Infinite Nanotubes Research Articles

(Invited) Is the [5,5] C120-D5d Fullertube a Metal?

Single-walled nanotubes (SWNTs) with a roll-up vector (n = m) have long been predicted to exhibit metallic behavior at infinite nanotube lengths.1 Moreover, in contrast with normal metals, armchair nanotubes e.g., [5,5] should result in exceptional ballistic transport properties.2 However, the question remains at what finite length of a SWNT or fullertube does metallic character begin, if at all. From a computational viewpoint, Cioslowski has shown that the HOMO-LUMO bandgap decreases to ~1 eV in an oscillatory fashion in approaching [5,5] C200 fullertubes.3 Although the HOMO-LUMO gap has been extensively used to predict the kinetic stability of fullerenes and metallofullerenes with less than 100 carbon atoms, Fowler has argued that the HOMO-LUMO gap can not be used to predict the kinetic stability of large fullerenes.4 More recently, Lilijeroth and coworkers have measured the experimental and DFT HOMO-LUMO gap for graphene nanoribbons (GNR) and find that GNRs with lengths of 5 nm have bandgaps of ~0.1 eV.5 These workers also point out that DFT calculated HOMO-LUMO bandgaps are always overestimated relative to experimental values. In this presentation, I will present the evidence in support of metallic character for [5,5] C120-D5d.6,7

Analyzing fine scaling quantum effects on the buckling of axially-loaded carbon nanotubes based on the density functional theory and molecular mechanics method

In this paper, the quantum effects of fine scaling on the buckling behavior of carbon nanotubes (CNTs) under axial loading are investigated. Molecular mechanics and quantum mechanics are respectively utilized to study the buckling behavior and to obtain the molecular mechanics coefficients of fine-scale nanotubes. The results of buckling behavior of CNTs with different chiralities with finite and infinite dimensions are given, and a comparison study is presented on them. The differences between finite and infinite nanotubes reflect the quantum effects of fine scaling on the buckling behavior. In addition, the results show that the dimensional changes highly affect the mechanical properties and the buckling behavior of CNTs to certain dimensions. Moreover, dimensional changes have a significant effect on the critical buckling strain. Beside, in addition to the structure dimensions, the arrangement of structural and boundary atoms have a major influence on the buckling behavior.

Solution of the Spectral Problem for (2m,m) Carbon Nanotubes by Green's Function Method

The exact solution of the spectral problem for an infinite (2m,m) carbon nanotube (CNT) is obtained from the analytic solution to the Schrödinger equation for the tight‐binding Hückel‐type Hamiltonian. Explicit expressions for Green's functions of chiral (2m,m) CNTs are obtained and the electronic structure of these CNTs is discussed. The (2m,m) nanotubes with a medium‐chiral angle equal to 19.1° are considered as an intermediate case between the thoroughly investigated achiral armchair and zigzag nanotubes.

Tuning of Structure Evolution and Electronic Properties through Palladium-Doped Boron Clusters: PdB16 as a Motif for Boron-Based Nanotubes.

Transition metal-doped electronic deficiency boron clusters have led to a vast variety of electronic bonding properties in chemistry and materials science. We have determined the ground state structures of PdBn0/- (n = 10-20) clusters by performing CALYPSO search and density functional theory (DFT) optimization. The identified lowest energy structures for both neutral and anionic Pd-doped boron clusters follow the structure evolution from two dimensional (2D) planar configurations to 3D distorted Pd-centered drum-like or tubular structures. Photoelectron spectra are simulated by time-dependent DFT theoretical calculations, which is a powerful method to validate our obtained ground-state structures. More interestingly, two "magic" number clusters, PdB12 and PdB16, are found with enhanced stability in the middle size regime studied. Subsequently, molecular orbital and adaptive natural density partitioning analyses reveal that the high stability of the PdB16 cluster originates from doubly σ π aromatic and bonding interactions of d-type atomic orbitals of the Pd atom with tubular B16 units. The tubular C8v PdB16 cluster, with robust relative stability, is an ideal embryo for forming finite and infinite nanotube nanomaterials.

Recirculation Flow of Nanofluid Through Periodic Nanotube with Hexagonal Cross-Section

In this paper, we have investigated the recirculation flow of a nanofluid in the developed flow zones of an infinite periodic nanotube with a hexagonal cross-section. A numerical analysis is commenced to identify the existence of single and double recirculation zones for various geometric parameters. The boundary element method (BEM) has been formulated for an unbound interim nanotube for solving the governing equations. We have developed the codes for the BEM method in FORTRAN 90, and the graphs have been plotted in MATLAB 2016. We have various geometric parameters to inaugurate circumstances for the onset of recirculation. We have found recirculation flow through this type of periodic tube for a set of geometric parameters such as amplitude, wavelength and throat radius etc. Firstly recirculation flow in the expansion region of the nanotube is prophesied to arrive beyond a critical amplitude and second order recirculation zone is also predicted for still higher amplitudes. The recirculation flow has great importance in the application, for example, it can be used in the particle separation process.

Energy barriers for collapsing large-diameter carbon nanotubes

Single-wall carbon nanotubes (SWNTs) are best known in their hollow cylindrical shapes, but the ground state of large-diameter tubes actually corresponds to a collapsed dumbbell-like structure, where the opposite sides of the nanotube wall are brought in contact and stabilized by van der Waals attraction. For those tubes, the cylindrical shape is metastable and it is interesting to investigate the energy barrier for jumping from one configuration to another. We calculate the energy barrier for SWNT collapse by considering a transition pathway that consists of an initial local deformation that subsequently propagates itself along the SWNT axis. This leads to finite and physically meaningful energy barriers in the limit of infinite nanotubes. Yet, such barriers are surprisingly large (tens of eV) and therefore virtually unsurmountable, which essentially prevents the thermal collapse of a metastable cylindrical at any reasonable temperatures. Moreover, we show that collapse barriers increase counterintuitively with SWNT diameter. Finally, we demonstrate that, despite such huge barriers, SWNTs may collapse relatively easily under external radial forces and we shed light on recent experimental observations of collapsed and cylindrical SWNTs of various diameters.

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules.

This article presents a detailed protocol for synthesis of small circular DNA molecules, annealing of circular DNA motifs, and construction of 1D and 2D DNA nanostructures. Over decades, the rapid development of DNA nanotechnology is attributed to the use of linear DNAs as the source materials. For example, the DAO (double crossover, antiparallel, odd half-turns) tile is well-known as a building block for construction of 2D DNA lattices; the core structure of DAO is made from two linear single-stranded (ss) oligonucleotides, like two ropes making a right hand grannyknot. Herein, a new type of DNA tiles called cDAO (coupled DAO) are built using a small circular ss-DNA of c64nt or c84nt (circular 64 or 84 nucleotides) as the scaffold strand and several linear ss-DNAs as the staple strands. Perfect 1D and 2D nanostructures are assembled from cDAO tiles: infinite nanowires, nanospirals, nanotubes, nanoribbons; and finite nano-rectangles. Detailed protocols are described: 1) preparation by T4 ligase and purification by denaturing PAGE (polyacrylamide gel electrophoresis) of small circular oligonucleotides, 2) annealing of stable circular tiles, followed by native PAGE analysis, 3) assembling of infinite 1D nanowires, nanorings, nanospirals, infinite 2D lattices of nanotubes and nanoribbons, and finite 2D nano-rectangles, followed by AFM (Atomic Force Microscopy) imaging. The method is simple, robust, and affordable for most labs.

Electronic and optical characteristics of phosphorus-doped carbon nanotubes: a first principle study

The electronic and optical properties of pure, phosphorus doped infinite and finite single walled carbon nanotubes (n, 0) (n = 4, 5 and 6) with different doping degree were investigated with the combination of density functional theory (DFT) and Non-Equilibrium Green’s function (NEGF) formalisms at room temperature. It was found that depending on the chirality, phosphorus atoms may eliminate the Van Hove Singularity energy or increase the density of states (DOS) at Fermi level. Also, replacing the carbons by phosphorus atoms increases DOS at Fermi level. The π bonds between carbon and phosphorus are responsible for extraordinary DOS at Fermi level as well. Moreover, each P atom in the simulated tubes contains about 2.62e-2.94e. Replacing carbon atoms by phosphorus eventuates in the reduction of optical susceptibility and the statics refractive index. Last but not least, despite pure SWCNTs, the doping results in the lower static refractive index as well as the increment of an intraband optical gap for the parallel to tube axis polarization through P-SWCNTs.

The electron properties of infinite length single-walled silicon nanotubes are studied by density functional theory

In this article, we aim to use LGTO-PBC-DFT calculation method with PBEPBE/6–31G(d) basis sets and PBC model to optimize geometric structure, obtain electron characteristics and band gaps of (n, m) chiral (6 ≤ n ≤ 16, 2 ≤ m ≤ 8); (n, 0) zigzag (3 ≤ n ≤ 15) and (n, n) armchair (2 ≤ n ≤ 8) pure infinite length single-walled Silicon nanotubes. We have obtained that the HOCO-LUCO gaps decrease with the radii of the SWSiNTs increase by using the PBEPBE functional and 6–31G(d) basis set. most of the infinite length SWSiNTs which we studied are narrow band gaps semiconductors. perhaps the surface structure is the most important factor affecting the band gap of the nanotubes. There have been a research on the infinite silicon nanotubes and with the increase of the tube radius, an indirectdirect band gap transition has been revealed. For all the armchair SWSiNTs, the infinite zigzag SiNTs (n,0), (3 ≤ n ≤ 9) and the infinite chiral SWSiNTs (6, 2), (9, 3), (10, 5), (12, 6) are semiconductors with indirect band gaps. While for the infinite zigzag SiNTs (n, 0) 15 ≥ n ≥ 10, and the infinite chiral SWSiNT (12, 4) are semiconductors with direct gaps at Ｘ point, the direct gaps open at Ｘ point. It is possible that direct band gap will become potential building blocks for electronic and optoelectronic devices.

The electron properties of infinite length single-walled silicon nanotubes are studied by density functional theory

In this article, we aim to use LGTO-PBC-DFT calculation method with PBEPBE/6–31G(d) basis sets and PBC model to optimize geometric structure, obtain electron characteristics and band gaps of (n, m) chiral (6 ≤ n ≤ 16, 2 ≤ m ≤ 8); (n, 0) zigzag (3 ≤ n ≤ 15) and (n, n) armchair (2 ≤ n ≤ 8) pure infinite length single-walled Silicon nanotubes.We have obtained that the HOCO-LUCO gaps decrease with the radii of the SWSiNTs increase by using the PBEPBE functional and 6–31G(d) basis set. Most of the infinite length SWSiNTs which we studied are narrow band gaps semiconductors. Perhaps the surface structure is the most important factor affecting the band gap of the nanotubes. There have been a research on the infinite silicon nanotubes and with the increase of the tube radius, an indirectdirect band gap transition has been revealed.For all the armchair SWSiNTs, the infinite zigzag SiNTs (n,0), (3 ≤ n ≤ 9) and the infinite chiral SWSiNTs (6, 2), (9, 3), (10, 5), (12, 6) are semiconductors with indirect band gaps. While for the infinite zigzag SiNTs (n, 0) 15 ≥ n ≥ 10, and the infinite chiral SWSiNT (12, 4) are semiconductors with direct gaps at Ｘ point, the direct gaps open at Ｘ point. It is possible that direct band gap will become potential building blocks for electronic and optoelectronic devices.

Magnetic excitations of carbon nanotubes in chiral model of graphene

Within the scope of the chiral model of graphene in 8-spinor realization, suggested earlier [1, 2], the combined spinor field Ψ is used as a new order parameter, which contains information on spin and quasispin excitations in graphene (8-spinor part) and also that on sp-hybridization effect of carbon valence electrons [SU(2)-matrix part]. This model admits two kinds of configurations describing, in the long-wave approximation, the graphene mono-atomic plane and the carbon nanotube respectively. The first one is given by the domain-wall (or kink-like) solution and the second one is described by the hedgehog ansatz with large topological charge (winding number n). We consider the infinite carbon nanotube in a static external magnetic field oriented along the tube and analyze the structure of the magnetic intensity on the outside. The diamagnetic behavior of the material is shown by the perturbation method which proves to be self-consistent for n ≫ 1.

Permeability of nanonet structures constructed on the basis of carbon tubes

An approximate integration of a potential of paired molecular interactions over the circumferential coordinate is used to find the potential of the interaction between a molecule and an infinite carbon nanotube (CNT). Based on the obtained energy of interaction between the tube and the molecules, local effective radii of the investigated carbon structures with respect to the molecules of the separated gas mixture are found. This makes it possible to calculate permeability of a single-layer, along with a two-layer CNT packing. The conducted research allowed calculating permeability of a nanonet structure as permeability of a two-layer packing of carbon nanotubes for the first time.

Modeling of Encapsulation of Alanine Amino Acid inside a Carbon Nanotube

Carbon nanotubes play a significant role in facilitating and controlling the transportation of drugs and biomolecules through their internal and external surfaces. Carbon nanotubes are also selective nano-devices because of their outstanding properties and huge potential use in many bio-medical and drug delivery applications. The proposed model aims to investigate the encapsulation of Alanine molecule inside a single-walled carbon nanotube, and to determine the minimum energy arising from the Alanine interacting with single-walled carbon nanotubes with variant radius r. We consider two possible structures as models of Alanine amino acid which are a spherical shell and discrete configuration modelled as comprising three components: the linear molecule, cylindrical group and CH3 molecule as a sphere, all interacting with infinite cylindrical single-walled carbon nanotube. The adsorption of Alanine amino acid and magnitude of total energy for each orientation calculated based on the nanotube radius r and the orientation angle φ which the amino acid makes with central axis of the cylindrical nanotube. Our results indicate that the Alanine molecule encapsulated inside the nanotubes of radius greater than 3.75 A, which is in excellent agreement with recent findings.

Distances on nanotubical structures

Nanotubical graphs are obtained by wrapping a hexagonal grid into a cylinder, and then possibly closing the tube with patches. In this paper we determine the number of vertices at distance d from a particular vertex in an open (k, l) nanotubical graph. Surprisingly, this number does not depend much on the type of the nanotubical structure, but mainely on its circumference. In particular, for \(d\ge 2k\) it is \(2\,(k+l)\) for an infinite open nanotube. This result can be used as a tool for precise evaluation of distance based topological indices for nanotubical structures. The presented results imply an interesting conclusion that these indices do not distinguish the type of the nanotubes very well.

DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13C NMR chemical shifts

13C NMR chemical shifts of selected finite-size models of pristine zigzag single walled carbon nanotubes (SWCNTs) with a diameter of ∼0.4–0.8nm and length up to 2.2nm were studied theoretically. Results for finite SWCNTs models containing 1, 4 and 10 adjacent bamboo-type units were compared with data obtained for infinite tubes in order to estimate the reliability of small finite models in predicting magnetic properties of real-size nanotubes and to assess their tube-length dependence. SWCNTs were fully optimized using unrestricted density functional theory (DFT-UB3LYP/6-31G*). Cyclacenes, as the shortest models of open-ended zigzag SWCNTs, with systematically varying diameter were calculated as well. GIAO NMR calculations on the SWCNT and cyclacene models were performed using the BHandH density functional combined with relatively small STO-3Gmag basis set, developed by Leszczyński and coworkers for accurate description of magnetic properties. Regular changes of carbon 13C chemical shifts along the tube axis of real size (6, 0) and (9, 0) zigzag carbon nanotubes were shown. The 13C NMR shifts according to increasing diameter calculated for zigzag (n, 0, n=5–10) cyclacenes followed the trends observed for zigzag (n, 0) SWCNTs. The results for 4-units long SWCNTs match reasonably well with the data obtained for infinite zigzag (n, 0) SWCNTs, especially to those with bigger diameter (n=8-15). The presence of rim hydrogens obviously affects theoretical 13C chemical shieldings and shifts in cyclacenes and thus cyclacenes can provide only approximate estimation of 13C NMR parameters of real-size SWCNTs. The NMR properties predicted for the longest 10-units long models of SWCNTs reliably correspond to results obtained for infinite nanotubes. They were thus able to accurately predict also recently reported experimental chemical shift of chiral (6, 5) SWCNT.

A mixed basis density functional approach for one-dimensional systems with B-splines

A mixed basis approach based on density functional theory is extended to one-dimensional (1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the third periodic direction. This approach will significantly reduce the number of the basis and therefore is computationally efficient for the diagonalization of the Kohn–Sham Hamiltonian. For 1D systems, B-spline polynomials are particularly useful and efficient in two-dimensional spatial integrations involved in the calculations because of their absolute localization. Moreover, B-splines are not associated with atomic positions when the geometry structure is optimized, making the geometry optimization easy to implement. With such a basis set we can directly calculate the total energy of the isolated system instead of using the conventional supercell model with artificial vacuum regions among the replicas along the two non-periodic directions. The spurious Coulomb interaction between the charged defect and its repeated images by the supercell approach for charged systems can also be avoided. A rigorous formalism for the long-range Coulomb potential of both neutral and charged 1D systems under the mixed basis scheme will be derived. To test the present method, we apply it to study the infinite carbon-dimer chain, graphene nanoribbon, carbon nanotube and positively-charged carbon-dimer chain. The resulting electronic structures are presented and discussed in detail.

Magnetization Reversal in a Double-Walled Infinite Nanotube

The nucleation fields of magnetization reversal is calculated here for an infinite, hollow nanotube formed by two ferromagnetic walls. The two tubes can reverse either by curling or by rotation in unison, and have thus four separate reversal modes. The properties of the reversal fields are summarized by means of a series of phase diagrams which display the dependence of the reversal mode on the inner and outer radius of the nanotube. Under certain conditions a large range of nucleation fields my be achieved by a small variation of the nanotube radius.

Bottom‐Up Construction of Mesoporous Nanotubes from 78‐Component Self‐Assembled Nanobarrels

AbstractSegmental and continuous hexagonal‐packed mesoporous metal–organic nanotubes (MMONTs) with outside diameters of up to 4.5 nm and channel sizes of 2.4 nm were hierarchically constructed by a rational multicomponent self‐assembly process involving starting from [L2Pd2(NO3)2] (L=o‐phenanthroline or 2,2′‐bipyridine) and 4‐pyridinyl‐3‐pyrazole. An unprecedented crystallization‐driven cross‐linking between discrete nanobarrel building units by spontaneous loss of the capping ligands to form infinite nanotubes was observed. Such a barrel‐to‐tube transformation provides new possibilities for the fabrication of MMONTs using the solution bottom‐up approach.

Bottom-Up Construction of Mesoporous Nanotubes from 78-Component Self-Assembled Nanobarrels.

Segmental and continuous hexagonal-packed mesoporous metal-organic nanotubes (MMONTs) with outside diameters of up to 4.5 nm and channel sizes of 2.4 nm were hierarchically constructed by a rational multicomponent self-assembly process involving starting from [L2Pd2(NO3)2] (L=o-phenanthroline or 2,2'-bipyridine) and 4-pyridinyl-3-pyrazole. An unprecedented crystallization-driven cross-linking between discrete nanobarrel building units by spontaneous loss of the capping ligands to form infinite nanotubes was observed. Such a barrel-to-tube transformation provides new possibilities for the fabrication of MMONTs using the solution bottom-up approach.

Electronic structure and transport in graphene/haeckelite hybrids: an ab initio study

We combine ab initio density functional theory (DFT) structural studies with DFT-based nonequilibrium Green's function calculations to investigate how the presence of non-hexagonal rings affects electronic transport in graphitic structures. We find that infinite monolayers, finite-width nanoribbons, and nanotubes formed of 5–8 haeckelite with only 5- and 8-membered rings are generally more conductive than their graphene-based counterparts. The presence of haeckelite defect lines in the perfect graphitic structure, a model of grain boundaries in CVD-grown graphene, increases the electronic conductivity and renders it highly anisotropic.