Encapsulation of small fullerenes into nitrogenated holey nanotubes: a density functional theory study

Encapsulation of fullerene into nanotubes based on a C₂N sheet, known as nitrogenated holey graphene, was investigated using density functional theory. The structural and electronic properties of these carbon hybrid materials, consisting of nitrogenated holey nanotubes and a small C₂₀ fullerene, were studied. The formation energies showed that encapsulation of the fullerene into the nitrogenated holey nanotube is an exothermic process. To characterise the electronic properties, the electronic band structure and density of states of armchair and zigzag nitrogenated holey nanotubes were calculated. Filling these nanotubes with the C₂₀ fullerene resulted in a p-type semiconducting character. The energy band gap of the nitrogenated holey nanotubes decreased with fullerene encapsulation. The results are indicative of the possibility of band gap engineering by encapsulation of small fullerenes into nitrogenated holey nanotubes.     

A study of carbon nanosystems using the Hubbard model

The Hubbard model is used as a framework for analyzing carbon nanosystems: the fullerenes C₆₀ and C₈₀ and open-ended carbon nanotubes with chiralities (5, 5) and (10, 10) of various lengths. In the strong-correlation limit, the model predicts that open carbon nanotubes have a lower energy per atom as compared to C₆₀ and C₈₀ fullerenes. This finding contradicts the conventional view that dangling bonds increase the energy of a system. However, the increase, if any, is due to the presence of five-member carbon rings in fullerenes. The energy per atom should be higher for the five-member carbon ring compared to the six-member one, because the former cannot exist in a lower energy singlet state. Carbon nanotube growth is explained. The ionization energies and electron affinities of C₆₀ and C₈₀ fullerenes are calculated and found to agree well with experimental data.     

One-dimensional self-assembly of C60 molecules on periodically wrinkled graphene sheet: A Monte Carlo approach

Periodically wrinkled graphene sheet is of interest as a building block to develop nanoelectronic devices. This work presents that periodically wrinkled graphene sheet can be applied to a pattern, to form one-dimensionally well-ordered C₆₀ molecules, via Monte Carlo simulations using the data obtained from atomistic calculations. Since the valleys of a sinusoidal graphene surface provide energetic ground sites for absorbed C₆₀ molecules, their motions seeking stable positions lead to one-dimensional self-assembly. The size of the wrinkles, the density of adsorbed C₆₀ molecules, and the temperature are very important parameters to obtain a one-dimensional C₆₀ molecules array. We estimate high one-dimensional diffusion coefficients of C₆₀ molecules on the wrinkled graphene surface. Our results can provide a possible approach to make a quantum information array, based on endohedral fullerenes and a graphene quantum dot array, by transforming C₆₀ molecules to graphene nanoflakes.     

Periodic Minimizers in 1D Local Mean Field Theory

There are not many physical systems where it is possible to demonstate rigorously that energy minimizers are periodic. Using reflection positivity techniques we prove, for a class of mesoscopic free-energies representing 1D systems with competing interactions, that all minimizers are either periodic, with zero average, or of constant sign. Examples of both phenomena are given. This extends our previous work where such results were proved for the ground states of lattice systems with ferromagnetic nearest neighbor interactions and dipolar type antiferromagnetic long range interactions.     

Fullerenes as mass sensors: A numerical investigation

This paper investigates the novel development of a mass sensitive nanosensor based on the use of individual spherical fullerenes. The main advantage of the mass sensing ability of spherical fullerenes in comparison with other nanomaterials such as carbon nanotubes (CNTs) or graphene nanoribbons (GNRs) is the fact that they present almost perfect geometric symmetry and thus a unique vibrational behavior which is independent from the location of the externally added nanoparticle. The study is conducted by the use of a computationally effective numerical scheme based on the adoption of appropriate three dimensional line spring elements as well as point mass elements to simulate the atomistic structure of fullerenes and interatomic interactions appearing between carbon atoms. The free vibration of C₂₀, C₆₀, C₈₀ and C₁₈₀ molecules is analyzed without and with an external nanoparticle of specific mass attached on their structure to calculate the arisen change in their natural frequencies and corresponding shape modes. A parametric study concerning the magnitude and location of the added mass is performed in order to evaluate the mass sensing ability of the fullerenes under consideration.     

Restricted Three Body Problems at the Nanoscale

In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C₆₀ fullerenes, and a carbon atom and two C₆₀ fullerenes. We model the van der Waals forces between the fullerenes by the Lennard–Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C₆₀ fullerenes at the nanoscale. We find that the maximum collective angular velocity of the two and three fullerenes systems reach the terahertz range and we also determine the stationary points and the points which have maximum velocity for the carbon atom, for the carbon atom and the two fullerenes system.     

Ground States of the 2D Sticky Disc Model: Fine Properties and N 3/4 Law for the Deviation from the Asymptotic Wulff Shape

We investigate ground state configurations for a general finite number N of particles of the Heitmann-Radin sticky disc pair potential model in two dimensions. Exact energy minimizers are shown to exhibit large microscopic fluctuations about the asymptotic Wulff shape which is a regular hexagon: There are arbitrarily large N with ground state configurations deviating from the nearest regular hexagon by a number of ～N ^3/4 particles. We also prove that for any N and any ground state configuration this deviation is bounded above by ～N ^3/4. As a consequence we obtain an exact scaling law for the fluctuations about the asymptotic Wulff shape. In particular, our results give a sharp rate of convergence to the limiting Wulff shape.     

Unravelling low lying phonons and vibrations of carbon nanostructures: The contribution of inelastic and quasi-elastic neutron scattering

We illustrate the contribution of inelastic neutron scattering to the understanding of the vibrations and lattice excitations of fullerenes and carbon nanotubes, through some significant experimental results. Particular emphasis is placed on the study of intra and inter-molecular modes of fullerene C₆₀, as well as on the order/disorder transition characteristic of these molecules. In addition, a significant part of this article is dedicated to various intercalation compounds of fullerenes and carbon nanotubes, such as the co-crystal ??fullerene-cubane?? consisting of an arrangement of molecules of spherical and cubic shapes, or the compound called ??peapods??, in which fullerene C₆₀ are inserted inside carbon nanotubes.     

Synthesis of multishell fullerenes by laser vaporization of composite carbon targets

Multishell fullerenes are the smallest among multishell carbon clusters, such as the larger graphitic onions or multishell nanotubes. Unlike classical fullerenes, which have a cage structure and are known to have been synthesized in a variety of sizes (C₆₀, C₇₀, C₈₄, C₁₀₂, etc.), multishell fullerenes have a cage-inside-cage concentric structure, such as double-shell C₆₀@C₂₄₀ or triple-shell C₆₀@C₂₄₀@C₅₆₀. We report on the synthesis of multishell fullerenes by laser vaporization of C₆₀-containing composite carbon targets. Transmission electron microscopy, Raman scattering spectroscopy, and other methods were used for characterization of the product. The yield of the process reaches up to 40%, which permits production in gram amounts even in laboratory conditions.     

The Influence of the Geometric Shape of Carbon Nanoparticles on the Strength Properties of Nanocomposite Materials Obtained by Filling an Epoxy Matrix

Abstract

The effects of filling an epoxy matrix modified with “Viniflex” with carbon nanotubes, fullerene C₆₀, or graphene on the mechanical properties, surface morphologies and glass transition temperatures of the composite materials obtained after curing were studied. It was shown that the largest decrease in glass transition temperature and an increase in impact strength was achieved by the introduction of 0.1 mass% graphene. Filling with graphene and carbon nanotubes increased the bending strength while filling with C₆₀ fullerenes provided the greatest compressive strength and elasticity modulus. An explanation of the results was based on ideas about the relationship of the geometrical shape of the nanofiller to the load direction and features of the phase composition of the composite materials. It is suggested that the carbon nanomaterials had a template effect on the packing of the epoxy matrix chains.     

Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges

We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.     

Stable Quasicrystalline Ground States

We give strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions, but rather are generic in some regions of phase space. We show this by constructing classical lattice-gas models with translation-invariant finite-range interactions and with a unique quasiperiodic ground state which is stable against small perturbations of two-body potentials. More generally, we provide a criterion for stability of nonperiodic ground states.     

On the encapsulation of azafullerenes inside the single-walled carbon nanotubes: Density-functional theory based treatments

We theoretically studied the encapsulation of azafullerene (C₅₉N) inside the single-walled carbon nanotubes (SWCNTs) from the first-principles. Adsorption energy is calculated, and the azafullerene affinities for the typical semiconducting and metallic nanotubes are investigated and compared with those of pure C₆₀ fullerene. It has been found that the azafullerene as well as the fullerene affinity for the semiconducting nanotubes is stronger than that for the metallic ones, and the energy values and binding distances are typical for the physisorption. Our first-principles results indicate that the interaction between SWCNTs and azafullerenes is comparable with the nanotubes-C₆₀ system. The charge analysis shows, however, that the charges have been transferred from the cage to the tube in the azafullerene peapods, while in the fullerene peapods the charges were found to be transferred from the tube to the fullerene nanocage. Furthermore, it was found that the interaction between the considered fullerenes and host nanotubes strongly depends on the tube diameters.     

Quasi-one-dimensional fullerene-nanotube composites: Structure, formation energetics, and electronic properties

Carbon nanotubes coated with close-packed C₆₀ (or C₇₀) fullerenes, which are “attached” to the nanotubes by van der Waals forces, are considered and classified as a new class of nanocomposites. Semiempirical and molecular-dynamics calculations reveal the most energetically stable systems and show that a topological (Stone-Wales) defect on a nanotube can promote a more favorable “attachment” of fullerene to the nanotube. It has been shown that the molecular interaction of the fullerene coating with the nanotube leads to a significant change in its electronic spectrum, namely, to the formation of minibands including a large number of branches associated with the lift of the degeneracy of levels of C₆₀ and to the consolidation of branches of the carbon nanotube into the Brillouin zone smaller than that in the carbon nanotube. This fact should strongly change the interaction of light with such a nanocomposite as compared to carbon nanotubes and fullerenes, which provides prospect of its application in photovoltaics.     

Optical diagnostics for temperature measurement in a DC arcjet reactor used for diamond deposition

2 a-state in this plume. LIF measurements of CH are complicated by the presence of C₃ and we discuss strategies to deal with this interference. The gas temperature describing the rotational distributions obtained for NO, C₂ and CH agree within experimental error. Optical emission measurements indicate that the rotational and vibrational distributions of the excited A-state of CH and a-state of C₂ are characterized by vibrational and rotational populations which are at least 1000 K above the ground state distributions. The excited states are collisionally quenched before their population distributions equilibrate with the gas temperature. We also determine relative populations of the ground and excited states along the axis of the plume between the arcjet nozzle and the substrate and relative populations for a cross section of the jet, midway between the nozzle orifice and the substrate. The measured relative ground and excited state populations for both CH and C₂ show different trends along the plume axis, indicating that the ground and excited states of these molecules are products of different chemical mechanisms; such mechanisms are discussed. Received: 16 July 1996/Revised version: 24 September 1996     

On the Crystallization of 2D Hexagonal Lattices

It is a fundamental problem to understand why solids form crystals at zero temperature and how atomic interaction determines the particular crystal structure that a material selects. In this paper we focus on the zero temperature case and consider a class of atomic potentials V = V ₂ + V ₃, where V ₂ is a pair potential of Lennard-Jones type and V ₃ is a three-body potential of Stillinger-Weber type. For this class of potentials we prove that the ground state energy per particle converges to a finite value as the number of particles tends to infinity. This value is given by the corresponding value for a optimal hexagonal lattice, optimized with respect to the lattice spacing. Furthermore, under suitable periodic or Dirichlet boundary condition, we show that the minimizers do form a hexagonal lattice. Dedicated with admiration to Professor Tom Spencer on occasion of his 60th birthday     

A Refined Threshold Theorem for (1 + 2)-Dimensional Wave Maps into Surfaces

The recently established threshold theorem for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) are globally regular and scatter on \({\mathbb{R}^{1+2}}\). In this note we give a refinement of this theorem when the target is a closed orientable surface, by taking into account an additional invariant of the problem, namely the topological degree. We show that the sharp energy threshold for global regularity and scattering is in fact twice the energy of the ground state for wave maps with degree zero, whereas wave maps with nonzero degree necessarily have at least the energy of the ground state. We also give a discussion on the formulation of a refined threshold conjecture for the energy critical SU(2) Yang–Mills equation on \({\mathbb{R}^{1+4}}\).     

Optical limiting with higher fullerenes

Optical limiting has been investigated for higher fullerenes and compared with C₆₀. The transmission through an aperture placed after solutions of C₇₆, C₇₈, and C₈₄ in tetrahydronaphthalene was measured using Q-switched laser pulses with a wavelength of 532 nm and a pulse width of 8 ns FWHM. Unlike C₆₀, the transmission for these higher fullerene solutions decreased linearly with increasing optical pulse energy. We attribute the linearized optical limiting response to self-defocusing of the optical beam and the absence of excited-state absorption. The ground state absorption spectra for the higher fullerenes suggest their use for optical limiting in the near infrared, and the C₈₄-tetrahydronaphthalene solution was found to be an optical limiter at 1.064 m.     

Energy spectrum of C60 fullerene

The energy spectrum of the C₆₀ fullerene has been calculated in terms of the Shubin-Vonsovskii-Hubbard model using an approximation of static fluctuations. Based on the spectrum, the optical absorption bands at 4.84, 5.88, and 6.30 eV observed experimentally have been successfully explained. It has been concluded that the model used is applicable for the calculation of the energy spectrum and the energy properties of other nanosystems, such as fullerenes of higher orders, carbon nanotubes, and grafen planes.