Zigzag Single-walled Carbon Nanotubes Research Articles

Spectra and Thermodynamic Properties of Zig-Zag Single – Walled Carbon Nanotube with Deng–Fan–Hulthen Potential

A theoretical investigation of the spectra and thermodynamic properties of zig-zag single-walled carbon nanotubes (6,0) is carried out within the framework of the Deng–Fan–Hulthen potential. We solved the Schr¨odinger wave equation analytically in the presence of magnetic and Aharonov–Bohm (AB) flux fields using the Nikiforov–Uvarov (NU) method and obtained the energy eigenvalues and eigenfunctions. It is observed that, in the absence of both magnetic and AB fields, there is a degeneracy in the energy spectra. The presence of the magnetic and AB flux fields led to an increase in the energy eigenvalues. The combined presence of both fields removed the degeneracy noticed in the system. We calculated the partition function and used it to evaluate the thermodynamic properties such as the mean energy, free energy, and entropy in respect to the temperature, magnetic field, AB flux field and the quantum numbers.

Modeling Electrochemical Vacancy Regeneration in Single-Walled Carbon Nanotubes.

Synthesis-induced defects in single-walled carbon nanotubes (SWCNTs) enable diverse catalytic reactions, but the nature of catalytic intermediates and how active species regeneration occurs are unclear. Using a quantum mechanics/molecular mechanics (QM/MM) hybrid methodology based on density functional theory (DFT) and a classical force-field, we explore the reactivity and electrochemical regeneration of a vacancy defect in a zigzag SWCNT. Our findings indicate that hydrolysis of the defect forms a ketone group on one carbon atom and C-H bonds on two adjacent carbons. Applying an electrochemical potential of ESHE = -0.740 V triggers a proton-coupled electron transfer (PCET), converting the ketone to a hydroxyl group. Further reduction at ESHE = -1.08 V induces another PCET, expelling the hydroxyl as water and forming an active carbon with carbene character that can react with hydrogen peroxide and perchlorate. The hydrogen atoms on neighboring carbons prevent further water dissociation, maintaining the catalytic vacancy.

Electronic properties of armchair & zigzag single-walled carbon nanotubes

This paper investigates the role of chirality and its impact on the electronic band structure in armchair and zigzag single-walled carbon nanotubes (SWCNTs). Simulating electronic band gaps for single-walled carbon nanotubes (SWCNTs) with various chiral indices has been done by using the tight-binding model. The increase in chirality results in an increase in the total number of bands in the electronic band structure. A study was conducted on the band gap at Fermi energy (E=0) and it was found that the electronic band structure in armchair and zigzag (SWCNTs) can be either metallic or semiconductor depending on chirality. The diameter of the tube and the band gap value are also provided. The effect of variations in the CNT channel length and oxide thickness on the gate capacitance and drain current of a single CNT have been analyzed. The results suggest that the simulated values are consistent with the theoretical values thus validating the results.

Atom-bond-connectivity (ABC) indices of graphene sheets, zigzag single walled carbon nanotubes and single walled carbon nanotori

Abstract Atom-bond-connectivity (ABC) indices are obtained in analytical forms for graphene sheets, zigzag single walled carbon nanotubes (SWCNTs), and single walled carbon nanotori in terms of number of rings (r) that measures the length and the number of hexagons in between two rings (h) that dictates the width of the concerned systems. The procedures followed for ABC index have been used to obtain the expressions of augmented Zagreb and Randić indices for such systems. Logarithm of ABC indices of zigzag SWCNTs are found to correlate linearly well with the bond dissociation energies per C–C bond and the Young’s moduli of said SWCNTs with fixed number of rings (r) but varying number of hexagons (h) in between two successive rings. The plot of logarithm of ABC index versus Young’s modulus of such SWCNTs in varying both r and h simultaneously is not a straight line but fits well with the sigmoidal (Boltzmann) curve. Wiener index, one of the important distance based index, has recently been found to have similar correlations with the concerned properties of such systems. Similar plots would appear for the said properties of the zigzag SWCNTs with other degree-based indices like augmented Zagreb and Randić indices, as have been indicated from their respective expressions obtained.

Structural and thermal analyses in semiconducting and metallic zigzag single-walled carbon nanotubes using molecular dynamics simulations.

Equilibrium molecular dynamics (EMD) simulations have been performed to investigate the structural analysis and thermal conductivity (λ) of semiconducting (8,0) and metallic (12,0) zigzag single-walled carbon nanotubes (SWCNTs) for varying ±γ(%) strains. For the first time, the present outcomes provide valuable insights into the relationship between the structural properties of zigzag SWCNTs and corresponding thermal behavior, which is essential for the development of high-performance nanocomposites. The radial distribution function (RDF) has been employed to assess the buckling and deformation understandings of the (8,0) and (12,0) SWCNTs for a wide range of temperature T(K) and varying ±γ(%) strains. The visualization of SWCNTs shows that the earlier buckling and deformation processes are observed for semiconducting SWCNTs as compared to metallic SWCNTs for high T(K) and it also evident through an abrupt increase in RDF peaks. The RDF and visualization analyses demonstrate that the (8,0) SWCNTs can more tunable under compressive than tensile strains, however, the (12,0) zigzag SWCNTs indicate an opposite trend and may tolerate more tensile than compressive strains. Investigations show that the tunable domain of ±γ(%) strains decreases from (-10%≤ γ ≤+19%) to (-5%≤ γ ≤+10%) for (8,0) SWCNTs and the buckling process shifts to lower ±γ(%) for (12,0) SWCNTs with increasing T(K). For intermediate-high T(K), the λ(T) of (12,0) SWCNTs is high but the (8,0) SWCNTs show certainly high λ(T) for low T(K). The present λ(T, ±γ) data are in reasonable agreement with parts of previous NEMD, GK-HNEMD data and experimental investigations with simulation results generally under predicting the λ(T, ±γ) by the ∼1% to ∼20%, regardless of the ±γ(%) strains, depending on T(K). Our simulation data significantly expand the strain range to -10% ≤ γ ≤ +19% for both zigzag SWCNTs, depending on temperature T(K). This extension of the range aims to establish a tunable regime and delve into the intrinsic characteristics of zigzag SWCNTs, building upon previous work.

Effects of Topological Parameters on Thermal Properties of Carbon Nanotubes via Molecular Dynamics Simulation

Due to their unique properties, carbon nanotubes (CNTs) are finding a growing number of applications across multiple industrial sectors. These properties of CNTs are subject to influence by numerous factors, including the specific chiral structure, length, type of CNTs used, diameter, and temperature. In this topic, the effects of chirality, diameter, and length of single-walled carbon nanotubes (SWNTs) on the thermal properties were studied using the reverse non-equilibrium molecular dynamics (RNEMD) method and the Tersoff interatomic potential of carbon–carbon based on the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). For the shorter SWNTs, the effect of chirality on the thermal conductivity is more obvious than for longer SWNTs. Thermal conductivity increases with increasing chiral angle, and armchair SWNTs have higher thermal conductivity than that of zigzag SWNTs. As the tube length becomes longer, the thermal conductivity increases while the effect of chirality on the thermal conductivity decreases. Furthermore, for SWNTs with longer lengths, the thermal conductivity of zigzag SWNTs is higher than that of the armchair SWNTs. Thermal resistance at the nanotube–nanotube interfaces, particularly the effect of CNT overlap length on thermal resistance, was studied. The simulation results were compared with and in agreement with the experimental and simulation results from the literature. The presented approach could be applied to investigate the properties of other advanced materials.

Temperature Dependence of the Band Gap of Completely Fluorinated/Hydrogenated Carbon Nanotubes: The Role of One-Dimensional Chains

The temperature dependence of the band gap Eg(T) in zigzag single-walled carbon nanotubes at the maximum (50%) fluorination and hydrogenation has been theoretically investigated for three coating versions. It has been shown that the character of coating dramatically affects the dependence Eg(T), which may vary over a wide range from very weak (typical of pure carbon nanotubes) to strong (typical of bulk semiconductors). The character of the temperature behavior Eg(T) is directly related to the formation of one-dimensional alternating chains in nanotubes. The main factors determining this dependence are the diameter of carbon nanotube, impurity position, and impurity type.

DFT study on adsorption of small gas molecules on Pt-capped armchair and zigzag single-walled carbon nanotubes

The adsorption of small gas molecules (CO, O2 and N2) on Pt-capped armchair and zigzag single-walled carbon nanotubes (SWCNT) has been investigated by density functional theory (DFT) method to determine the potential for gas sensor detection. Results indicated that O2 and N2 molecules with lower adsorption energies (1.66 eV and 1.00 eV) exhibited weak chemical adsorption on SWCNT(4,4)-Pt. However, CO demonstrates strong chemical adsorption with a high adsorption energy of 2.23 eV on SWCNT(4,4)-Pt. The adsorption energy of CO on SWCNT(7,0)-Pt shows the chemical adsorption between CO and SWCNT(7,0)-Pt. In addition, these findings also implied Pt-capped SWCNT could act as small gas molecule sensors to detect CO toxic gas at room temperature. In this system, CO is the electron donor and SWCNT-Pt is the electron receptor. The interaction of Pt and carbon nanotube backbone delocalized π electrons could not only increases the conductivity of SWCNT-Pt, but also enhances the conductivity of SWCNT-Pt-CO. The HOMO-LUMO gap (Δε) of Pt-capped SWCNT(7,0) reduced from 0.43 eV to 0.39 eV after CO adsorption, and the Δε value of Pt-capped SWCNT(4,4) decreased by 0.08 eV. The electrical conductivity of Pt-capped armchair and zigzag SWCNT has increased after the adsorption of CO molecule. The results may be helpful for designing a promising Pt-capped SWCNT-based CO sensors.

Observing Axial Chirality of Chiral Single-Wall Carbon Nanotubes by Helicity-Dependent Raman Spectra.

Helicity-dependent Raman spectra of an isolated, chiral, single-wall carbon nanotube (SWNT) are reported using circularly polarized light. A polar plot of polarized Raman intensity for the radial breathing mode (RBM), which is excited by left-handed or right-handed circularly polarized light, shows asymmetric angle dependence relative to the nanotube axis direction, which reflects the axial chirality of a SWNT. The asymmetry in the polar plot of the RBM can be analyzed by a complex Raman tensor. The complex phase of each component of the Raman tensor has a maximum at chiral angle θ = 15° of a SWNT which is between two achiral SWNTs, that is, zigzag (θ = 0°) and armchair (θ = 30°) SWNTs. Considering the interaction between the chiral SWNT and the circularly polarized light, we discuss the origin of the complex phases excited by the opposite helicity of the circularly polarized light.

Glycine Active Sites Analysis from a Geometrical Perspective: A DFT Study.

Density functional theory calculations of 2D materials and biological molecules have been used to evaluate disease progression through biosensing. In this case, a glycine molecule in normal and zwitterionic form was evaluated on its interaction with zigzag single-walled carbon nanotubes, graphene sheets, and molybdenum disulfide sheets. Glycine was rotated in order to interact with the materials at different active sites. Binding and cohesion energies, band gaps, and charge transfer for the systems were obtained. Binding and cohesion for the interaction between normal glycine and 2D materials result in better outcomes with the presence of a dangling bond using van der Waals correction, giving the more stable results for glycine and carbon nanotubes in the plane ZY and glycine with graphene in the plane YX, respectively. For zwitterion glycine, binding and cohesion energies are better without a dangling bond supported on graphene in the plane ZX. Charge transfer results for normal glycine show a better interaction for glycine and molybdenum disulfide in the plane ZY, while for zwitterion glycine, higher charge transfer is reported in graphene (ZX). Furthermore, the density of states of normal glycine exhibits an improvement in the band gap for carbon related materials (more semiconductor behavior) and a slight decrease in semiconductor behavior for molybdenum disulfide.

Wiener indices of zigzag single walled carbon nanotubes and related nanotories

The Wiener indices of zigzag single walled carbon nanotubes (SWCNT) designated as (h, 0) and respective nanotori are expressed analytically as well recursively. The bond dissociation energies per CC bond (BDEC-C) and Young’s modulus of such nanotubes with fixed r but varying h (>5) are found to bear excellent linear correlations with the logarithm of their Wiener indices. Young’s moduli data for nanotubes (h, 0) with varying both h and r do not correlate linearly with the logarithm of Weiner indices but fit well with the sigmoidal (Boltzmann) curve.

Electronic and optical properties of SWCNTs and spin-orbit coupling effect on their electronic structures: First-principle computing

In this research, electronic and optical properties of armchair (7,7), zigzag (7,0), and chiral (4,2) configurations of Single-Walled Carbon Nanotubes (SWCNT) and the effect of spin-orbit coupling (SOC) on their electronic structures were studied with density functional theory (DFT) computing. The armchair, zigzag, and chiral SWCNT structures were built using the CASTEP software. Then, this code was used to calculate the band structures, density of states and optical properties of these systems. Electronic and optical properties of SWCNT material could be influenced by its configuration, such as the bandgap energy, total density of states (TDOS) and partial density of states (PDOS), absorption coefficient, dielectric function, optical conductivity, complex refractive index, and the loss function. In the absence or presence of SOC effect, armchair, zigzag and chiral nanotubes are semiconductors. SOC causes the bandgap energy to increase and the TDOS of "armchair, zigzag, and chiral SWCNTs" to alter. These results provide crucial physical information regarding the control of the electronic properties of SWCNTs using SOC.

The carrier transport properties of zigzag carbon nanotubes with intrinsic defects: An investigation from first principles

Through first-principles calculations, the effects of intrinsic defects on the carrier transport properties of zigzag single-walled carbon nanotubes are investigated. The calculation includes three intrinsic defects: Stone-Wales (SW) defects, single vacancy (SV) defects, and double vacancy (DV) defects. According to the results of the calculations, SW defects improve the carrier mobility of CNT(7, 0), whereas SV and DV defects hinder these properties of CNT(7, 0). The band structure and current-voltage characteristics provide additional support for this conclusion. In addition, the effect of size on the carrier transport properties of intrinsically defective CNT(n, 0) n = 7–15 is considered. When SW defects are introduced into pure CNT(n, 0), the obtained results indicate that the electron mobilities of 3N + 1 and 3N + 2 group structures will increase significantly, and the carrier transport properties will be enhanced. However, the presence of SV or DV defects will increase the effective carrier mass of pure CNT(n, 0). In these instances, the electron and hole mobility in the majority of structures will decrease.

Energies Exploration for the Troponine Molecule Supported on Carbon Nanomaterials: DFT Study.

Density functional theory calculations have been used to elucidate structural parameters of pristine cardiac Troponin I and its interaction with carbon nanomaterials. In this case, zigzag single-walled carbon nanotubes and graphene sheets were selected. Troponin I interacted horizontally (leusine terminal) and vertically (lysine terminal) with the nanomaterials. Cohesion and binding energies, band gaps, and charge transfer for the systems were obtained. Cohesion for troponin I supported on graphene and single-walled carbon nanotube in the horizontal position was found to be the most viable system. Binding for the interaction between troponin I and a nanotube in the horizontal position was found to be the most stable with a value of 0.002 eV that increases to 0.004 eV with a van der Waals correction. Furthermore, the density of states exhibits an improvement in band gap for graphene sheets, and finally, a higher charge transfer was reported for troponin I in its horizontal form supported on a zigzag single-walled carbon nanotube.

Analytical forms of the coefficients of the factored characteristic polynomials for zigzag SWCNT graphs

Factors of characteristic polynomials (CP) of zigzag single walled carbon nanotube (SWCNT) graphs have been constructed in generalized forms using rotational symmetry with respect to the tube axis. The CP coefficients in the factors have been expressed in analytical forms involving derivatives of different powers of pj, where pj=(1+ωj)(1+ωj*), ωj=0,1,2,…,(R−1), are the R-th roots of unity and R is the number of fused hexagonal rings per belt in the SWCNT graph. Some important results regarding total π-electron energy per electron, HOMO-LUMO energy gap and number of Kekulé structures for the SWCNTs have been derived from an analysis of the CPs and graph eigenspectra.

Chemical covalent connection of carbon nanotubes for related structural manufacturing: A molecular dynamics study

Carbon nanotubes (CNTs) with junction plays an important role in nanomaterial and nano-devices, especially the junction constructed by covalent bonds. However, the connection process between single-walled carbon nanotubes (SWCNTs) could hardly be observed experimentally on an atomic scale and its connection strength is difficult to accurately measure. Hence, this work investigates the atomic reconstruction and evolution of the structure of SWCNTs at joint area and the connection strength of the joined SWCNTs by molecular dynamics (MD) simulation. Various connection effects between two types of typical SWCNTs, i.e. metallic SWCNTs and semiconducting SWCNTs, are investigated for the smooth covalent connection with high mechanical strength. The simulation results indicate that energy parameters (pulse-widths, pulse number, and temperature) and structure parameters (relative rotation angles, end type and chirality of SWCNTs) have great influence on the connection process. However, the size of energy zone and diameter for both armchair and zigzag SWCNTs make little difference to its connection process and connection strength under certain conditions. This study reveals that whether armchair or zigzag SWCNTs, there is an optimal set of energy and structure parameters to connect them into an ideal hexagonal junction with high mechanical strength. The critical technical parameters are obtained in this study for the optimal covalent connection of SWCNTs, which provides enlightening significance to manufacture the covalent SWCNTs junctions.

An extended model for chirality selection in single-walled carbon nanotubes.

The chirality selective production of single-walled carbon nanotubes (SWCNTs) continues to represent one of the most important technological challenges. In this study, an extended model which considers all steps of the SWCNT growth process, including adsorption, decomposition, diffusion, and incorporation, is applied, for the first time, to obtain chirality selection in the SWCNT populations. We show that the dependence of the population distribution on chirality, defined as a product of the nucleation probability and the growth rate, has a volcano-shape. The model is in good agreement with the reported experimental studies and supports the results which show the surplus of near armchair or near zigzag SWCNTs. The present work emphasizes the role of the catalyst in chirality selection via optimization of chemisorption strength between the carbon species and the catalyst surface needed to achieve stable nucleation and fast growth rates. The obtained results can be used in catalyst designs to define the pathways towards the growth of SWCNTs with specific chiralities exhibiting distinguished electronic properties.

Nanofacet-density scaling on zig-zag carbon nanotubes within the kinetic 5-vertex growth model

Nanofacets density at the edge of a growing zig-zag single-walled carbon nanotube is investigated by means of a kinetic 5-vertex model. The model comprises, carbon atoms deposition and diffusion events that are assumed Markov processes. The nanotube synthesis temperature, the carbon atomic flux from the catalyst nanoparticles, and the diffusion length are the model physical parameters considered. The kinetic equation describing the nanotube growth is solved by Kinetic Monte Carlo simulations and the average nanofacet density at the nanotube edge is calculated. It is found that this quantity displays interesting behaviors, in particular a power-law behavior with the diffusion length and the growth time.

Effects of Doping Cadmium Atoms on the Electronic and Optical Properties of (n, 0) Zigzag SWCNTs: DFT Approach

Effects of doping cadmium atoms on the electronic and optical properties of (n, 0) zigzag single-wall carbon nanotubes SWCNTs are investigated by density functional theory DFT, using ultrasoft pseudopotential generalized gradient approximation GGA approach. The electronic and optical properties of the zigzag SWCNTs are susceptible and dependent on the n index and diameter of the tube; these features have only in nanotubes. Adding any impurity to the Zigzag SWCNTs must be caused to change in properties. The density of states for Cd-doped and un-doped SWCNTs increases with an increase in n index because of overlap valence and conduction bands in all situations (small bandgap). All samples have metallic characteristics. Almost all absorption and reflectivity spectra peaks are produced in the UV range. It can be noted that the peaks of the un-doped samples are higher than that of Cd-doped. Consequently, the material’s ability to store energy and photon absorption for un-doped nanotubes is larger than Cd-doped zigzag SWCNTs. These results are achieved in the figures of dielectric functions.

Diameter-Change-Induced Transition in Buckling Modes of Defective Zigzag Carbon Nanotubes.

In general, the insertion of Stone-Wales (SW) defects into single-walled carbon nanotubes (SWNTs) reduces the buckling resistance of SWNTs under axial compression. The magnitude of reduction is more noticeable in zigzag-type SWNTs than armchair- or chiral-type SWNTs; however, the relation between the magnitude of reduction and aspect ratio of the zigzag SWNTs remains unclear. This study conducted molecular dynamics (MD) simulation to unveil the buckling performance of zigzag SWNTs exhibiting SW defects with various tube diameter. The dependencies of energetically favorable buckling modes and the SW-defect induced reduction in the critical buckling point on the tube diameter were investigated in a systematic manner. In particular, an approximate expression for the critical buckling force as a function of the tube diameter was formulated based on the MD simulation data.