductors [8]. So when considering a practical fibre of, for example, 10 μm diameter and made only of single walled armchair nanotubes of (10.10) chirality, we may calculate a theoretical limit of conductivity. Assuming a dense hexagonal packing of (10.10) nanotubes in a round cross-sectional area of 5 μm radius, the fibre will have approximately 31 million nanotubes that should be in direct contact with a metal contact pad. Hence the conductance of the fibre due to connections cannot be higher than approximately 4600 S which, in turn translates to theoretical values of 5.9 × 1011 S/m, 5.9 × 1013 S/m and 5.9 × 1016 S/m for a 1 cm, 1 m and 1 km long fibre, respectively (see online Supplementary Materials for calculation details). Obviously for other chiralities these values will change as the number of nanotubes in a given cross-section depends on the diameter of the nanotubes. Calculations of conductivity performed for one length
and dimeter of the wire but various armchair nanotubes show that the conductivity scales inversely proportionally to CNT diameter (Fig. 4 a)). Considering the fact, that not all armchair nanotubes will be practically useful as the (2.2) and (3.3) nanotubes were found stable only as inner walls of multi-walled CNTs [9,10] and nanotubes beyond (15.15) are prone to collapsing [11], we may show that e.g. for a 1 m long wire of 10 μm diameter the conductivities will vary from as much as 2.1 × 1014 S/m for (4.4) nanotubes to 3 × 1013 S/m for (15.15). Thus, summing up all the energy losses expected from an ideal theoretical CNT fibre, we might expect it to be significantly better than any conventional metallic conductor. However, this is conditional on the fibres having the ideal structure explained above. In our recent extensive review paper, we recognized a set of research challenges to overcome in current fibre manufacturing processes, so as to obtain these ultimate CNT conductors [3]. These include the simultaneous elimination of multi-walled CNTs and synthesis/use of longer nanotubes, the precise control of chirality, removal of impurities and defects and finally the ensuring of perfect alignment and densification of the fibres. However, it is just as important to consider the very practical aspects such as the length and diameter of
Fig. 2. a) Three main parts of the generator: stator (left) with two permanent magnets which accommodates the rotor (middle) with CNT windings and a plastic cap (right) with metal brushes and electrical terminals to connect the generator to external circuitry. b) A close up of the generator rotor with carbon nanotube windings.
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Fig. 3. a) A schematic diagram of the generator tested in no load conditions excited by an external motor with a varying rotational speed. b) The relationship between the maximum voltage produced by the generator and the angular velocity in revolutions per minute. The red line presents the linear fit to the data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
produced fibres, speed of manufacture, continuity of processes, costs involved, industrial viability etc. Based on our examination of the current literature we have recognized the potential of the existing spinning method dependent techniques which may be used to improve certain areas of the fibre morphology as well as the processes that are the most likely to succeed in reaching all the above listed goals, simultaneously [3]. Yet, with all this, it is still difficult to predict when the successful structure of the fibres may be achieved.
3. Specific conductivity It is quite probable that gradual structural advancements will lead first to improvements in specific conductivity i.e. the conductivity over density parameter. This is due to the extremely low theoretical density of nanotubes. For example, for a (10.10) nanotube density will amount to 1.4 g/cm3 and for the fibre considered in a section above, made solely of such (10.10) nanotubes the density would amount to approximately 1.3 g/cm3 ((see online Supplementary Materials for calculation details). Thus, we may expect a specific conductivity of 4.5 × 105 S/m/g/m3, 4.5 × 107 S/m/g/m3 and 4.5 × 1010 S/m/g/m3 for 1 cm, 1 m and 1 km long fibre samples, respectively. Obviously, similarly to the section above we may show that both density and specific conductivity depend on exact chirality. However, analogous calculations performed for all practically useful armchair chiralities and 1 m long wire of 10 μm diameter show that the specific conductivity although decreases with increasing dimeter, remains very
high (Fig. 4 b)). In comparison, the specific conductivity of copper and aluminium amounts to 6.52 S/m/g/m3 and 14.15 S/m/g/m3 respectively. These orders of magnitude differences between traditional conductors and CNT wires seem very exciting as any decrease in the weight of wires may be of paramount importance in, for example, aeroplanes where any decrease in the weight of wiring may significantly cut the use of fuel and running costs. Another example is the electric motor where lowering of the weight of windings will decrease the moment of inertia and thus increase the rotational speed of the machine. However, it is also a very tricky parameter in the case of non-ideal CNT fibres, as there are windows of specific conductivity values which may be higher than for copper and aluminium due to the very low density, but of not sufficiently high real conductivity. Such conductors would produce increased losses and in case of traditional machines both lower efficiency and a compromise on the performance. The performance here may include e.g. lowering of rotational speed of a motor due to smaller acceptable current density of windings or an increase in the volume of wires, so as to maintain a comparable current density, which entails the use of larger cores and thus an increase of the overall volume and weight of the machine. Still, there may be some applications where the volume or efficiency maybe traded for weight such as in power cables or novel machine designs for space or medical applications. Nevertheless, the ultimate solution for all DC applications is to reach an ideal structure of the fibre and thus an improvement in both conductivity and weight [3,7]. There is however an additional concern and
Fig. 4. a) Conductivity and b) specific conductivity values for theoretical 1 m long fibres of 10 μm diameter made of armchair nanotubes with a chirality shown as a label of each data point.
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question; Will the ideal morphology of the fibre presented in the previous section be optimal for every application? 4. AC electrical transport within the fibre Examining the example of copper, its very good DC conductivity does not ensure its performance at high frequencies, causing issues in telecommunications, power grids, electrical machines and many other applications. The major problems here are skin and proximity effects i.e. the phenomena of AC current displacement in the conductor crosssection that increases with frequency. In the case of currently produced CNT wires the AC losses are largely due to undesired resistances and capacitances within the fibre [12–14]. Getting rid of all poorly conducting nanotubes and resistive connections from the fibre would significantly reduce these issues, and would leave us with only some minor capacitive losses on the CNT metal contacts and inductances within the fibre. But what of the skin effect? Theoretically, an individual nanotube due to its tubular structure should be devoid of skin effect as it conducts current only through its circumference at any frequency. However, the CNT fibre cross-section comprises millions of these little tubules, which in an ideal sample should form a practically resistanceless network. To the best of our knowledge, up to now no theoretical studies exist that show quantum transport in the frequency domain between carbon nanotubes of various chiralities. Therefore, it is not unexpected that, the ideal structure of a CNT fibre proposed by Xu et al. has not been considered yet [7]. However, even without going into the complex quantum transport calculations we may draw some very interesting conclusions from the standard classical calculations which consider the role of the specific geometry of the fibres. To portray the frequency dependent current distribution in a nanotubular conductor we first modelled a copper wire of 12.5 nm diameter with a cross-section made of 111 tubules of 1.4 nm diameter and 0.34 nm wall thickness i.e. emulating (10.10) carbon nanotubes (Fig. 5) and for comparison, a solid copper wire of the same 12.5 nm diameter and a copper tubes of 12.5 nm and 9.5 nm of external and internal diameter, respectively. The simulations were performed in COMSOL Multiphysics® Modelling Software, using classical Maxwell equation (Eq. 1) in a complex number domain, where magnetic field potential A was defined in the formula (Eq. 2) and current density distribution (Eq. 3) was used for conductive and non-conductive (Eq. 4a and b) regions respectively. ∇H¼ J
ð1Þ
B¼∇A
ð2Þ
J ¼ γE þ jωD þ Je
ð3Þ
E ¼ jωA
ð4aÞ
J ¼ jωD
ð4bÞ
Where, J is a current density vector, E – electric field vector, D – electric flux vector, γ – conductivity, ω – pulsation of the AC field, j – imaginary unit, Je – is an external current density and A stands for magnetic potential vector. As shown in Fig. 5 a) and b) at 500 THz the solid wire suffers most from the skin effect and the tube is practically unaffected (Fig. 5 b), d)). The nanotube fibre-like cross-section significantly suppresses the onset of current dislocation yet it does not eradicate it fully (Fig. 5 e), f)). The extremely high frequency used in this modelling is related to the extremely small diameter of the wires and relatively high conductivity of copper. Further simulations showed that the dependency of the skin effect on the diameter of the potentially useful nanotubes, such as armchair (6.6), (9.9), (10.10), (12.12), is negligible (Fig. 6) [7,15,16]. However, a
Fig. 5. a) Geometry and b) current distribution in a solid conductor, c), d) tube and a e), f) tubular conductor made of copper at frequency of 500 THz.
notable result is that the fibre like geometry causes locally an increase in surface magnetic flux density, which may be an important and helpful property in electric machine designs.
Fig. 6. Comparison of skin effect for fibres made fully of armchair nanotubes of one chirality or copper of analogous geometry. The current density is calculated over the blue envelope of the fibre (inset of the figure).
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All of the above indicates that the ideal structure of fibre, as predicted for DC current, although decreases the skin effect in comparison to a solid conductor of the same conductivity, does not ensure full mitigation of the AC related issues. Therefore, in the case of AC it would be worth considering some alternative CNT wire structures, such as the production of concentric wires of armchair nanotubes and semiconducting nanotubes which could ensure better use of the full volume of the conductor (Fig. 7 a)). Another solution could be combination of several fibres each one with nanotubes of different indices e.g. one fibre with only (6.6), one with (9.9) and one with (12.12) nanotubes, which will ensure a slightly resistive electron transport between such fibres (Fig. 7 b)) or perhaps a traditional method of insulation as used in copper Litz wires (Fig. 7 c)). Finally, it should be noted that in comparing geometrically similar conductors composed of copper nanotubules, non-armchair CNTs and armchair CNTs, the latter ones show skin effect at the lowest frequencies (Fig. 6). This is an expected result predicted by classical skin effect theory related simply to the conductivity of the material. Yet it has to be taken into account that a limiting factor for copper is its current carrying capacity, which may not be the case for CNT fibres. 5. Current transport The maximum current density of individual nanotubes in vacuum is several orders of magnitude higher than that of copper or aluminium and even higher than the critical current density of superconductors and amounts to 109–1010 A cm−2 (experimental values) [17–19]. However, up until now calculations have not been made on how this number translates into the theoretically acceptable current density of an ideal CNT fibre operating under specific ambient conditions including vacuum, air, polymeric insulation etc. and how this will change for AC and DC. Estimation of the maximum current density of a CNT fibre has to take account of two critical factors, these are heat and electric field induced failure. The latter one could for example play a significant role in a perfectly cooled fibre in which the connections between its nanotubes are resistive, thus allowing the electric field induced discharge between CNTs. However, considering the earlier described ideal fibre with negligible resistances present we may expect that the maximum current observed for individual CNTs should not be significantly influenced by electric field induced effects. However, the situation is quite different in case of thermal phenomena. It will probably not come as any great surprise that the heat removal efficiency of a CNT fibre made of many tightly packed nanotubes would be slightly lower than that of a single free-standing nanotube. Although a ballistic heat conduction phenomenon along the nanotube has been found, the currently reported length scales, at room temperature, were not excessive, yet there is still a debate about the theoretical limits of ballistic transport in long nanotubes [20]. Similarly debatable, is the dependence of thermal conductivity on chirality [20]. This is probably
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why, to the best of our knowledge, up to now there exist no studies regarding the conduction of heat between CNTs of same armchair chirality which would aid the calculation of the overall heat transport in an ideal fibre proposed by Xu et al. [7]. These quantum transport calculations will point at any potential constraints on the heat flow through the fibre which influences the heat removal efficiency and thus the thermal failure defined maximum current density. However, even if the maximum current density of an ideal fibre will be slightly lower than for a free-standing individual CNT, we may expect that,the characteristic features of CNT fibres may ensure a higher current transport than in the case of copper or aluminium. Classical theory states that heat generated in a body by the electric current flow may be removed via radiation, convection and conduction. Thus, we have: P ¼ ε σ Srad T 4 þ αSconv ðT−T 0 Þ þ
λAcond ðT−T 0 Þ d
ð5Þ
where, P stands for electric power, ε - emissivity, σ – StefanBoltzmann constant, Srad – radiation area, T - temperature, T0 – room temperature, α - convection heat transfer coefficient, Srad – convection area, λ - thermal conductivity, Acond – cross-section area. Comparing all the above parameters we may show that CNT fibres should remove heat much more efficiently than metallic conductors. Firstly, we may expect that emissivity of CNT fibre will be high and constant [21,22]. It is well known that in case of bare aluminium and copper wires operating in ambient conditions, the emissivity changes over time due to oxidation of their surface area. Over many years of service this emissivity can increase from an initial value of approximately 0.2 to a value as high as 0.9 (average value used for most calculations - 0.5) [23,24]. This indicates that it takes many years for the wire to reach the level of emissivity which may be easily expected from the CNT fibres. The emissivity of currently produced CNT fibres, which are not very well condensed and pure, amounts to 0.85 [22]. An ideal fibre should easily increase this value to the 0.9 range, although it is difficult to predict an exact number, due to the fact, that the surface of any fibre will be always wavy and bent. Yet, a good approximation of the number could be potentially obtained using classical differential equations. It is finally worth mentioning that the interaction of CNT fibres with ambient conditions should not influence their emissivity, keeping it constant over years. Considering further the parameters of Equation 5 we may observe that the CNT fibres will have a larger lateral surface area for convective and radiative heat removal as compared to a round-shaped metal wire. For R = 5 μm radius fibre made of (10.10) nanotubes, the lateral surface will be approximately 60% larger than for a smooth round wire (see online Supplementary Materials for more details). The amount of convective heat removed per unit of time is also determined by a heat transfer coefficient α, which is dependent on many factors including the type of material, dimensions, and structure of a body, surrounding medium and its temperature/pressure etc.
Fig. 7. Theoretical structures of CNT fibres that could decrease skin effect. a) concentric rings of armchair and semiconducting nanotubes b) Litz-like wire with strands made of various types of armchair chiralities, c) or with insulated strands.
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Therefore, the calculations of this parameter are quite complicated. However, based on the experimental values found for CNT materials we may draw some initial conclusions. Coefficients measured for currently produced CNT fibres amounted to approx. 103 W /mK for fibre of approximately 40 μm diameter and 25–190 W /mK for 150–800 μm diameter [22,25]. The scaling with the diameter is well-expected and observed also for other materials. The convective heat coefficient observed for macro-scale copper amounts to 2–25 W /mK while for micro-wire of 40 μm diameter increases to 450 W /mK [22,26]. These values indicate that α could be larger than for copper. However, finding the theoretical values for ideally structured fibres will require further studies and calculations, as the internal structure of the fibre such as packing density was found to be a very important parameter in the experimental studies. Heat removal via conduction will need to be strongly based on the results of quantum transport calculations, as these will determine the ballistic length scales and potential limits of heat transfer between nanotubes which will define an overall thermal conductivity λ. Up to now the measurements of thermal conductivity of practical CNT fibres were not satisfactory, yet the values for doped fibres reached 635 W / mK [27]. Taking into account, that thermal conductivity of individual nanotubes was calculated to be even as high as 6600 W /mK we may expect that λ of an ideal fibre may be well above copper or aluminium [28]. Therefore, even the fact that cross-sectional area used for conduction will be decreased due to voids present in the fibre (e.g. for (10.10) fibre the share of pores will amount to approx. 40%), and the whole fibre will be a very porous material thanks to the efficient heat transport between nanotubes the overall heat removal should not suffer significantly. To summarize, we may well expect that the heat removal from CNT fibre should be much better than in case of copper or aluminium, which should ensure much higher current carrying capacity. Considering these electrically related thermal phenomena in the fibre, it is also worth mentioning that the temperature coefficient of resistivity of an ideal CNT fibre may differ from conventional metals, but its exact theoretical value, which for current fibres changes with morphology, would have to be calculated [29]. Finally, when considering the media surrounding the fibres it may be necessary to remember that the mechanism of carbon nanotube assembly thermal failure in air, is based on the rapid oxidation and does not involve any melting as in the case of metal, which may influence future current ratings for this material [30,31].
however, taking into account that the operation of copper in acidic environment is mostly impossible, a small permanent offset of conductivity in case of CNT fibres should be quite acceptable [36]. It is worth mentioning that at the current stage of fibre development, the doping of semiconducting or semi-metallic and defected nanotubes as well as their contacts in the fibre, can produce unexpectedly good results in terms of conductivity and specific conductivity [37–39]. It is possible that for the time being such an approach may suffice for practical applications, therefore is definitely worth exploring. Even more interesting may be a combination of carbon nanotube fibres with metals [40,41]. Unfortunately, these topics go well beyond the scope of this paper.
6. Doping
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Last but not the least to consider is the influence of environment on the electrical transport in CNT fibres. It is well known that copper and aluminium left in contact with oxygen undergo an oxidation of their surface layers. The oxides are fully insulating but passivate the surface thus preventing further in-depth oxidation. Unfortunately, when the metals are in contact with more harmful chemicals they may even fully dissolve such as in case of dipping in strong acids. Carbon, in contrast, is not structurally damaged by any of these factors at standard ambient conditions. Yet, it is a well-known adsorbent of many species such as oxygen, water vapour or acids that may, in turn, change the electronic properties by various mechanisms of doping [32–34]. In most cases these adsorbates were reported to p-dope nanotubes and increase their conductivity. However, as indicated by the simulations, armchair nanotubes should be the least prone to doping, therefore an ideal structure of fibre is one made fully of armchair SWNTs and this should ensure a lower fluctuation of conductivity upon contact with oxygen [35]. Also the ideal packing of nanotubes, described above, should decrease porosity, which normally facilitates adsorption. If needed additional protection could be provided by a simple insulation of the CNT wire. In the case of acids, it may be difficult to fully prevent doping,
7. Summary The discussion presented above is intended to capture the ultimate goals of research on carbon nanotube fibres, for use as electrical conductors. An in-depth analysis of the current issues indicates that, firstly, there may not be one ideal structure for the fibre, but it may depend on the application. Secondly, the performance of an ideal CNT fibre will differ from that of an individual nanotube considerably and so to predict it, an account needs to be taken of number of assembly-related phenomena. Moreover, the research on currently produced CNT fibres does not include enough about the performance which we should expect from these ultimate CNT fibres and a vast amount of theoretical work is still needed to predict their properties. Finally, the behaviour of even ideal CNT fibres will almost certainly differ considerably from any metallic conductors, therefore new standards will need to be introduced in order to operate them in existing or future electrical circuits. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.scriptamat.2016.11.027. Acknowledgements A.L.- R. T. G., L. K. and K.K.K. thank the European Research Council (under the Seventh Framework Program FP7/2007–2013, grant agreement 259061) for funding. K.K. is also grateful to the Royal Society for further financial support and A.L.-R. to National Centre for Research and Development, Poland for grant Lider VI (agreement number LIDER/220/L-6/14/NCBR/2015). References
Please cite this article as: A. Lekawa-Raus, et al., Electrical transport in carbon nanotube fibres, Scripta Materialia (2016), http://dx.doi.org/ 10.1016/j.scriptamat.2016.11.027
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Please cite this article as: A. Lekawa-Raus, et al., Electrical transport in carbon nanotube fibres, Scripta Materialia (2016), http://dx.doi.org/ 10.1016/j.scriptamat.2016.11.027