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Toroidal and Coiled Carbon Nanotubes

Written By

Lizhao Liu and Jijun Zhao

Submitted: 01 March 2012 Published: 09 May 2013

DOI: 10.5772/51125

From the Edited Volume

Syntheses and Applications of Carbon Nanotubes and Their Composites

Edited by Satoru Suzuki

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1. Introduction

The perfect graphite and carbon nanotube (CNT) are composed of hexagonal rings of carbon atoms. However, non-hexagonal rings like pentagons and heptagons usual exist in the realistic CNT. Due to the change of topology, different arrangements of the pentagons and heptagons would lead to various structures, such as CNTs with Stone-Wales defects [1], CNT junctions [2], toroidal CNTs [3], and coiled CNTs [4, 5]. Each type of these CNT-based structures has its unique physical and chemical properties; as a consequence, the diversity in morphology extends the applications of CNTs. In this chapter, we will review the current progress on two important members of the CNT family, i.e., the toroidal CNTs at the first and coiled CNTs in the second.

The toroidal CNT (also known as carbon nanotorus or carbon nanoring) is a kind of zero-dimensional CNT-based nanostructure. In other words, a carbon nanotorus can be considered as a giant molecule and directly used as a nanoscale device. As for the synthesis of the toroidal CNTs, numerous methods have been proposed, including laser-growth method, ultrasonic treatments, organic reactions, and chemical vapour deposition (CVD), which will be illustrated in the following. In addition to experimental synthesis, various theoretical efforts have been devoted to construct the structural models of the toroidal CNTs. In general, there are two kinds of toroidal CNTs: one is formed by pristine nanotube with pure hexagon networks, and the other contains certain amount of pentagon and heptagon defects. Due to the circular geometry of the carbon nanotorus and incorporation of pentagon/heptagon defects, it may exhibit novel mechanical, electronic and magnetic properties different from the straight CNTs.

Another kind of curved CNT-based nanostructure is the coiled CNT, which is also known as carbon nanocoil or carbon nanospring. Different from the zero-dimensional toroidal CNT, the coiled CNT is a kind of quasi one-dimensional CNT-based nanostructures with a certain spiral angle. Intuitionally, a carbon nanocoil is like a spring in geometry. Therefore, mechanic properties of the coiled CNTs attract lots of attentions. Among various methods to produce the coiled CNTs, CVD approach is predominant due to the high quality and good controllability. Besides, several methods have been proposed to build the structural models of the coiled CNTs. An important feature of the carbon nanocoil models is the periodic incorporation of pentagons and heptagons in the hexagonal network. In addition, due to the excellent properties of the coiled CNTs, they have promising applications in many fields, such as sensors, electromagnetic nano-transformers or nano-switches, and energy storage devices.


2. Toroidal CNTs

In this section, we summarize experimental fabrication and theoretical modelling of the toroidal CNTs, as well as their physical and chemical properties. The toroidal CNTs are predicted to be both thermodynamic and kinetically stable. Due to the circular geometry, the toroidal CNTs possess excellent properties, especially the electronic and magnetic properties.

2.1. Fabrication

Synthesis and characterization of the toroidal CNTs are of key importance in the carbon nanotorus related fields. Early in 1997, Liu et al. reported synthesis of the toroidal CNTs with typical diameters between 300 and 500 nm by using the laser growth method [3]. From the measurement of scanning force microscopy (SEM) and transmission electron microscopy (TEM), it was shown that the toroidal CNTs were form by single-walled carbon nanotube (SWNT) ropes consisting of 10 to 100 individual nanotubes. Soon after, the toroidal CNTs were also found in the CNT samples prepared by catalytically thermal decomposition of hydrocarbon gas [6] and an ultrasound-aided acid treatment [7, 8]. Later, a variety of experimental approaches were developed to fabricate carbon nanotori, such as organic reactions [9, 10], chemical vapor deposition (CVD) [11, 12], and depositing hydrocarbon films in Tokamak T-10, the facility for magnetic confinement of high-temperature plasma [13]. In addition, incomplete toroidal CNTs [13, 14], large toroidal CNTs with diameters of~200–300 nm, sealed tubular diameters of 50–100 nm [15], and patterning of toroidal CNTs [16, 17] were also achieved in laboratory. In particular, the tubular diameter of a carbon nanotorus is now controllable. Toroidal CNTs from single-walled [7-10, 18, 19], double-walled [20], triple-walled [21], and multi-walled CNTs [6] have been achieved. Combining the experimental measurements and a simple continuum elastic model, formation of the toroidal CNTs was supposed to involve a balance between the tube-tube van der Waals adhesion, the strain energy resulting from the coiling-induced curvature and the strong interaction with the substrate [8, 14]. Various kinds of the toroidal CNTs are presented in Figure 1.

Figure 1.

Experimental fabrications of various kinds of toroidal CNTs.

2.2. Structural models and thermodynamic stabilities

Prior to the experimental synthesis, Dunlap proposed to construct the structural model of a carbon nanotorus by connecting two CNTs with different diameters [22]. Almost at the same time, researchers in Japan built a C360 nanotorus from C60 fullerene [23] and then generated a series of toroidal CNTs with 120 to 1920 carbon atoms using the prescription of Goldberg [24, 25]. So far, there have been six major approaches to construct the structural models of toroidal CNTs: (1) bending a finite CNT and connecting its ends together [26-29]; (2) connecting CNTs with different diameters by introducing pentagons and heptagons [22, 30-32]; (3) constructing from fullerenes [23-25] by employing the prescription of Goldberg [33]; (4) built through the connection of one zigzag-edged chain of hexagons and another armchair-edged chain of hexagons [34]; (5) sewing the walls of a double-walled CNT at both ends [35]; (6) constructing from only pentagons and heptagons [36]. To summarize, there are two kinds of toroidal CNTs: one is formed by pure hexagonal networks and the other is a hexagonal structure with pentagon-heptagon defects. In a more detailed way, Itoh et al. classified the toroidal CNTs into five types using the parameters of the inner (ri) and outer (ro) diameters, and the height (h) [37]. As depicted in Figure 2, type (A) indicates a nanotorus with ri ≈ ro, h << ri, and h ≈ (ro - ri), type (B) is the case of ri ~ ro ~h and h ≈ (ro̶ri), type (C) denotes h << (ro̶ ri), type (D) is the case of ri< ro, ro ~ h, and h ~ (ro̶ ri), and type (E) means (ro̶ ri) << h, respectively.

After establishing the structural models, one important issue is to examine the thermodynamic stabilities of the toroidal CNTs. Many groups demonstrated that toroidal CNTs are more stable than C60 fullerene through comparing their binding/cohesive energies calculated by means of empirical potential methods [22-25]. Besides, molecular dynamics (MD) simulations also demonstrated that toroidal CNTs can survive under high temperature [23, 29, 38, 39]. Generally, the thermodynamic stability of a carbon nanotorus depends on its geometric parameters, such as ring and tubular diameter, symmetry, curvature, and position of the pentagons and heptagons. Ihara et al. showed that the cohesive energy of a carbon nanotorus derived from C60 fullerene decreased with increasing number of carbon atoms in the carbon nanotorus [24]. The ring and tubular diameter can also affect the thermodynamic stability of a carbon nanotorus [40-42]. At a fixed tubular diameter, there was a preferable ring diameter where the nanotorus possesses the lowest formation energy [40]. Besides, dependence of the stability on the rotational symmetry was also reported for the toroidal CNTs [32, 37]. Among the toroidal CNTs constructed from (5, 5), (6, 6), and (7, 7) armchair CNTs, the one with D6h symmetry is energetically favourable [32]. Despite the dependence on the geometric details, it was believed [43, 44] that for the toroidal CNTs with large ring diameters, the pure hexagonal structure is energetically more stable, but for the ones with small ring diameters, the mixture of hexagonal networks and pentagon-heptagon defects is energetically more favourable. In [44], this critical ring diameter is given by the equation Rc = πr2Y/(4σ), where r is the tubular diameter of the initial CNT, Y is the Young’s modulus of the initial CNT, and σ is the surface tension of graphite perpendicular to the basal planes. For example, taking the Y = 1.0 TPa, a Rc of 90 nm can be obtained for a carbon nanotorus made of a (10,10) nanotube (r = 0.68 nm).

Figure 2.

Schematic diagram for five types of toroidal CNTs classified by the parameters of the inner diameter ri, the outer diameter ro, and the height h, respectively. Reprinted with permission from [37]. Copyright (1995) Elsevier.

2.3. Mechanical properties

Mechanical property is of fundamental importance for the applications of a material. Employing MD simulation with a reactive force field, Chen et al. investigated the mechanical properties of zero-dimensional nanotorus, one-dimensional nanochain and two-dimensional nanomaile constructed from toroidal CNTs [45]. For a nanotorus constructed from bending a (5, 5) CNT, its Young’s modulus increases monotonically with tensile strain from 19.43 to 121.94 GPa without any side constraints and from 124.98 GPa to 1560 GPa with side constraints, respectively, where the side constraint means fixing the position of small regions of carbon atoms at left and right sides. Besides, the tensile strength of the unconstrained and constrained nanotorus was estimated to be 5.72 and 8.52 GPa, respectively. In addition, the maximum elastic strain is approximate 39% for the nanochain and 25.2% for thenanomaile. For a nanotorus obtained from bending a (10, 10) CNT, its Young’s modulus along the tube axis was 913 GPa by taking [46]. Later, buckling behavior of toroidal CNTs under tension was investigated using the molecular mechanics (MM) computations, including the toroidal CNTs formed from (5, 5), (8, 8) and (9, 0) CNTs [47, 48]. It was found that the buckling shapes of the toroidal CNTs constructed from both armchair and zigzag CNTs with an odd number of units are unsymmetrical, whereas those with an even number of units are symmetrical. Recently, reversible elastic transformation between the circular and compressed nanotorus in a colloid has been observed under TEM [17]. This geometric reversibility was also predicted theoretically by using a nonlinear continuum elastic model [49, 50], suggesting the potential application of toroidal CNTs as ultrasensitive force sensors and flexible and stretchable nanodevices.

2.4. Electronic properties

It is well-known that a CNT can be expressed by a chiral vector Ch (n, m) and a translation vector T (p, q) and can be either metallic or semiconducting, depending on its chirality [51]. Since a carbon nanotorus can be considered as a bended CNT or a CNT incorporated with pentagons and heptagons, it would be interesting to explore will the bending behavior or inclusion of pentagons and heptagons affect the electronic properties of the pristine CNT. For a carbon nanotorus formed by bending a (n, m) CNT, it can be divided into three types: (1) if m ‒ n = 3i, and p ‒ q = 3i (i is an integral), the carbon nanotorus is metallic; (2) if m ‒ n = 3i, and p ‒ q ≠ 3i, the carbon nanotorus is semiconducting; (3) if m ‒ n ≠ 3i, and p ‒ q = 3i, the carbon nanotorus is insulating [52]. This classification was partly confirmed by the tight-binding (TB) calculation that a metallic carbon nanotorus can be constructed by bending a metallic CNT and also follows the rule of divisibility by three on the indices of chiral and twisting vectors [53]. Moreover, delocalized and localized deformations play different roles on the electronic properties of a carbon nanotorus built bending a CNT [27]. The delocalized deformations only slightly reduce the electrical conductance, while the localized deformations will dramatically lower the conductance even at relatively small bending angles. Here the delocalized deformation means the deformation induced by the mechanical bending of the CNT, and the localized deformation indicates the deformation induced by the pushing action of the tip of AFM. In addition, Liu et al. reported the oscillation behavior of the energy gap during increasing size of the nanotorus and the gap was eventually converged to that of the infinite CNT [54].

Meanwhile, in the case of incorporation of pentagons and heptagons, a HOMO-LUMO gap can be expected for the carbon nanotorus. For a carbon nanotorus C1960 constructed by connecting (6, 6) and (10, 0) CNTs, a gap of 0.05 eV was calculated by a TB approach [44]. Using both the TB and semiempirical quantum chemical approaches, a series of toroidal CNTs with total number of atoms ranging from 120 to 768 were investigated and most of them have HOMO-LUMO gaps [55]. Besides, employing the extended-Hückel method, energy gaps of 0.4-0.32µB eV were predicted for the toroidal CNTs of C170, C250, C360, C520, and C750 [56]. Further accurate DFT examination also showed that the nanotorus C444 has a gap of 0.079 eV and the nanotorus C672 has a gap of 0.063 eV, respectively [57].

2.5. Magnetic properties

The unique circular geometry endows its advantage to study the magnetic response when ring current flows in a carbon nanotorus. Early in 1997, Haddon predicted that the nanotorus C576 has an extremely large and anisotropic ring-current diamagnetic susceptibility, which can be 130 times larger than that of the benzene molecule [58]. Afterwards, colossal paramagnetic moment was also reported in the metallic toroidal CNTs, which was generated by the interplay between the toroidal geometry and the ballistic motion of the π-electrons [28], as shown in Figure 3. For example, the nanotorus C1500 built from a (5, 5) CNT possesses a large paramagnetic moment of 88.4 µB at 0 K. Similarly, the nanotorus C1860 built from a (7, 4) CNT has a giant zore-temperature magnetic moment of 98.5 µB. In addition to the paramagnetic moments, existence of ferromagnetic moments at low temperatures in the toroidal CNTs without heteroatoms was also predicted by using a π-orbital nearest-neighbor TB Hamiltonian with the London approximation, which is attributed to the presence of pentagons and heptagons [59]. Another important phenomenon, i.e., the Aharonov–Bohm effect can be also observed in the toroidal CNTs [60-64]. Indeed, the magnetic properties of the toroidal CNTs are affected by many factors. Liu et al. pointed out that the paramagnetic moments of the toroidal CNTs decrease distinctly as temperature increases [28]. Such temperature dependence was also confirmed by several successive studies [65-68]. Moreover, the magnetic properties of a toroidal CNT also rely on its geometric parameters, such as ring diameter, curvature, chirality, and the arrangement of pentagons and heptagons [65-67].

Figure 3.

Induced magnetic moment as a function of temperature for various toroidal CNTs in a perpendicular magnetic field of 0.1 T (solid line) and 0.2 T (dashed line), respectively. Reprinted figures with permission from [Liu L, Guo GY, Jayanthi CS, Wu SY. Colossal Paramagnetic Moments in Metallic Carbon Nanotori. 88, 217206 (2002)]. Copyright (2002) by the American Physical Society.

2.6. Modification of the toroidal CNTs

Chemical modification is an important approach to tailor the properties of materials. A common approach of chemical modification is doping. It was found that doping electrons or holes into a carbon nanotorus could vary its magnetic properties through altering the band-filling configuration [69]. Our previous work also demonstrated that substitutional doping of boron or nitrogen atoms could modify the electronic properties of the toroidal CNTs due to change of the six π-electron orbitals [32]. Moreover, compared with the hexagonal rings, existence of pentagons favours the doping of nitrogen atoms and existence of heptagons prefers the doping of boron atoms. Besides, the toroidal CNTs coated with beryllium can be used as candidates for hydrogen storage. Each beryllium atom can adsorb three H2 molecules with moderate adsorption energy of 0.2-03 eV/H2 [70].

Since the toroidal CNTs also have the hollow tubular structures similar to the CNTs, atoms or molecules can be encapsulated into the toroidal CNTs. Early in 2007, Hilder et al. examined the motion of a single offset atom and a C60 fullerene inside a carbon nanotorus to explore its application as high frequency nanoscale oscillator [71]. They demonstrated that the C60 fullerene encapsulated carbon nanotorus can create high frequency up to 150 GHz, which may be controlled by changing the orbiting position. By inserting the chains of Fe, Au, and Cu atoms into a carbon nanotorus, Lusk et al. investigated the geometry, stability and electronic magnetic properties of this nano-composite structure [72]. Reduced HOMO-LUMO gap and ferromagnetism of the nanotorus were predicted by encapsulating chains of metal atoms. In addition, diffusion behavior of water molecules forming two oppositely polarized chains in a carbon nanotorus was studied by MD simulations. It was demonstrated that Fickian diffusion is in the case of a single chain and the diffusion for two or more chains is consistent with single-file diffusion [73].


3. Coiled carbon nanotube

Similar to the case of the toroidal CNTs, we first introduce the experimental synthesis and theoretical methods to construct the structural models, as well as their formation mechanism and stabilities. Then the mechanic properties and electronic properties of the coiled CNTs are summarized. Finally, the promising applications of coiled CNTs in various fields compared with their straight counterparts owing to their spiral geometry and excellent properties will be discussed in the end of this section.

3.1. Fabrication and formation mechanism

The coiled CNTs were first experimentally produced through catalytic decomposition of acetylene over silica-supported Co catalyst at 700 °C in 1994 [4, 5]. Afterwards, numerous methods have been proposed to synthesize the coiled CNTs, including the laser evaporation of the fullerene/Ni particle mixture in vacuum [74], opposed flow flame combustion of the fuel and the oxidizer streams [75], electrolysis of graphite in fused NaCl at 810 °C [76], self-assembly from π-conjugated building blocks [77, 78], and CVD method [79-83]. Among these various methods, the CVD approach is predominant due to its high quality, which has been reviewed by several literatures [84-86]. To fabricate the coiled CNTs, CVD process involves the pyrolysis of a hydrocarbon (e.g. methane, acetylene, benzene, propane) over transition-metal catalysts (e.g. Fe, Co, Ni) at high temperatures. Compared to the high growth temperature (> 2000 °C) of CNT through arc discharge and laser evaporation process, the relatively low growth temperature of CVD method (500–1000 °C) allows carbon atoms move slowly and form non-hexagonal carbon rings [84]. In 2006, Lau et al. reviewed the three major CVD-based methods to fabricate the coiled CNTs, including the catalyst supported CVD growth, on substrate CVD growth and template-based CVD growth [84]. Later, synthetic parameters of CVD growth of the coiled CNTs, such as catalyst, gas atmosphere and temperature, were introduced and catalogued by Fejes et al. [85] and Shaikjee et al. [86], respectively. Moreover, Shaikjee et al. [86] presented different types of the coiled CNTs with non-linear morphology, which are shown in Figure 4.

Figure 4.

Experimental fabrications of various kinds of the coiled CNTs. Reprinted with permission from [86]. Copyright (2011) Elsevier.

As for the formation mechanism of the coiled CNTs, Fonseca et al. presented a formation of (chiral and achiral) knees on a catalyst particle to further form toroidal and coiled CNTs, which can be described by a simple formalism using the heptagon-pentagon construction [87]. In addition, formation of the coiled CNTs is closely related to the catalyst. Pan et al. suggested that the catalyst grain is crucial to the geometry of a carbon nanocoil and the nonuniformity of carbon extrusion speed in the different parts of the catalyst grain leads to the helical growth of the coiled CNTs [88]. Chen et al. pointed out that the driving force of coiling straight CNTs was the strong catalytic anisotropy of carbon deposition between different crystal faces [89]. For growth of carbon microcoils, the catalyst grain rotates around the coil axis which is on the symmetric face of the deposition faces; while for the twisted carbon nanocoils, the catalyst grain rotates around the axis which is perpendicular to the symmetric face of the deposition faces. Taking both the energy and entropy into account, Bandaru et al. proposed a mechanism that for a given volume of material, the helical form occupies the least amount of space and the entropy of the ambient conditions should increase to compensate for the close packing of the helices, which in turn is facilitated by nonwetting catalyst particles or induced by catalyst/ambient agitation in the CVD growth [90].

3.2. Structural models and thermodynamic stabilities

An important feature of a carbon nanocoil is incorporation of pentagons and heptagons in the hexagonal network. Dunlap [22, 91] showed that connecting two CNTs with pentagons and heptagons could result in a curved structure or knee structure. Based on the knee structure, Fonseca et al. was able to construct the toroidal and coiled CNTs using the knee segments as building blocks, where the former is an in-plane structure and the latter is out of plane [92]. In addition, researchers in Japan proposed two kinds of methods to construct structures of the coiled CNTs. One approach is to cut the toroidal CNTs into small pieces and recombine them to form the coiled CNTs with one pitch containing one nanotorus [37, 93]. For the coiled CNTs built from toroidal segments, Setton et al. suggested that the toroidal segments were only feasible for single-shell or at best two-shell nanocoils [94]. The other way is to insert pentagons and heptagons into a perfect graphene network and then roll up this structure to form a carbon nanocoil [95, 96]. Similarly, Birό et al. proposed to build the coiled CNTs from rolling up the Haeckelite structure, a graphite sheet composed of polygonal rings [97]. Recently, we were able to construct the carbon nanocoils from segment of CNTs in which the tube chirality is maintained [98]. Through introducing a pair of pentagons in the outer side and another pair of heptagons in the inner side into the segment of an armchair CNT, a curved structure can be obtained. Using this curved structure as a building block, a carbon nanocoil can be formed by connecting the building blocks with a rotate angle. This method was also employed to construct the structural models of the toroidal CNTs, as mentioned above [32]. A simple schematic diagram of this method is presented in Figure 5. Usually, a carbon nanocoil can be expressed by the parameters of inner coil diameter (Di), outer coil diameter (Do), tubular diameter (Dt) and coil pitch (λ) [84, 86], as illustrated in Figure 6.

In addition to the structural models of the coiled CNTs, several works have been devoted to investigating their thermodynamic stabilities. Employing MD simulation, Ihara et al. [93] obtained the cohesive energies of 7.41, 7.39 and 7.43 eV/atom for C360, C540 and C1080 nanocoils, respectively, which are close to that of graphite sheet (7.44 eV/atom) and lower than that of the C60 fullerene (7.29 eV/atom). Therefore, these carbon nanocoils are more stable than C60 fullerene. Moreover, these carbon nanocoils can maintain the coiled geometry without collapse at a temperature up to 1500 K, which further confirms their thermodynamical stability. By taking into account the volume free energy, the surface energy, and the curvature elastic energy, it was found that there is a threshold condition for the formation of straight multiwall CNTs [99]. Below that the straight multiwall CNTs become unstable and would undergo a shape deformation to form the coiled CNTs.

Figure 5.

Schematic diagram for constructing the structural models of (6, 6) carbon nanotorus and nanocoil by introducing pairs of pentagons (highlighted in blue) and heptagons (highlighted in red).

Figure 6.

Parameters of inner coil diameter Di, outer coil diameter Do, tubular diameter Dt and coil pitch λ to describe a carbon nanocoil.

3.3. Mechanical properties

Intuitively, a carbon nanocoil is similar to a spring in geometry. It is well-known that spring exhibits excellent mechanic properties and is very useful in the mechanics-based devices. Therefore, mechanical properties of the coiled CNTs as “nanospring” have attracted lots of attentions. Early in 2000, Volodin et al. measured the elastic properties of the coiled CNTs with atomic force microscopy (AFM) and showed that the coiled CNTs with coil diameters (> 170 nm) possess high Young’s modulus of 0.4–0.9 TPa [100]. Using a manipulator-equipped SEM, Hayashida reported the Young’s modulus of 0.04–0.13 TPa and the elastic spring constants of 0.01–0.6 N/m for the coiled CNTs with coil diameters ranging from 144 to 830 nm [101]. Remarkable spring-like behavior of an individual carbon nanocoil has been demonstrated by Chen et al. [102], as presented in Figure 7. A spring constant of 0.12 N/m in the low-strain regime and a maximum elastic elongation of 33% were obtained from AFM measurement. In contrast to the high measured Young’s modulus, the shear modulus of the coiled CNTs is extremely low. Chen et al. [102] considered the coiled CNTs with a Do of ~126±4 nm but different Di. For the case of Di = 3/4 Do, a shear modulus of ~2.5±0.4 GPa was estimated; if Di = 1/2 Do, the corresponding shear modulus was ~2.3±0.4 GPa; and if Di = 0, a shear modulus of ~2.1±0.3 GPa can be obtained. Afterwards, Huang [103] studied the coiled CNTs under uniaxial tension in simple explicit expressions and obtained a maximum elastic elongation of ~30%, a shear modulus of 2.8–3.4 GPa and a spring constant of ~0.1–0.4 N/m for the double nanocoils formed by twisting two single nanocoils, which is comparable to the experimental result [102]. Later, Chang et al. reported a shear modulus of 3±0.2 GPa for the double coiled CNTs [104]. In addition, Poggi et al. demonstrated the compression behavior of the coiled CNTs and presented that repeated compression/buckling/decompression of the nanocoil was very reproducible with a limiting compression of 400 nm [105].

Figure 7.

Measurement of the mechanical properties of a carbon nanocoil using the AFM cantilevers: (b) the initial state, (c) at a tensile strain of 20%, and (d) at a tensile strain of 33%. Reprinted with permission from [102]. Copyright (2003) American Chemical Society.

In addition to the experimental measurements, numerous theoretical simulations were carried out to investigate the mechanical properties of the coiled CNTs. Using the Kirchhoff rod model, Fonseca et al. derived a series of expressions to obtain the Young’s modulus and Poisson’s ratios for the coiled CNTs. Taking the parameters for the carbon nanocoil reported by Chen et al. [102], Fonseca et al. estimated the Young’s modulus of 6.88 GPa for a nanocoil with a coil diameter of 120 nm, a Poisson’s ratio of 0.27 and a shear modulus of 2.5 GPa [106, 107]. Besides, equations were derived to calculate the elastic constants of the forests of the coiled CNTs, which shows that the entanglement among neighboring nanocoils will contribute to the mechanical properties of the nanocoil forests [108]. Employing the DFT and TB calculations, we computed the Young’s modulus and elastic constant of a series of single-walled carbon nanocoils built from the armchair CNTs [98]. The Young’s modulus ranges from 3.43 to 5.40 GPa, in good agreement with the Fonseca’s reports [106, 107] and the elastic constant lies between 15.37 to 44.36 N/m, higher than the experimental values [100, 102]. Furthermore, superelastic behavior of the coiled CNTs was also predicted from our computations where the coiled CNTs can undertake an elastically tensile strain up to ~60% and compressive strain up to ~20–35%. Such superelasticity is due to the invariance of bond length under strain associated with the strong covalent C-C bonding. In a recent computation on the mechanic properties of the single-walled carbon nanocoils using the finite element ANSYS code, spring constants ranging from 15–30 N/m were obtained for the armchair carbon nanocoils with different tubular diameters [109]. As the tubular diameter increases, the spring constant increases accordingly. Generally speaking, the calculated Young’s modulus and elastic constants for the coiled CNTs are more or less different from that of the experimental measurements. This difference may be attributed to the structural details of the synthesized carbon nanocoils, especially the larger sizes of experimental nanocoil samples.

3.4. Electronic and transport properties

Similar to the toroidal CNTs, pentagons and heptagons exist in the coiled CNTs, which may lead to different electric properties with regard to that of the pristine CNTs. Using the two and four probes methods, Kaneto et al. measured the electric conductivity of the micro carbon nanocoils, which lies in 30–100 S/cm [110]. Later, it was found that for a carbon nanocoil with a coil diameter of 196 nm and a length of 1.5 mm, the conductivity is about 180 S/cm [101], which is much smaller than a straight CNT (~104 S/cm) [111]. Recently, Chiu et al. reported a very high conductivity of 2500 S/cm and an electron hopping length of ~5 nm for the single carbon nanocoils measured at low temperature [112]. An even higher electron hopping length of 5–50 nm was predicted by Tang et al. [113]. Moreover, the temperature dependence of the electric resistance was also observed where resistivity of the carbon nanocoil decreases as the annealing temperature increases [114]. Therefore, the measured electric properties of the coiled CNTs are closely related to the temperature and details of the samples.

Theoretically, employing a simple TB model, Akagi et al. [95, 96] calculated the band structures and electron density of states of the carbon nanocoils and suggested that the coiled CNTs could be metallic, semiconducting and semimetallic, depending on the arrangement of the pentagons and heptagons. Compared with the pristine CNTs, the semimetal property is unique for the carbon nanocoil [96]. Recently, we investigated the electric conductance of a series of armchair carbon nanocoils through using a π-orbital TB model combined with the Green’s function approach [115]. Using the metallic armchair CNTs as the electrodes, we calculated the quantum conductance of the (5, 5), (6, 6) and (7, 7) carbon nanocoils, as presented in Figure 8. Clearly, there is a transport gap in the conductance spectrum. Further analysis of the electronic states indicates that only incorporation of pentagons and heptagons (such as Stone-Wales defects) can not lead to gap opening, and thus creation of the band gap should be attributed to the existence of sp3 C-C bonds caused by coiling the CNTs. In addition, change of quantum conductance for the armchair carbon nanocoils under uniaxial elongation or compression is not distinct due to the nearly invariant bond length under strain, i.e. superelasticity [98].

Figure 8.

Structural model to calculate conductance of the (5, 5) carbon nanocoil (a) and conductance of the (5, 5), (6, 6) and (7, 7) carbon nanocoils (b). Reprinted with permission from [115]. Copyright (2011) Science China Press and Springer-Verlag Berlin Heidelberg.

3.5. Applications

Owing to the spiral geometry and unusual properties, the coiled CNTs have promising applications in various fields compared with their straight counterparts [84-86, 116]. One important application of the carbon nanocoils is to act as the sensors. In 2004, Volodin et al. [117] reported the use of coiled nanotubes as self-sensing mechanical resonators, which is able to detect fundamental resonances ranging from 100 to 400 MHz, as illustrated in Figure 9. The self-sensing carbon nanocoil sensors are sensitive to mass change and well suited for measuring small forces and masses in the femtogram range. After measuring the mechanical response of the coiled CNTs under compression using AFM, Poggi et al. pointed out that a nonlinear response of the carbon nanocoil can be observed, which is associated with compression and buckling of the nanocoil [105]. Bell et al. demonstrated that the coiled CNTs can be used as high-resolution force sensors in conjunction with visual displacement measurement as well as electromechanical sensors due to the piezoresistive behavior without an additional metal layer [118]. Besides, the applications of carbon nanocoils as magnetic sensors [119], tactile sensors [120], and gas sensors [121] were also exploited.

Another kind of major applications of the carbon nanocoils is to form composites with other materials. It was found that incorporation of carbon nanocoils in epoxy nanocomposites can enhance the mechanic properties of the epoxy nanocomposites [122-125]. Besides, the coiled CNT/silicone–rubber composites show high resistive sensitivity, relying on the density of the carbon nanocoil [126, 127]. In addition, metal-coated carbon nanocoils can also display some properties different from the pristine coiled CNTs. Tungsten-containing carbon nanocoils can expand and contract as flexibly as macro-scale springs and the elastic constants of the tungsten-containing carbon nanocoils rises along with increasing content of tungsten [128]. Bi et al. [129] found that the coiled CNTs coated with Ni have enhanced microwave absorption than the uncoated ones, which is results from stronger dielectric and magnetic losses.

Figure 9.

The carbon nanocoil to act as a mechanical resonator: (a) AFM image of the carbon nanocoil, (b) circuit contains two broad-band radio frequency transformers and the carbon nanocoil, and (c) resonant response of the carbon nanocoil device to electromechanical excitation. Reprinted with permission from [117]. Copyright (2004) American Chemical Society.

In addition, field emission [79, 130], energy storage [131, 132] and biological applications [133] of the coiled CNTs were also reported. Nowadays, the coiled CNT have been used as sensors [117-121], flat panel field emission display [79], microwave absorbers [134] and additives in the cosmetic industry [86].


4. Conclusion

Experimental fabrication and theoretical modelling of the toroidal and coiled CNTs were reviewed in this chapter. Compared with the pristine CNTs, the zero-dimensional toroidal CNTs exhibit excellent electromagnetic properties, such as persistent current and Aharonov–Bohm effect. Moreover, electronic properties of the toroidal CNTs can be tuned by chemical modification. In contrast to the toroidal CNTs, the coiled CNTs are quasi one-dimensional CNT-based nanostructures. Due to the spring-like geometry, the coiled CNTs possess fascinating mechanical properties, which are known as superelastic properties. This superelasticity allows the carbon nanocoils to act as electromechanical, electromagnetic, and chemical sensors. In addition, the coiled CNTs have been used commercially to fabricate flat panel field emission display, microwave absorbers and cosmetics.

As mentioned above, the toroidal CNTs synthesized experimentally are usually formed by the bundle of single-walled CNTs and have large ring diameters. Therefore, fabrications of the single-walled toroidal CNTs, as well as the toroidal CNTs of controllable ring diameters, are great challenges. Moreover, achievement of inserting atoms/molecules into the toroidal CNTs is another key issue under solution. On the other hand, since the formation mechanism of the coiled CNTs depends closely on the catalysts, searching for the optimal catalysts is significant for the quality and quantity of the nanocoil samples. Besides, finding appropriate geometry and concentration of the coiled CNTs is also necessary to improve performance of nanocomposites with the carbon nanocoils. Further experimental and theoretical works are expected to carry out to solve these problems.



This work was supported by the National Natural Science Foundation of China (No. 11174045, No. 11134005).


  1. 1. hang P. Lammert P. E. Crespi V. H. 1998 Plastic Deformations of Carbon Nanotubes Physical Review Letters 81 24 5346 5349
  2. 2. Yao Z. Postma H. W. C. Balents L. Dekker C. 1999 Carbon nanotube intramolecular junctions Nature 402 6759 273 276
  3. 3. Liu J. Dai H. J. Hafner J. H. Colbert D. T. Smalley R. E. Tans S. J. Dekker C. 1997 Fullerene’crop circles. Nature 385 6619 780 781
  4. 4. Amelinckx S. Zhang X. B. Bernaerts D. Zhang X. F. Ivanov V. Nagy J. B. 1994 A Formation Mechanism for Catalytically Grown Helix-Shaped Graphite Nanotubes. Science 265 5172 635 639
  5. 5. Zhang X. B. Zhang X. F. Bernaerts D. Tendeloo G. v. Amelinckx S. Landuyt J. v. Ivanov V. Nagy J. B. Ph L. Lucas A. A. 1994 The Texture of Catalytically Grown Coil-Shaped Carbon Nanotubules. Europhysics Letters 27 2 141 146
  6. 6. Ahlskog M. Seynaeve E. Vullers R. J. M. Van Haesendonck C. Fonseca A. Hernadi K. B. Nagy J. 1999 Ring formations from catalytically synthesized carbon nanotubes. Chemical Physics Letters 202
  7. 7. Martel R. Shea H. R. Avouris P. 1999 Rings of single-walled carbon nanotubes. Nature 398 6725 299 299
  8. 8. Martel R. Shea H. R. Avouris P. 1999 Ring Formation in Single-Wall Carbon Nanotubes The Journal of Physical Chemistry B 103 36 7551 7556
  9. 9. Sano M. Kamino A. Okamura J. Shinkai S. 2001 Ring Closure of Carbon Nanotubes. Science 293 5533 1299 1301
  10. 10. Geng J. Ko Y. K. Youn S. C. Kim Y. H. Kim S. A. Jung D. H. Jung H. T. 2008 Synthesis of SWNT Rings by Noncovalent Hybridization of Porphyrins and Single-Walled Carbon Nanotubes. The Journal of Physical Chemistry C 112 32 12264 12271
  11. 11. Song L. Ci L. J. Sun L. F. Jin C. Liu L. Ma Liu W. Zhao D. Luo X. Zhang S. Xiang Z. Zhou Y. Zhou J. Ding W. Wang Y. Z. L. Xie S. 2006 Large-Scale Synthesis of Rings of Bundled Single-Walled Carbon Nanotubes by Floating Chemical Vapor Deposition. Advanced Materials 18 14 1817 1821
  12. 12. Zhou Z. Wan D. Bai Y. Dou X. Song L. Zhou W. Mo Y. Xie S. 2006 Ring formation from the direct floating catalytic chemical vapor deposition. Physica E: Low-dimensional Systems and Nanostructures 33 1 24 27
  13. 13. Kukushkin A. B. Neverov V. S. Marusov N. L. Semenov I. B. Kolbasov B. N. Voloshinov V. V. Afanasiev A. P. Tarasov A. S. Stankevich V. G. Svechnikov N. Y. Veligzhanin A. A. Zubavichus Y. V. Chernozatonskii L. A. 2011 Few-nanometer-wide carbon toroids in the hydrocarbon films deposited in tokamak T-10. Chemical Physics Letters 265 268
  14. 14. Wang X. Wang Z. Liu Yq. Wang C. Bai C. Zhu D. 2001 Ring formation and fracture of a carbon nanotube Chemical Physics Letters 339 1-2 36 40
  15. 15. Lyn M. E. He J. Koplitz B. 2005 Laser-induced production of large carbon-based toroids. Applied Surface Science 246 1-3 44 47
  16. 16. Motavas S. Omrane B. Papadopoulos C. 2009 Large-Area Patterning of Carbon Nanotube Ring Arrays. Langmuir 25 8 4655 4658
  17. 17. Chen L. Wang H. Xu J. Shen X. Yao L. Zhu L. Zeng Z. Zhang H. Chen H. 2011 Controlling Reversible Elastic Deformation of Carbon Nanotube Rings. Journal of the American Chemical Society 133 25 9654 9657
  18. 18. Komatsu N. Shimawaki T. Aonuma S. Kimura T. 2006 Ultrasonic isolation of toroidal aggregates of single-walled carbon nanotubes. Carbon 44 10 2091 2093
  19. 19. Guo A. Fu Y. Guan L. Zhang Z. Wu W. Chen J. Shi Z. Gu Z. Huang R. Zhang X. 2007 Spontaneously Formed Closed Rings of Single-Wall Carbon Nanotube Bundles and Their Physical Mechanism. The Journal of Physical Chemistry C 111 9 3555 3559
  20. 20. Colomer J. F. Henrard L. Flahaut E. Van Tendeloo G. Lucas A. A. Lambin P. 2003 Rings of Double-Walled Carbon Nanotube Bundles. Nano Letters 3 5 685 689
  21. 21. Yu H. Zhang Q. Luo G. Wei F. 2006 Rings of triple-walled carbon nanotube bundles.Applied Physics Letters 89 22 223106
  22. 22. Dunlap B. I. 1992 Connecting carbon tubules. Physical Review B 46 3 1933 1936
  23. 23. Itoh S. Ihara S. Kitakami J. I. 1993 Toroidal form of carbon C360. Physical Review B 47 3 1703 1704
  24. 24. Ihara S. Itoh S. Kitakami J. I. 1993 Toroidal forms of graphitic carbon. Physical Review B 47 19 12908 12911
  25. 25. Itoh S. Ihara S. 1993 Toroidal forms of graphitic carbon II. Elongated tori. Physical Review B 48 11 8323 8328
  26. 26. Kirby E. C. Mallion R. B. Pollak P. 1993 Toroidal polyhexes. Journal of the Chemical Society, Faraday Transactions 89 12 1945 1953
  27. 27. Liu L. Jayanthi C. S. Wu S. Y. . 2001 Structural and electronic properties of a carbon nanotorus: Effects of delocalized and localized deformations Physical Review B 64 3 033412
  28. 28. Liu L. Guo G. Y. Jayanthi C. S. Wu S. Y. 2002 Colossal Paramagnetic Moments in Metallic Carbon Nanotori. Physical Review Letters 88 21 217206
  29. 29. Hod O. Rabani E. Baer R. 2003 Carbon nanotube closed-ring structures Physical Review B 67 19 195408
  30. 30. Cox B. J. Hill J. M. 2007 New Carbon Molecules in the Form of Elbow-Connected Nanotori. The Journal of Physical Chemistry C 111 29 10855 10860
  31. 31. Baowan D. Cox B. J. Hill J. M. 2008 Toroidal molecules formed from three distinct carbon nanotubes. Journal of Mathematical Chemistry 44 2 515 527
  32. 32. Liu L. Zhang L. Gao H. Zhao J. 2011 Structure, energetics, and heteroatom doping of armchair carbon nanotori. Carbon 49 13 4518 4523
  33. 33. Klein D. J. Seitz W. A. Schmalz T. G. 1986 Icosahedral symmetry carbon cage molecules. Nature 323 6090 703 706
  34. 34. Itoh S. Ihara S. 1994 Isomers of the toroidal forms of graphitic carbon. Physical Review B 49 19 13970 13974
  35. 35. Nagy C. Nagy K. Diudea M. 2009 Elongated tori from armchair DWNT. Journal of Mathematical Chemistry 45 2 452 459
  36. 36. László I. Rassat A. 2001 Toroidal and spherical fullerene-like molecules with only pentagonal and heptagonal faces. International Journal of Quantum Chemistry 84 1 136 139
  37. 37. Ihara S. Itoh S. 1995 Helically coiled and toroidal cage forms of graphitic carbon. Carbon 33 7 931 939
  38. 38. Taşcı E. Yazgan E. Malcıoğlu O. B. Erkoç Ş. 2005 Stability of Carbon Nanotori under Heat Treatment: Molecular-Dynamics Simulations. Fullerenes, Nanotubes and Carbon Nanostructures 13 2 147 154
  39. 39. Chen C. Chang J. G. Ju S. P. Hwang C. C. 2011 Thermal stability and morphological variation of carbon nanorings of different radii during the temperature elevating process: a molecular dynamics simulation study. Journal of Nanoparticle Research 13 5 1995 2006
  40. 40. Yang L. Chen J. Dong J. 2004 Stability of single-wall carbon nanotube tori Physica Status Solidi (b) 241 6 1269 1273
  41. 41. Feng C. Liew K. M. 2009 Energetics and structures of carbon nanorings Carbon. 47 7 1664 1669
  42. 42. Liu P. Zhang Y. W. Lu C. . 2005 Structures and stability of defect-free multiwalled carbon toroidal rings. Journal of Applied Physics 113522
  43. 43. Han J. 1998 Energetics and structures of fullerene crop circles. Chemical Physics Letters 282 2 187 191
  44. 44. Meunier V. Lambin P. Lucas A. A. 1998 Atomic and electronic structures of large and small carbon tori. Physical Review B 57 23 14886 14890
  45. 45. Chen N. Lusk M. T. van Duin A. C. T. Goddard W. A. I. I. I. 2005 Mechanical properties of connected carbon nanorings via molecular dynamics simulation. Physical Review B 72 8 085416
  46. 46. Çağin T. Gao G. Goddard I. I. I. W. A. 2006 Computational studies on mechanical properties of carbon nanotori. Turkish Journal of Physics 30 4 221 229
  47. 47. Feng C. Liew K. M. 2009 A molecular mechanics analysis of the buckling behavior of carbon nanorings under tension Carbon 47 15 3508 3514
  48. 48. Feng C. Liew K. M. 2010 Buckling Behavior of Armchair and Zigzag Carbon Nanorings. Journal of Computational and Theoretical Nanoscience 7 10 2049 2053
  49. 49. Zheng M. Ke C. 2010 Elastic Deformation of Carbon-Nanotube Nanorings. Small 6 15 1647 1655
  50. 50. Zheng M. Ke C. 2011 Mechanical deformation of carbon nanotube nano-rings on flat substrate. Journal of Applied Physics 109 7 074304 074310
  51. 51. Saito R. Dresselhaus G. Dresselhaus M. S. 1998 Physical properties of carbon nanotubes London Imperial College Press
  52. 52. Zhenhua Z. Zhongqin Y. Xun W. Jianhui Y. Hua Z. Ming Q. Jingcui P. 2005 The electronic structure of a deformed chiral carbon nanotorus. Journal of Physics: Condensed Matter 17 26 4111 4120
  53. 53. Ceulemans A. Chibotaru L. F. Bovin S. A. Fowler P. W. 2000 The electronic structure of polyhex carbon tori. The Journal of Chemical Physics 112 9 4271 4278
  54. 54. Liu C. P. Ding J. W. 2006 Electronic structure of carbon nanotori: the roles of curvature, hybridization, and disorder. Journal of Physics Condensed Matter 18 16 4077 4084
  55. 55. Oh D. H. Mee Park. J. Kim K. S. 2000 Structures and electronic properties of small carbon nanotube tori. Physical Review B 62 3 1600 1603
  56. 56. Yazgan E. Taşci E. Malcioğlu O. B. Erkoç Ş. 2004 Electronic properties of carbon nanotoroidal structures. Journal of Molecular Structure: THEOCHEM 681 1-3 231 234
  57. 57. Wu X. Zhou R. Yang J. Zeng X. C. 2011 Density-Functional Theory Studies of Step-Kinked Carbon Nanotubes. The Journal of Physical Chemistry C 115 10 4235 4239
  58. 58. Haddon R. C. 1997 Electronic properties of carbon toroids Nature 388 6637 31 32
  59. 59. Rodríguez-Manzo J. A. López-Urías F. Terrones M. Terrones H. 2004 Magnetism in Corrugated Carbon Nanotori: The Importance of Symmetry, Defects, and Negative Curvature. Nano Letters 4 11 2179 2183
  60. 60. Lin M. F. Chuu D. S. 1998 Persistent currents in toroidal carbon nanotubes. Physical Review B 57 11 6731 6737
  61. 61. Latil S. Roche S. Rubio A. 2003 Persistent currents in carbon nanotube based rings. Physical Review B 67 16 165420
  62. 62. Shyu F. L. Tsai C. C. Chang C. P. Chen R. B. Lin M. F. 2004 Magnetoelectronic states of carbon toroids. Carbon 42 14 2879 2885
  63. 63. Margańska M. Szopa M. Zipper E. 2005 Aharonov-Bohm effect in carbon nanotubes and tori. Physica Status Solidi (b) 242 2 285 290
  64. 64. Zhang Z. H. Yuan J. H. Qiu M. Peng J. C. Xiao F. L. 2006 Persistent currents in carbon nanotori: Effects of structure deformations and chirality. Journal of Applied Physics 99 10 104311
  65. 65. Tsai C. C. Shyu F. L. Chiu C. W. Chang C. P. Chen R. B. Lin M. F. 2004 Magnetization of armchair carbon tori Physical Review B 70 7 075411
  66. 66. Liu C. P. Chen H. B. Ding J. W. 2008 Magnetic response of carbon nanotori: the importance of curvature and disorder. Journal of Physics: Condensed Matter 20 1 015206
  67. 67. Liu C. P. Xu N. 2008 Magnetic response of chiral carbon nanotori: The dependence of torus radius. Physica B: Condensed Matter 403 17 2884 2887
  68. 68. Zhang Z. Li Q. 2010 Combined Effects of the Structural Deformation and Temperature on Magnetic Characteristics of the Single-walled Chiral Toroidal Carbon Nanotubes. Chinese Journal of Electronics 19 3 423 426
  69. 69. Rodríguez-Manzo J. A. López-Urías F. Terrones M. Terrones H. 2007 Anomalous Paramagnetism in Doped Carbon Nanostructures. Small 3 1 120 125
  70. 70. Castillo-Alvarado F. d. L. Ortíz-López J. Arellano J. S. Cruz-Torres A. 2010 Hydrogen Storage on Beryllium-Coated Toroidal Carbon Nanostructure C120 Modeled with Density Functional Theory. Advances in Science and Technology 72 188 195
  71. 71. Hilder T. A. Hill J. M. 2007 Orbiting atoms and C60 fullerenes inside carbon nanotori. Journal of Applied Physics 101 6 64319
  72. 72. Lusk M. T. Hamm N. 2007 Ab initio study of toroidal carbon nanotubes with encapsulated atomic metal loops. Physical Review B 76 12 125422
  73. 73. Mukherjee B. Maiti P. K. Dasgupta C. Sood A. K. 2010 Single-File Diffusion of Water Inside Narrow Carbon Nanorings. ACS Nano 4 2 985 991
  74. 74. Koós A. A. Ehlich R. Horváth Z. E. Osváth Z. Gyulai J. Nagy J. B. Biró L. P. 2003 STM and AFM investigation of coiled carbon nanotubes produced by laser evaporation of fullerene Materials Science and Engineering: C 23 1-2 275 278
  75. 75. Saveliev A. V. Merchan-Merchan W. Kennedy L. A. 2003 Metal catalyzed synthesis of carbon nanostructures in an opposed flow methane oxygen flame. Combustion and Flame1351-2 27 33
  76. 76. Bai J. B. Hamon A. L. Marraud A. Jouffrey B. Zymla V. 2002 Synthesis of SWNTs and MWNTs by a molten salt (NaCl) method Chemical Physics Letters 365 1-2 184 188
  77. 77. Ajayaghosh A. Vijayakumar C. Varghese R. George S. J. 2006 Cholesterol-Aided Supramolecular Control over Chromophore Packing: Twisted and Coiled Helices with Distinct Optical, Chiroptical, and Morphological Features. Angewandte Chemie 118 3 470 474
  78. 78. Yamamoto T. Fukushima T. Aida T. Shimizu T. 2008 Self-Assembled Nanotubes and Nanocoils from ss-Conjugated Building Blocks. Advances in Polymer Science 220 1 27
  79. 79. Lujun P. Hayashida T. Mei Z. Nakayama Y. 2001 Field emission properties of carbon tubule nanocoils. Japanese Journal of Applied Physics 40 3B L235 L237
  80. 80. Jining X. Mukhopadyay K. Yadev J. Varadan V. K. 2003 Catalytic chemical vapor deposition synthesis and electron microscopy observation of coiled carbon nanotubes. Smart Materials and Structures 12 5 744 748
  81. 81. Hou H. Jun Z. Weller F. Greiner A. 2003 Large-Scale Synthesis and Characterization of Helically Coiled Carbon Nanotubes by Use of Fe(CO)5 as Floating Catalyst Precursor. Chemistry of Materials 15 16 3170 3175
  82. 82. Zhong D. Y. Liu S. Wang E. G. 2003 Patterned growth of coiled carbon nanotubes by a template-assisted technique. Applied Physics Letters 83 21 4423 4425
  83. 83. Tang N. Wen J. Zhang Y. Liu F. Lin K. Du Y. 2010 Helical Carbon Nanotubes: Catalytic Particle Size-Dependent Growth and Magnetic Properties. ACS Nano 4 1 241 250
  84. 84. Lau K. T. Lu M. Hui D. 2006 Coiled carbon nanotubes: Synthesis and their potential applications in advanced composite structures. Composites Part B: Engineering 37 6 437 448
  85. 85. Fejes D. Hernádi K. 2010 A Review of the Properties and CVD Synthesis of Coiled Carbon Nanotubes. Materials 3 4 2618 2642
  86. 86. Shaikjee A. Coville N.J. 2012 The synthesis, properties and uses of carbon materials with helical morphology. Journal of Advanced Research 3 3 195 223
  87. 87. Fonseca A. Hernadi K. Nagy J. B. Lambin P. Lucas A. A. 1996 Growth mechanism of coiled carbon nanotubes Synthetic Metals 77 1-3 235 242
  88. 88. Pan L. J. Zhang M. Nakayama Y. 2002 Growth mechanism of carbon nanocoils. Journal of Applied Physics 91 12 10058 10061
  89. 89. Chen X. Yang S. Takeuchi K. Hashishin T. Iwanaga H. Motojiima S. 2003 Conformation and growth mechanism of the carbon nanocoils with twisting form in comparison with that of carbon microcoils. Diamond and Related Materials 12 10-111836 1840
  90. 90. Bandaru P. R. Daraio C. Yang K. Rao A. M. 2007 A plausible mechanism for the evolution of helical forms in nanostructure growth Journal of Applied Physics 101 9 094307
  91. 91. Dunlap B. I. 1994Relating carbon tubules. Physical Review B49 8 5643 5651
  92. 92. Fonseca A. Hernadi K. Nagy J. b. Lambin P. Lucas A. A. 1995 Model structure of perfectly graphitizable coiled carbon nanotubes. Carbon 33 12 1759 1775
  93. 93. Ihara S. Itoh S. Kitakami J. i. 1993 Helically coiled cage forms of graphitic carbon. Physical Review B 48 8 5643 5647
  94. 94. Setton R. Setton N. 1997 Carbon nanotubes: III. Toroidal structures and limits of a model for the construction of helical and S-shaped nanotubes Carbon 35 4 497 505
  95. 95. Akagi K. Tamura R. Tsukada M. Itoh S. Ihara S. 1995 Electronic Structure of Helically Coiled Cage of Graphitic Carbon. Physical Review Letters 74 12 2307 2310
  96. 96. Akagi K. Tamura R. Tsukada M. Itoh S. Ihara S. 1996 Electronic structure of helically coiled carbon nanotubes: Relation between the phason lines and energy band features. Physical Review B 53 4 2114 2120
  97. 97. Biro L. P. Mark G. I. Lambin P. 2003 Regularly coiled carbon nanotubes Nanotechnology, IEEE Transactions on 2 4 362 367
  98. 98. Liu L. Gao H. Zhao J. Lu J. 2010 Superelasticity of Carbon Nanocoils from Atomistic Quantum Simulations Nanoscale Research Letters 5 3 478 483
  99. 99. Zhong-can O. Y. Su Z. B. Wang C. L. 1997 Coil Formation in Multishell Carbon Nanotubes: Competition between Curvature Elasticity and Interlayer Adhesion. Physical Review Letters 78 21 4055 4058
  100. 100. Volodin A. Ahlskog M. Seynaeve E. Van Haesendonck C. Fonseca A. Nagy J. B. 2000 Imaging the Elastic Properties of Coiled Carbon Nanotubes with Atomic Force Microscopy. Physical Review Letters 84 15 3342 3345
  101. 101. Hayashida T. Pan L. Nakayama Y. 2002 Mechanical and electrical properties of carbon tubule nanocoils. Physica B: Condensed Matter 323 1-4352 353
  102. 102. Chen X. Zhang S. Dikin D. A. Ding W. Ruoff R. S. Pan L. Nakayama Y. 2003 Mechanics of a Carbon Nanocoil. Nano Letters 3 9 1299 1304
  103. 103. Huang W. M. 2005 Mechanics of coiled nanotubes in uniaxial tension Materials Science and Engineering: A 408 1-2 136 140
  104. 104. Neng-Kai C. Shuo-Hung C. 2008 Determining Mechanical Properties of Carbon Microcoils Using Lateral Force Microscopy. IEEE Transactions on Nanotechnology 7 2 197 201
  105. 105. Poggi M. A. Boyles J. S. Bottomley L. A. Mc Farland A. W. Colton J. S. Nguyen C. V. Stevens R. M. Lillehei P. T. 2004 Measuring the Compression of a Carbon Nanospring. Nano Letters 4 6 1009 1016
  106. 106. Fonseca A. F. d. Galvão D. S. 2004 Mechanical Properties of Nanosprings. Physical Review Letters 92 17 175502
  107. 107. Fonseca A. F. d. Malta C. P. Galvão D. S. 2006 Mechanical properties of amorphous nanosprings. Nanotechnology 17 22 5620 5626
  108. 108. Coluci V. R. Fonseca A. F. Galvão D. S. Daraio C. 2008 Entanglement and the Nonlinear Elastic Behavior of Forests of Coiled Carbon Nanotubes. Physical Review Letters 100 8 086807
  109. 109. Ghaderi S. H. Hajiesmaili E. 2010 Molecular structural mechanics applied to coiled carbon nanotubes. Computational Materials Science 55 0 344 349
  110. 110. Kaneto K. Tsuruta M. Motojima S. 1999 Electrical properties of carbon micro coils. Synthetic Metals 103 1-3 2578 2579
  111. 111. Ebbesen T. W. Lezec H. J. Hiura H. Bennett J. W. Ghaemi H. F. Thio T. 1996 Electrical conductivity of individual carbon nanotubes. Nature 382 6586 54 56
  112. 112. Chiu H. S. Lin P. I. Wu H. C. Hsieh W. H. Chen C. D. Chen Y. T. 2009 Electron hopping conduction in highly disordered carbon coils. Carbon 47 7 1761 1769
  113. 113. Tang N. Kuo W. Jeng C. Wang L. Lin K. Du Y. 2010 Coil-in-Coil Carbon Nanocoils: 11 Gram-Scale Synthesis, Single Nanocoil Electrical Properties, and Electrical Contact Improvement. ACS Nano 4 2 781 788
  114. 114. Fujii M. Matsui M. Motojima S. Hishikawa Y. 2002 Magnetoresistance in carbon micro-coils obtained by chemical vapor deposition. Thin Solid Films 409 1 78 81
  115. 115. Liu L. Gao H. Zhao J. Lu J. 2011 Quantum conductance of armchair carbon nanocoils: roles of geometry effects. SCIENCE CHINA Physics, Mechanics & Astronomy 54 5 841 845
  116. 116. Motojima S. Chen X. Yang S. Hasegawa M. 2004 Properties and potential applications of carbon microcoils/nanocoils. Diamond and Related Materials 13 11-12 19895 1992
  117. 117. Volodin A. Buntinx D. Ahlskog M. Fonseca A. Nagy J. B. Van Haesendonck C. 2004 Coiled Carbon Nanotubes as Self-Sensing Mechanical Resonators. Nano Letters 4 9 1775 1779
  118. 118. Bell D. J. Sun Y. Zhang L. Dong L. X. Nelson B. J. Grützmacher D. 2006 Three-dimensional nanosprings for electromechanical sensors. Sensors and Actuators A Physical 130-131 0 54 61
  119. 119. Kato Y. Adachi N. Okuda T. Yoshida T. Motojima S. Tsuda T. 2003 Evaluation of induced electromotive force of a carbon micro coil. Japanese Journal of Applied Physics 42 8 5035 5037
  120. 120. Shaoming Y. Xiuqin C. Aoki H. Motojima S. 2006 Tactile microsensor elements prepared from aligned superelastic carbon microcoils and polysilicone matrix. Smart Materials and Structures 15 3 687 694
  121. 121. Greenshields M. W. Hummelgen I. A. Mamo M. A. Shaikjee A. Mhlanga S. D. van Otterlo W. A. Coville N. J. 2011 Composites of Polyvinyl Alcohol and Carbon (Coils, Undoped and Nitrogen Doped Multiwalled Carbon Nanotubes) as Ethanol, Methanol and Toluene Vapor Sensors. Journal of Nanoscience and Nanotechnology 11 11 10211 10218
  122. 122. Lau K. t. Lu M. Liao K. 2006 Improved mechanical properties of coiled carbon nanotubes reinforced epoxy nanocomposites. Composites Part A: Applied Science and Manufacturing 37 10 18375 18405
  123. 123. Yoshimura K. Nakano K. Miyake T. Hishikawa Y. Motojima S. 2006 Effectiveness of carbon microcoils as a reinforcing material for a polymer matrix Carbon 44 13 2833 2838
  124. 124. Li X. F. Lau K. T. Yin Y. S. 2008 Mechanical properties of epoxy-based composites using coiled carbon nanotubes. Composites Science and Technology 68 14 2876 2881
  125. 125. Sanada K. Takada Y. Yamamoto S. Shindo Y. 2008 Analytical and Experimental Characterization of Stiffness and Damping in Carbon Nanocoil Reinforced Polymer Composites. Journal of Solid Mechanics and Materials Engineering 2 12 1517 1527
  126. 126. Katsuno T. Chen X. Yang S. Motojima S. Homma M. Maeno T. Konyo M. 2006 Observation and analysis of percolation behavior in carbon microcoils/silicone-rubber composite sheets. Applied Physics Letters 88 23 232115 232113
  127. 127. Yoshimura K. Nakano K. Miyake T. Hishikawa Y. Kuzuya C. Katsuno T. Motojima S. 2007 Effect of compressive and tensile strains on the electrical resistivity of carbon microcoil/silicone-rubber composites. Carbon 45 10 1997 2003
  128. 128. Nakamatsu K. Igaki J. Nagase M. Ichihashi T. Matsui S. 2006 Mechanical characteristics of tungsten-containing carbon nanosprings grown by FIB-CVD. Microelectronic Engineering 83 4-9 808 810
  129. 129. Bi H. Kou K. C. Ostrikov K. Yan L. K. Wang Z. C. 2009 Microstructure and electromagnetic characteristics of Ni nanoparticle film coated carbon microcoils. Journal of Alloys and Compounds. 478 1-2 796 800
  130. 130. Zhang G. Y. Jiang X. Wang E. G. 2004 Self-assembly of carbon nanohelices: Characteristics and field electron emission properties. Applied Physics Letters 84 14 2646 2648
  131. 131. Wu X. L. Liu Q. Guo Y. G. Song W. G. 2009 Superior storage performance of carbon nanosprings as anode materials for lithium-ion batteries. Electrochemistry Communications 11 7 1468 1471
  132. 132. Raghubanshi H. Hudson M. S. L. Srivastava O. N. 2011 Synthesis of helical carbon nanofibres and its application in hydrogen desorption. International Journal of Hydrogen Energy 36 7 4482 4490
  133. 133. Motojima S. 2008 Development of ceramic microcoils with 3D-herical/spiral structures. Journal of the Ceramic Society of Japan 116 1357 921 927
  134. 134. Motojima S. Hoshiya S. Hishikawa Y. 2003 Electromagnetic wave absorption properties of carbon microcoils/PMMA composite beads in W bands. Carbon 41 13 2658 2660

Written By

Lizhao Liu and Jijun Zhao

Submitted: 01 March 2012 Published: 09 May 2013