Keywords

Carbon nanotubes; mass production; high quality; theoretical analysis

1.1 General

In 1991, Iijima [1] reported his discovery of needle-like carbon nanotubes (CNTs) using an arc-discharge evaporation method in NEC corporation. Shortly thereafter, Iijima and Ichihashi [2] and Bethune et al. [3] separately reported the growth of single-walled CNTs (SWCNTs) which opened a fresh chapter on nanoscience and nanotechnology. CNTs were marked as one of the top ten advances in “Materials Today” [4]. From the viewpoint of chemical composition, CNTs are the simplest materials, having pure C–C atomic bonding configuration. Nevertheless, the simple covalently bonded carbon network leads to an extremely unique nanostructure and makes CNTs perhaps the most diverse and richest among nanomaterials in regard to structures and structure–property relations [5]. In the past two decades, CNTs have attracted intense interest due to their exceptional mechanical, chemical, electrical, and thermal properties along with specific low density, being regarded as promising for a broad range of potential applications. For example, SWCNTs have exhibited great electrical conductivity, closely related with their chirality, which allows the miniaturization of electronics. From the viewpoint of chemical composition, CNTs are the simplest materials, having a pure C–C atomic bonding configuration. Nevertheless, the simple covalently bonded carbon network leads to an extremely unique nanostructure and makes CNTs perhaps the most diverse and richest among nanomaterials in regard to structures and structure–property relations [5].

The molecular structure of an SWCNT is regarded as a seamless hollow cylindrical structure formed by rolling up a graphene along a (m, n) index which determines its diameter and chirality. An SWCNT is an ideal slender structure with ultrahigh aspect ratio, typically approximately 1.5 nm in diameters and up to dozens of micrometers in lengths. An individual SWCNT with an atomically monolayered surface and curved π-boding configuration can be either metallic or semiconducting, depending on its chirality (the chiral angle between hexagons and the tube axis) and diameter [6]. As far as SWCNTs are concerned, their band gaps can be relatively large (~0.5 eV) or small (~10 meV) even if they have nearly identical diameters (typical diameter of 1.5 nm) [5]. More interestingly, the band gap of the same-chirality semiconducting SWCNT is inversely proportional to its diameter. Such an intriguing character of an SWCNT strongly motivates worldwide efforts to study its fundamental nature and explore the potential application. For instance, various kinds of SWCNTs have been promising for advanced electrical interconnects on the basis of their low resistivity [7–10], high thermal conductivities (~3500 W/m/K), and current-carrying capacities (~10⁹ A/cm²) [11,12].

The covalently carbon hexagonal network creates an extremely stable structure. Arguably, CNTs are the strongest nanomaterial in nature. Elastic properties of CNTs have been measured by various means. Both experimental measurements and theoretical calculations reveal that the axial Young’s modulus of CNTs is typically in the range from 1 to 1.8 TPa [13–20], while the breaking strength of SWCNT bundles is up to 50 GPa [20,21], corresponding to ~50 times that of density-normalized strength of steel wires [17]. Simultaneously, various derived geometrical patterns of CNTs, such as rings [22,23], X-, T-, and Y-junctions [24,25], quantum dots [26], and crossing objects [27] also have been experimental observed. Such abovementioned geometrical shapes give rise to novel properties which are desirable for the successful application of SWCNTs to the design and manufacture of devices. What’s more, material properties of CNTs are greatly sensitive to chemical modification or atomic doping which suggests a promising remarkable application for brand-new quantum materials. Therefore, there are infinite possibilities in these kinds of CNTs.

In the past two decades, intensive theoretical and experimental efforts have been made in order to illuminate the effect of atomic structures on the electronic properties of CNTs [28–30]. CNTs can be synthesized by several means, such as arc-discharge, laser ablation, chemical vapor deposition (CVD) methods, and metallic and semiconducting CNTs have been found. As an ideal quasi-1D structure, metallic SWCNTs have been selected as model systems to explore the rich quantum phenomena, involving single-electron charging, Luttinger liquid, quantum interference, weak localization, and ballistic transport [28,29,31,32]. Besides, semiconducting CNTs have been utilized as novel building blocks in the field of nanoelectronics, such as transistors and logic, memory, and sensory devices [28–30].

The recently rapid development and great progress in the synthesis of CNTs have greatly facilitated CNTs characterizations and nanodevice exploitations. Conversely, the strong requirements of various aspects of fundamental research and practical application have been positively motivating synthetic methods in order to acquire more perfect materials. They are mutually complementary and promote each other. Nowadays, the synthesis of CNTs becomes more focused in consciously controlling the growth rather than, as previously, enabling growth. As mentioned, the electronic properties are extremely sensitive to the atomic structure of CNTs which has led to rich scientific research. However, it encounters a significant challenge to precisely control the CNT diameter and chirality for chemical synthesis methods. It is necessary to exquisitely control atomic arrangements along the CNTs in order to synthesize CNTs with predictable properties. In reality, it is the ultimate task for chemists in the CNT synthesis field.

Various approaches, such as arc-discharge, laser ablation, and CVD, have been mainly adopted to synthesize CNTs [33]. The first two approaches use solid-state carbon precursors to provide carbon sources for CNT growth and vaporize carbon at thousands of degrees Celsius. These methods are well established to produce high-quality and ideal CNT structures, in spite of a mass of by-products associated with them. Hydrocarbon gases are used to provide sources for carbon atoms, while metal catalyst particles are utilized as “seeds” for CNTs growth by means of CVD which takes place at relatively lower temperatures (500–1000°C) [33]. However, as far as SWCNTs synthesis is concerned, none of the abovementioned three synthesis methods are capable of yielding bulk materials with homogeneous diameter and chirality thus far. It is noteworthy that SWCNTs with impressively narrow diameter distributions averaging ~1.4 nm have been produced by arc-discharge and laser ablation techniques. By utilizing electrical transport and microscopy and spectroscopy measurement, CVD methods have experienced a long process from producing carbon fibers, filaments, and MWCNTs to synthesizing SWCNTs [33–39] with high crystallinity and perfection comparable to those of arc [40] and laser [41] materials.

1.2 Atomic Structure of CNTs

A graphene is a carbon-based repeated hexagonal cellular structure, in which each carbon atom is connected to three neighboring atoms. An SWCNT can be conceptualized as a three-dimensional seamless hollow cylindrical graphitic membrane, with a thickness of only one atom, by rolling up a graphene, while MWCNTs can be regarded as a form by rolling up multiple layers of graphene. The ends of CNTs can be either capped or not.

The chirality of an SWCNT is determined by the rolling direction $\tilde{\mathrm{\Gamma }}$ on the graphene (shown in Fig. 1.1). The chirality and diameter of an SWCNT can be characterized by a (n, m) index and thus chiral vector $\tilde{\mathrm{\Gamma }}$ is expressed by:

$\tilde{\mathrm{\Gamma }}=n{\tilde{\mathbf{a}}}_1+m{\tilde{\mathbf{a}}}_2,n\ge m$ (1.1)

(1.1)

where ${\tilde{\mathbf{a}}}_1$ and ${\tilde{\mathbf{a}}}_2$ are unit vectors in the graphene. The length of the chiral vector is $l=a\sqrt{n^2+m^2+nm}$ and the diameter is $l/\pi$, where $a=\sqrt{3}{l}_b$ with $l_b$ being the C–C bond length. The chiral angle θ is calculated by:

$\theta =\arctan \left(\frac{\sqrt{3}m}{2n+m}\right)$ (1.2)

(1.2)

CNTs can be classified into three categories according to the chirality. The chiral angle θ is 0 degrees when m=0 and 30 degrees when n=m, and these tubes are corresponding to zigzag and armchair, respectively. The others are chiral tube with a chiral angle 0 degree < θ < 30 degrees. The atomic structures of different kinds of SWCNTs are shown in Fig. 1.2A–C. Fig. 1.2D and E are the side view and top view of a DWCNT. It contains two layers of coaxial SWCNTs which correlate with each other by the weak vdW forces. The spacing between the outer and inner layers is determined by vdW force and approximately 0.34 nm slightly influenced by the total number of layers. Although graphene is always a semiconductor, CNTs can exhibit either metallic or semiconducting properties. The electrical properties are largely dependent on the chirality and diameter of CNTs [42–45]. In general, CNTs are semiconductive. Nevertheless, CNTs exhibit a metallic property when the (n, m) index satisfies $n-m=3I$, where I is an integer [45]. Note that different from other kinds of CNTs, armchair CNTs are always metallic. As illustrated in Fig. 1.3, circled dots are metallic CNTs, while small dots are semiconducting CNTs.

On the other hand, capped CNTs are regarded as elongated fullerenes, in which the walls of the tubes consist of cylindrical graphenes with their ends capped by fullerene hemispheres [1]. We can specify an SWCNT by bisecting a C₆₀ molecule at the equator and joining the two resulting hemispheres with a cylindrical tube one layer thick and of the same diameter as the C₆₀ molecule. If the C₆₀ molecule is bisected normal to a fivefold axis, an armchair nanotube is formed (see Fig. 1.4B), while if it is bisected normal to a threefold axis, then a zigzag nanotube is formed (see Fig. 1.4C) [46]. Armchair and zigzag CNTs with larger diameters and correspondingly larger caps can likewise be defined, as shown in Fig. 1.4B and C. In addition, a large number of capped chiral CNTs can be formed with a variety of hemispherical caps. A representative chiral CNT is shown in Fig. 1.4D.

1.3 General Development and Current Situation of CNTs in Nanoscience and Nanotechnology

In the mechanical properties testing of individual MWCNTs, an elastic modulus of ~1 TPa and a tensile strength of ~100 GPa, which is over 10-fold higher than any industrial fiber in nature, has been measured [47]. As far as the electrical properties are concerned, SWCNTs can be either metallic or semiconducting, relying on the their chirality, while MWCNTs are always metallic and can carry currents of up to 10⁹ A/cm² [48]. The thermal conductivity of an individual SWCNT can reach up to 3500 W/m/K at room temperature [11] which largely exceeds that of diamond (2000 W/m/K). Based on a more and more comprehensive understanding of CNTs, numerous potential applications have been proposed to full make use of their prominent superiority, including heat conductive and ultrahigh-strength composites, energy storage and conversion devices, sensors and high frequency oscillator, field emission displays and radiation sources, hydrogen storage media and drug encapsulation, nanometer-sized semiconductor devices and probes, interconnects, etc. So far, some of these applications have already been realized in products and others are still in the initial stage of exploring advanced devices.

So far, the low production output of CNTs has inhibited mass consumer products in spite of diverse potential applications reported to be utilizing CNTs. According to the statistics, CNT-related commercial activity has substantially and constantly increasingly grown during the past decade. The data demonstrates that the worldwide annual production capacity of CNTs has increased at least 10-fold in 2011, compared to that produced in 2006 [49]. Although there are more and more commercial suppliers of CNTs, such as BlueNano (USA), Chengdu Organic Chemical Co. Ltd. (China), Hyperion Catalysis (USA), NanoLab (USA), Nanocyl S.A. (Belgium), Southwest Nanotechnology Inc. (USA), Nanointegris (USA), Thomas & Swan Co. Ltd. (UK) and so on, it is still a serious challenge to meet the demand for CNTs. The main reason is that CNTs are too expensive, ranging from US$2.50 g⁻¹ for MWCNTs (NanoLab) to US$2500 g⁻¹ for SWCNTs (CNI) [50,51]. It is noted that since 2005 the low-cost production of CNTs were supplied by Cheap Tubes, Inc. [52] (US$275–300 g⁻¹ for 90% pure SWCNT), prices of high-quality CNTs have little changed in the past 10 years. The high cost is argued to be related to the low production capacity. Similar to the other high-value materials in history such as silicon wafers and aluminum, the price of CNTs is expected to drop to an acceptable level or even much lower with the improvement of manufacture technology and increment [53]. Tables 1.1–1.3 list the worldwide known industrial activity and commercial products.

1.4 Fundamental Properties and General Behaviors of CNTs

Many experiments have been conducted to excavate the intrinsic property of CNTs. These kinds of methods can provide intuitive knowledge of fundamental properties and general behaviors of CNTs. Pan et al. [54] produced a very long (approximately 2 mm) MWCNTs using pyrolysis of acetylene over iron/silica substrates method. In accordance with the theoretical prediction, Qin et al. [55] reported the possible smallest CNT with a diameter of 0.4 nm which is imprisoned inside an MWCNT. They found that these smallest CNTs are always metallic no matter what their helicities or chiralities are. Inspired by the good toughness of spider silk, Dalton et al. [56] spun 100 μm-long CNT fibers to make supercapacitors and wove them into textiles. They predicted these supercapacitors CNT textiles show promising to be applied in sensors, electronic interconnects, electromagnetic shields, antennas, and batteries. Dillon et al. [57] found that hydrogen was condensed to high density inside SWCNTs from temperature-programmed desorption spectroscopy. This suggests that CNTs have potential to be used in hydrogen-storage. Iijima and Ichihashi [2] synthesized single-shell tubes with diameters of approximately 1 nm in abundance. Ruoff et al. [58] exhibited flat morphology deformed by vdW forces between adjacent nanotubes and predicted this effect is observable. The experimental study of Dai et al. [59] showed the potential of CNTs to be used for SPM because of their flexibility and slenderness. As materials would exhibit unique properties owing to their morphologies, Ajayan and Tour [60] coaxed carbon atoms into several topologies to study their application in composite. Cumings et al. [61] successfully peeled and removed the outer layers at the end of MWCNTs to produce a sharpened structure. Under the help of an improved electric arc technique, Sun et al. [62] created a CNT with a diameter of 0.5 nm. Journet et al. [40] produced abundant SWCNTs using the electric-arc technique and suggested that the growth mechanism of SWCNTs was independent on the technique. Treacy et al. [18] measured the Young’s modulus of individual CNTs by transmission electron microscopy and found it could reach an order of terapascals. Odom et al. [63] reported the atomic structure and electronic properties of SWCNTs using scanning tunneling microscopy (STM), and suggested that SWCNTs exhibit different structures and the electronic properties of CNTs are dependent on diameter and helicity. Wildöer et al. [64] examined electronic properties of individual SWCNTs by STM and spectroscopy. Both metallic and semiconducting CNTs are observed and electronic properties are in fact dependent on wrapping angle. Falvo et al. [65] reported that MWCNTs could be repeatedly bent over large angles by means of AFM which confirms CNTs are remarkably flexible and resilient. Tsang et al. [66] opened CNTs at the end and filled them with a variety of metal oxides using wet chemical techniques. Lu [67] obtained an average Young’s modulus of approximately 1 TPa by testing a series of SWCNTs. The experimental results indicated that the modulus is insensitive to the tube’s radius and chirality. Wagner et al. [68] observed fragmentation in SWCNTs and obtained a tensile strength of 55 GPa. Walters et al. [21] conducted large elastic strain tests and applied a tensile load on the lateral wall in ropes of SWCNTs using an AFM. The elastic strains of the ropes were investigated when freely supported with tension proportional to lengthening. The results produced by elastic deformation for more than 10 cycles indicate that the maximum strain of SWCNTs ropes is 5.8% (±0.9%), which corresponds to a lower circumscription of 45 (±7) GPa for the tensile strength. Yu et al. [20] investigated the mechanical properties of 15 separate SWCNT bundles by applying a tensile load on the perimeter of each bundle. The results demonstrated that the average tensile strength of SWCNTs ranges from 13 to 52 GPa with the maximum tensile strain of 5.3%. Yu et al. [13] measured the mechanical properties of 19 individual MWCNTs by tensile loading. They found that the tensile strain of MWCNTs breaking is approximately 12%, corresponding to a tensile strength in the outermost layer ranging from 11 to 63 GPa. Li et al. [69] reported an average tensile strength of 22 GPa by measuring a resin-based SWCNT composite using the hypothesis of treating the interfacial load applied on the composite. Demczyk et al. [70] reported the results of pulling and bending tests on individual CNTs, demonstrating that the tensile strength of breaking a CNT is approximately 150 GPa. Considering the temperature effect on the mechanical properties of CNTs, Huang et al. [71] conducted large deformation tests of individual SWCNTs at high temperatures, demonstrating that they can undergo superplastic deformation. The CNTs can be lengthened by nearly 280% and narrowed 15 times before fracturing. These results are useful for the fabrication of composite materials and the toughening of ceramics at high temperatures. In addition, experimental studies of vibration characteristics of carbon nanostructures [72–75] show CNTs are good candidates as electromechanical oscillator and resonators.

1.5 Theories for Mechanical Behaviors of CNTs

The aforementioned experimental results show that CNTs have higher levels of stiffness and strength than other known structures. However, there is a broad discrepancy in these results on the stiffness and strength. This is mainly due to the very small size of CNTs. The variations reveal that, despite their visualization, experimental tools can provide only rough results and are limited to the study of certain mechanisms and lack universality. In addition, it is difficult to accurately conduct and control experiments when the specimen size reaches to the nanometer level. Therefore, strenuous efforts have been made by theoretical researchers in an effort to explore the inherent mechanisms underlying the mechanical behaviors of nanomaterials. Theoretical analysis is an accurate tool to investigate the material characteristics of these carbon nanostructures as it is easy to conduct and control the boundary conditions. In general, theoretical approaches mainly include three categories: atomistic simulations, continuum models, and hybrid approaches.