Pentagon-heptagon Pair Defects Research Articles

Molecular Dynamics of Chirality Definable Growth of Single-Walled Carbon Nanotubes.

In order to achieve the chirality-specific growth of single-walled carbon nanotubes (SWCNTs), it is crucial to understand the growth mechanism. Even though many molecular dynamics (MD) simulations have been employed to analyze the SWCNT growth mechanism, it has been difficult to discuss the chirality determining kinetics because of the defects remaining on the SWCNTs grown in simulations. In this study, we demonstrate MD simulations of defect-free SWCNTs, that is, chirality definable SWCNTs, under the optimized carbon supply rate and temperature. The chiralities of the SWCNTs were assigned as (14,1), (15,2), and (9,0), indicating the preference of near-zigzag and pure-zigzag SWCNTs. The SWCNTs contained at least one complete row of defect-free walls consisting of only hexagons. The near-zigzag SWCNTs grew via a kink-running process, in which bond formation between a carbon atom at a kink and a neighboring carbon chain led to formation of a hexagon with a new kink at the SWCNT edge. Defects including pentagons and heptagons were sometimes formed but effectively healed into hexagons on metal surfaces. The pure-zigzag SWCNTs grew by the kink-running and the hexagon nucleation processes. In addition, chirality change events along SWCNTs with incorporation of pentagon-heptagon pair defects were observed in the MD simulations. Here, pentagons and heptagons were frequently observed as adjacent pairs, resulting in ( n, m) chirality changes by (±1,0), (0,±1), (1,-1), or (-1,1).

Exploring pentagon-heptagon pair defects in the triangular graphene quantum dots: A computational study

We have applied density functional calculations to investigate Stone Wales (SW) and carbon ad-dimer (CD) defect formation in triangular graphene quantum dots (GQDs). According to our results, defect formation energies depend on the positions of SW defects, such that the rotation of the CC bond located near the vertex of triangular GQD is easier than the rotation of other CC bonds. Therefore, the multiply defective GQDs with isolated SW defect sites are the most favorable while the formation of pentalene like structures in the connected SW defect sites costs larger formation energies. Introducing of carbon dimer defects on a triangular GQD induces a curvature at the defective sites, which leads to a more complex defect configuration with cone-like structure in the CD defective GQD with three defective sites. Then, formation energies for CD defective GQDs are higher than those for SW defective ones. The electrophilicity values calculated for SW and CD defective GQDs are greater than those for pristine GQDs. Moreover, perturbation of strong sp2 bonding network of graphitic carbons on the GQD, leading to the formation of more localized CC bonds, results in further electron deficiency of multiply SW and CD defective GQDs with increasing of electrophilicity values.

A refined finite element analysis on the vibrational properties of ideal and degenerated carbon nanostructures

Abstract Different types of degenerated nanostructures were simulated and their eigenfrequencies and corresponding eigenmodes were evaluated by applying the well-established finite element method. In addition, the structural and vibrational stability of these nanoparticles was examined under the influence of microscopic modifications. For this purpose, four common types of atomic defects (i.e. different types of vacancy defects, perturbation, pentagon–heptagon pair defect and chemical doping) were introduced to the finite element models and their vibrational properties were obtained and finally compared to those of perfect, i.e. defect-free, structures. The detailed geometry around a defected area was calculated based on density functional theory and implemented in the finite element model. Based on the results, it was shown that all these structural modifications changes the natural frequency and as a result, reduce the vibrational stability of degenerated nano-materials.

On the tensile behavior of hetero-junction carbon nanotubes

Several straight hetero-junctions carbon nanotubes (CNTs) are constructed and their tensile behavior are investigated. It is pointed that the Young's modulus of hetero-junctions is lower than the values of their fundamental homogeneous CNTs due to the existence of pentagon–heptagon pair defects. In addition, it is revealed that the Young's modulus of homogeneous zigzag CNTs increases by increasing the chiral number of these nano-structures. Finally, it is concluded that as the connecting length of the hetero-junctions increases the Young's modulus of these particular CNTs decreases. Therefore, the tensile strength of hetero-junctions depends on the presence of pentagon–heptagon pair defects.

Numerical modeling of eigenmodes and eigenfrequencies of hetero-junction carbon nanotubes with pentagon–heptagon pair defects

This study examines the vibrational behavior of numerous hetero-junctions and their fundamental CNTs under different boundary conditions. The natural frequencies of homogeneous CNTs (zigzag and armchair) were obtained analytically and through a finite element method and compared with each other. In addition, the computational results of hetero-junctions were obtained and also compared with their constituent homogeneous CNTs. It has been shown that the natural frequency of straight hetero-junction CNTs lies within the range of the values of their fundamental CNTs in the case that the wider tube fixed. In addition, it was also concluded that the eigen-values of straight hetero-junctions and their fundamental CNTs increase by increasing the chiral number of CNTs. Finally, it was also shown that the armchair CNTs are more stable in their vibration due to higher natural frequencies than zigzag configurations.

What is the role of defects in single-walled carbon nanotubes for nonlinear optical property?

In carbon nanotubes (CNTs), there exist various kinds of defects which may influence the electrical, thermal and mechanical properties of carbon nanotubes. However, how the defect influences the nonlinear optical (NLO) property is still unknown. This paper exhibits the role of defects on the static first hyperpolarizability (β0) for topological Stone-Wales (SW), single vacancy (SV) and double vacancy (DV) defects. For eight carbon nanotubes with defects and one relevant perfect nanotube, the obtained order of the β0 values is 0 (Perfect) < 5.0 × 102 (DV585-z) < 5.3 × 102 (SW5577-z) < 4.6 × 103 (DV585-xz) < 6.0 × 103 (DV555777) < 7.3 × 103 (SV-xz) < 1.1 × 104 (SV-z) < 3.3 × 104 (SW5577-xz) < 2.2 × 105 a.u. (SW57-75). The results show that the defect plays an important role on greatly enhancing the β0 value due to lowering the transition energy. Four interesting relationships between the defect and the β0 value are observed. (1) The defects bring a large increase of the β0 values. (2) For the SW and DV defects, the direction of the defect is an important factor to enhance the β0 value. For example, β0 values of SW5577 structures are 3.3 × 104 (near xz direction) ≫ 5.3 × 102 a.u. (the z direction along the tube axis). (3) Interestingly, not vacancy defects but the topological defect can bring the largest β0 value (2.2 × 105 a.u. for the SW57-75). (4) For the topological SW defects, the separate pentagon-heptagon pair defect (57–75, the β0 value of 2.2 × 105 a.u.) may be more efficient than the fused one (5577, 3.3 × 104 a.u.) to enhance the β0 value. This work suggests a new strategy, introducing the right defect on CNTs to enhance the nonlinear optical response.

Vacancy cluster-limited electronic transport in metallic carbon nanotube

We investigate the electronic properties of metallic (7,7) carbon nanotubes (CNT) in the presence of a variety of tetra- and hexa-vacancy defects, by using the first principles density functional theory (DFT) combined with the non-equilibrium Green’s function technique. From the view point of energetic stability large vacancies tend to split into pentagon and heptagon (5–7) defects. However, this does not preclude the presence of “holes” in the carbon nanotube by the nanoelectronic lithography technique. We show that the states linked to large vacancies hybridize with the extended states of the nanotubes to modify their band structure. As a consequence, the hole-like defects in the CNT lead to more prominent electronic transport compared to the situation in the defective CNT consisting of pentagon–heptagon pair defects. Our study suggests the possibility to improve the electronic properties of a defective carbon nanotube via morphological modifications induced by irradiation techniques.

The role of pentagon–heptagon pair defect in carbon nanotube: The center of vacancy reconstruction

We show that pentagon–heptagon (5–7) pair defects in carbon nanotube play an important role as the center of vacancy reconstruction using tight-binding molecular dynamics simulations and ab initio total energy calculations. Single vacancy defect diffuses toward and coalesces with 5–7 pair defects and the coalescence structure is reconstructed into a new and more stable 5–7 pair defect plus an adatom by an exchange mechanism. In the case of four single vacancy defects, the vacancy defects coalesce with 5–7 pair defects and form defect structures with nonhexagonal rings. Finally, these defective structures reconstruct into two new 5–7 pair defects.

The formation of pentagon-heptagon pair defect by the reconstruction of vacancy defects in carbon nanotube

The reconstruction process of vacancy hole in carbon nanotube is investigated by tight-binding molecular dynamics simulations and by ab initio total energy calculations. In the molecular dynamics simulation, a vacancy hole is found to reconstruct into two separated pentagon-heptagon pair defects. As the result of reconstruction, the radius of the carbon nanotube is reduced and the chirality of the tube is partly changed. During the vacancy hole healing process, the formation of pentagonal and heptagonal rings is proceeded by the subsequent Stone-Wales [Chem. Phys. Lett. 128, 501 (1986)] transformation.

Imaging active topological defects in carbon nanotubes

A single-walled carbon nanotube (SWNT) is a wrapped single graphene layer, and its plastic deformation should require active topological defects--non-hexagonal carbon rings that can migrate along the nanotube wall. Although in situ transmission electron microscopy (TEM) has been used to examine the deformation of SWNTs, these studies deal only with diameter changes and no atomistic mechanism has been elucidated experimentally. Theory predicts that some topological defects can form through the Stone-Wales transformation in SWNTs under tension at 2,000 K, and could act as a dislocation core. We demonstrate here, by means of high-resolution (HR)-TEM with atomic sensitivity, the first direct imaging of pentagon-heptagon pair defects found in an SWNT that was heated at 2,273 K. Moreover, our in situ HR-TEM observation reveals an accumulation of topological defects near the kink of a deformed nanotube. This result suggests that dislocation motions or active topological defects are indeed responsible for the plastic deformation of SWNTs.

Magnetic-field effects on transport in carbon nanotube junctions

Here we address a theoretical study on the behaviour of electronic states of heterojunctions and quantum dots based on carbon nanotubes under magnetic fields. Emphasis is put on the analysis of the local density of states, the conductance, and on the characteristic curves of current versus voltage. The heterostructures are modeled by joining zigzag tubes through single pentagon-heptagon pair defects, and described within a simple tight binding calculation. The conductance is calculated using the Landauer formula in the Green functions formalism. The used theoretical approach incorporates the atomic details of the topological defects by performing an energy relaxation via Monte Carlo calculation. The effect of a magnetic field on the conductance gap of the system is investigated and compared to those of isolated constituent tubes. It is found that the conductance gap of the studied CNHs exhibits oscillations as a function of the magnetic flux. However, unlike the pristine tubes case, they are not Aharonov-Bohm periodic oscillations.

Field emission properties and synthesis of carbon nanotubes grown by rf plasma-enhanced chemical vapor deposition

Plasma-enhanced chemical vapor deposition (PECVD) method was employed to grow the Fe-catalyzed carbon nanotubes (CNTs). The grown CNTs with a uniform diameter in the range of about 10–20 nm and the typical lengths beyond 1 μm resulted in a very high aspect ratio. The Raman and TEM results showed that the grown CNTs contained a large amount of carbonaceous particles and crystal defects, such as pentagon–heptagon pair defects. XPS measurement indicated that the CNTs had C H covalent bonds. Field emission characteristics exhibited the low turn-on threshold field of 2.75 V/μm and the maximum emission current density of 7.75 mA/cm 2 at 6.5 V/μm. The growth mechanism of CNTs and the effects of hydrogen plasma on their structure were discussed.

Atomistic Simulations of Rare Gas Transport through Breathable Single-wall Nanotubes with Constrictions and Knees

We present the results of molecular dynamics (MD) computer simulations of rare gas diffusion through breathable nanotubes with pentagon–heptagon pair defects resulting in constrictions and knees. Diffusion involves interrupted high speed “choppy” motion with intermittent reversal in velocity direction. Single atoms exhibit a spiral-like path, in contrast to atoms traveling in groups. Considerable resistance to flow appears to reside in the upstream section of the nanotube where density gradients are small, prior to the constriction. Subsequently, considerable density gradients are present and speeds increase, becoming greatest at the tube exit. For the nanotubes examined, Kr and Xe diffusion was too hindered to provide reliable results. Diffusion of He through the nanotubes with knees occurs in a single-file fashion nearly along the center of the tube and the knee has no detectable effect on the diffusion kinetics. Transport diffusion coefficients are in the order of 10-4–10-2 cm2/s.

Direct observation of localized defect States in semiconductor nanotube junctions.

We report scanning tunneling microscopy of semiconductor-semiconductor carbon nanotube junctions with different band gaps. Characteristic features of the wave functions at different energy levels, such as a localized defect state, are clearly exhibited in the atomically resolved scanning tunneling spectroscopy. The peaks of the Van Hove singularity on each side penetrate and decay into the opposite side across the junction over a distance of approximately 2 nm. These experimental features are accounted for, with the help of tight-binding calculation, by the presence of pentagon-heptagon pair defects at the junction.

Electronic properties of carbon nanotubes with pentagon–heptagon pair defects

Introduction of a pentagon–heptagon pair defect in the perfect hexagonal network of two carbon nanotubes can change the helicity of the tube and alter its electronic structure. Using a tight binding method to calculate the electronic structure of such a system, we show that this pentagon–heptagon pair defect in the nanotube structure is not only responsible for the change in nanotube diameter, but also governs the electronic behavior around the Fermi level. This configuration is explored in order to understand the influence of the defect on the electronic properties of the system. Topological aspects associated with the presence of the defect are also discussed.

Electronic properties of carbon nanotubes with a pentagon-heptagon pair defect

The features of energetics and electronic properties of carbon nanotubes, containing a pentagon-heptagon pair (5/7) topological defect in the hexagonal network of the zigzag configuration, are investigated using the extended Su-Schriffer-Heeger model based on the tight binding approximation in real space. Our calculations show that this pentagon-heptagon pair defect in the nanotube structures is not only responsible for a change in nanotube diameter, but also governs the electronic behaviour around Fermi level. Furthermore, we have calculated the densities of states of the (9,0)-(8,0) and (8,0)-(7,0) systems. For the (9,0)-(8,0) system, a narrow gap exists in the vicinity of the Fermi energy. In contrast, for the (8,0)-(7,0) system, a little peak of the density of states occurs at the Fermi energy. These can be attributed to the addition of a pair of pentagon-heptagon defects in the interface between two isolated carbon nanotubes.

Propriétés structurales des jonctions de nanotubes de carbone

The junction between two different nanotubes can be realized by the simple insertion of a pentagon-heptagon pair defect while preserving the triple coordination of each C atom. This insertion bends the structure to an angle depending on the distance between the pentagonand heptagon. The atomic structure of several of these junctions was optimized with the help of empirical potentials, the nanotubes on both sides of the junctions being considered as infinitely long. Local densities of σ + π electronic states were evaluated in the interfacial regions from a tight-binding Hamiltonian. From there, the electronic energy of these junctions was calculated and compared with that of the isolated nanotubes. It was established that the energy associated with the pentagon-heptagone pair in a graphitic tubule is of the order of 6 eV. An automatic generation algorithm for connecting any two tubules was developed. By restricting the Hamiltonian to the sole π orbitals, this algorithm made it feasible to study the energetics of the pentagon-heptagon defect in a systematical way.

Electronic and Structural Properties of Carbon Nanotubes Molecular Junction

AbstractThe electronic and structural properties of finite junctions produced by connecting two C nanotubes, saturated with hydrogens in both edges, are investigated using first-principles calculations, through self-consistent field Hartree-Fock-Roothaan method. The main target of our study is a molecular junction, which connects (10,0) and (6,6) tubes by the introduction of pentagon-heptagon pair defects diametrically opposed in the structure. The charge distributions, the character of the highest occupied molecular orbitals and the densities of states are determined for the finite (10,0) and (6,6) nanotubes and for the formed junction. An energetic analysis is also performed using ab-initio approach and empirical Tersoff potential.

Propriétés structurales des jonctions de nanotubes de carbone

The junction between two different nanotubes can be realized by the simple insertion of a pentagon-heptagon pair defect while preserving the triple coordination of each C atom. This insertion bends the structure to an angle depending on the distance between the pentagon and heptagon. The atomic structure of several of these junctions was optimized with the help of empirical potentials, the nanotubes on both sides of the junctions being considered as infinitely long. Local densities of C electronic states were evaluated in the interfacial regions from a tight-binding Hamiltonian. From there, the electronic energy of these junctions was calculated and compared with that of the isolated nanotubes. It was established that the energy associated with the pentagon-heptagone pair in a graphitic tubule is of the order of 6 eV. An automatic generation algorithm for connecting any two tubules was developed. By restricting the Hamiltonian to the sole orbitals, this algorithm made it feasible to study the energetics of the pentagon-heptagon defect in a systematical way.

Tight-Binding Computation of the STM Image of Carbon Nanotubes

STM imaging of single-wall carbon nanotubes has recently been achieved with atomic resolution, revealing the chirality of the carbon network. In this work, a theoretical modeling of scanning tunneling microscopy of the nanotubes is presented, based on a tight-binding $\ensuremath{\pi}$-electron Hamiltonian. This theory is simple enough to be used routinely for the computation of STM images and current-voltage characteristics, making it possible to investigate specific effects of the network curvature and topology such as a pentagon-heptagon pair defect.