Graphene Cones Research Articles

Multi-stable straw-like carbon nanotubes for mechanical programmability at microscale

ABSTRACT Inspired by macroscale 3D pixel mechanical metamaterials and microscale straw-like carbon nanotube, we propose a design of multi-stable straw-like carbon nanotubes (MSCNT) via optimizing the structure of a unit to obtain multiple stable states under displacement loading by molecular dynamics. The unit of MSCNT is mirror-symmetrically connected two truncated graphene cones with specific apex angles. By switching the LJ term in AIREBO potential, we verify that the bistability of unit is co-determined by snap-through instability and microscale adhesions. Moreover, we examine the validity of the multi-stability of the unit cells arranged in series and in parallels. Simulation results indicate that the MSCNT can achieve mechanical programmability in microscale, which triggers many potential applications in need of customizing nanoscale mechanical behaviors.

Quantitative crystallographic analysis of individual carbon nanofibers using high resolution transmission electron microscopy and electron diffraction

High resolution transmission electron microscopy (HRTEM) and electron diffraction allow for a thorough crystallographic characterization of the herringbone structure of carbon nanofibers (CNF). A newly developed method for an extended quantitative structural evaluation of single carbon nanofibers is applied. The method is based on quantitative analysis of radial and azimuthal profiles extracted from selected area electron diffraction (SAED) patterns, nano beam electron diffraction (NBED) patterns or power spectra obtained by Fourier transformation of HRTEM images. Precise quantification of structural parameters, in particular cone apex angle, interlayer spacing and undulation of graphene layers is carried out. For the first time a profound interpretation of CNF diffraction patterns is given, proving the rotational disorder of the turbostratic structure and suggesting a random rotation between successive graphene cones. A series of crystallographic analyses along the axis of a single CNF reveal a continuous increase of the interlayer spacing during CNF growth. Additionally, the different techniques HRTEM, SAED, and NBED are evaluated in terms of attainable structural information, precision and applicability to different diameters of CNFs.

Nanochimneys: Topology and Thermal Conductance of 3D Nanotube–Graphene Cone Junctions

Pillared 3D carbon architectures, with the graphene layers and carbon nanotubes connected by topological junctions, have been produced and observed, as reported recently. However, the atomistic details of such junctions are hard to discern in microscopy and remain presently unclear. The simplest junction contains six heptagons in the transition region between the nanotube and graphene. Although these junctions make the pillared architectures possible, they are susceptible to failure when the whole structure undergoes mechanical or thermal stress. In this work we consider “nanochimneys”, a variety of special junctions with cones in between the nanotube and graphene parts. We explore the structures of the nanochimneys (NCs) and determine their underlying topological requirements. We also study the thermal conductance of these pillared architectures and show that NCs conduct heat better than regular simple junctions.

On the linear dependence of a carbon nanofiber thermal conductivity on wall thickness

Thermal transport in carbon nanofibers (CNFs) was thoroughly investigated. In particular, individual CNFs were suspended on T-type heat nanosensors and their thermal conductivity was measured over a range of temperatures. Unexpectedly, thermal conductivity was found to be dependent on CNF wall thickness and ranging between ca. 28 and 43 W/(m⋅K). Further investigation of the CNF walls with high resolution electron microscopy allowed us to propose a tentative description of how wall structure affects phonon heat transport inside CNFs. The lower thermal conductivities, compared to other CNTs, was attributed to unique CNF wall structure. Additionally, wall thickness is related to the conducting lattice length of each constituent graphene cone and comparable to the Umklapp length. Hence, as the wall thickness and thus lattice length increases there is a higher probability for phonon scattering to the next layer.

Helical superstructure of continuum graphene cone uncovered by TEM analysis of herringbone-striped pattern in graphitic whiskers

Cone-shaped graphitic whiskers (CGWs) are a form of pyrolytic carbon, consisting of conically stacked hexagonal carbon layers with an apex angle of ~135–140°. Under transmission electron microscopy (TEM), CGWs often exhibit herringbone-striped patterns. Bright-field (BF) and dark-field (DF) TEM images indicated that the stripes are due to periodical appearance of a strong inter-planar reflection, which is consistent with helical rotation of layers with stepwise “layer overlap”. High-resolution TEM revealed that the period was ~14–15 layers. The relationship between apex angle and stripe periodicity of CGWs could be consistently explained in terms of a helical superstructure of tightly coiled continuous graphene cone.

The Effect of Tilted Magnetic Field in Graphene Cone

We investigate the combined effect of both homogeneous and tilted magnetic fields on the energy spectrum of gapped graphene cones together with long range Coulomb impurity in the framework of perturbation theory. The results illustrate that the tilted magnetic field can significantly affect the spectrum of single particle low-energy effective Hamiltonian, besides lifting the degeneracy of angular momentum channels in the presence of topological defects. The breaking of the electron-hole symmetry by magnetic fields is explained as a direct consequence of sub band Landau-level coupling.

Corrigendum to: The Effect of Tilted Magnetic Field in Graphene Cone

Corrigendum to: The Effect of Tilted Magnetic Field in Graphene Cone

Coulomb screening in graphene with topological defects

We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green’s function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green’s function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.

Tuning the pseudo-Zeeman splitting in graphene cones by magnetic field

The effect of a homogeneous magnetic field on the energy spectrum of gapped graphene cones with long range charged Coulomb impurity is investigated within the framework of the perturbation theory. It is found that, besides lifting the degeneracy of angular momentum channels due to topological defects, the size of the corresponding splitting is enhanced by the introduction of a homogeneous magnetic field. This indicates that the level splitting may be controlled by the strength of a magnetic field in topological cones. Therefore, our results show that the magnetic field may be used as a tool to tune the pseudo-Zeeman splitting in graphene cones.

H2 Production from Biomass for H2/O2 Biofuel Cells

Fuel cells using renewable resources are attractive devices able to take up the energy challenges launched by fossil fuel exhaustion. Hydrogen can be produced from biomass and biocatalysts can replace noble metals such as platinum. Hydrogenase enzymes arise as particularly efficient biocatalysts for H2 oxidation. However, bottlenecks must be overcome before the development of these biofuel cells: 1- biohydrogen production is rate limited, 2- many hydrogenases are inhibited by oxygen and CO, 3- the size of the enzymes limits their electrical connection, hence the current densities. This work will discuss some solutions to get through these limitations, such as controlled bacterium consortia to determine the biophysical parameters able to enhance bioproduction of H2, and the efficient immobilization of an O2-tolerant hydrogenase which allows the development of a new generation of H2/O2 biofuel cell.A multidisciplinary approach including microbiology, microscopies and electrochemistry was used for the study of a synthetic microbial consortium in view of the optimization of biohydrogen production. Electrochemical tools, associated to the full characterization of carbon materials, were used to design a H2/O2 biofuel cell.Numerous microorganisms can produce hydrogen by “dark fermentation”. Literature essentially reports the use of pure microbial cultures to produce biohydrogen from simple sugars. In this work one bacterium from Clostridium (H2 producer) and one from Desulfovibrio (H2 producer or consumer depending on its environment) have been studied as pure and mixed cultures. We demonstrate in this work (i) a physical interaction between the strains via nanotubes, (ii) an exchange of cytoplasmic constituents, (iii) a higher hydrogen production by the consortium compared to isolated bacteria. A modification in the metabolic pathway is proposed that can explain such results.1 Besides, screening energetic pathways in exotic micro-organisms lead to the identification of a membrane-bound hydrogenase which oxidizes hydrogen into protons with high efficiency while presenting outstanding O2, CO and temperature resistances.2,3 When immobilized onto carbon nanotube networks and in combination with a multicopper oxidase for O2 reduction, this enzyme has been proved to be a valuable candidate in a preliminary H2/O2 biofuel cell.4 Fishbone carbon nanofibers (CNFs) are other promising carbon materials which are electrically conductive, and bear lots of reactive sites due to the stacking of graphene cones. They can be quite easily functionalized for an efficient entrapment of proteins. We report in this work the use of such synthesized CNFs for modification of electrodes and immobilization of hydrogenase. We discuss the physico-chemical parameters that limit the efficiency of the bioelectrode, and define their optimization for a great enhancement of the current densities for H2 oxidation.Combined with a thermophilic multicopper oxidase at the cathode, immobilization of hydrogenase on CNFs allow to design a new generation of a high power H2/O2 biofuel cell able to be fed in the future with H2 produced from biomass.5 References[1] Y. Rafrafi et al., Int. J. Hydrogen Energ. 38 (2013) 4975.[2] X. Luo et al., J. Biol. Inorg. Chem. 14(2009)1275.[3] A. Ciaccafava et al., Angew. Chem. Int. Ed., 51(2012)953.[4] A. Ciaccafava et al., Electrochem. Com. 23(2012)25.[5] A. de Poulpiquet et al., PCCP(2013)

Topologically induced confinement of collective modes in multilayer graphene nanocones measured by momentum-resolved STEM-VEELS

In the expanding field of plasmonics, accurate control of the degree of plasmon localization is of crucial importance for tailoring optical properties at the nanoscale. In this paper, the degree of plasmon localization is directly probed by recording the momentum transfer dependence (i.e. the dispersion) of plasmon resonance energies using electron energy loss spectroscopy in the aberration-corrected scanning transmission electron microscope. Limited by the uncertainty principle, resolution in momentum space can easily be tuned by the beam convergence, and it is shown that localization is clearly identifiable, even at low-momentum resolution. In this proof-of-principle study, this technique was applied to multilayer graphene cones containing a varying number of topological defects at their apex. It is shown that a high degree of confinement of the π and π+σ volume plasmons is reached for five pentagonal defects at the cone apex. This effect was attributed to the presence of the topological defects themselves. Furthermore, slight negative refraction was observed for the five-pentagon cone, predominantly affecting the collective excitation of the π electrons.

Topology, cosmic strings and quantum dynamics – a case study with graphene

We explore the possibility to study the quantum dynamics of Dirac fermions in presence of a cosmic string by introducing a conical topological defect in gapped graphene in the presence of a Coulomb charge. When the Coulomb charge exceeds a certain critical strength, quantum instability sets in. Below the critical regime and for certain values of the system parameters, the allowed boundary conditions in gapped graphene cone can be classified in terms of a single real quantity. Observables such as local density of states, scattering phase shifts and the bound state spectra are dependent on the value of this real parameter, which has to be determined empirically. For a supercritical Coulomb charge, we analyze the system with a regularized potential as well as with a zigzag boundary condition and find the effect of the sample topology on the observable features of the system.

Effect of topological defects and Coulomb charge on the low energy quantum dynamics of gapped graphene

We study the combined effect of a conical topological defect and a Coulomb charge impurity on the dynamics of Dirac fermions in gapped graphene. Beyond a certain strength of the Coulomb charge, quantum instability sets in, which demarcates the boundary between sub- and supercritical values of the charge. In the subcritical regime, for certain values of the system parameters, the allowed boundary conditions in a gapped graphene cone can be classified in terms of a single real parameter. We show that the observables such as local density of states, scattering phase shifts and the bound state spectra are sensitive to the value of this real parameter, which is interesting from an empirical point of view. For a supercritical Coulomb charge, we analyze the system with a regularized potential as well as with a zigzag boundary condition and find the effect of the sample topology on the observable features of the system.

Properties of Metal–Graphene Contacts

We present a study on the metal-graphene contact properties. Utilizing a dual-gate field-effect transistor device, an energetic separation between the Fermi level and the Dirac point in the contact areas can be adjusted deliberately by applying an appropriate front-gate voltage that acts only on the channel. This front-gate voltage is compensated by an opposite large-area back-gate voltage, thereby mimicking the metal induced doping effect. A back-gate voltage sweep enables identifying two distinct resistance peaks-a result of the combined impact of the graphene cones in the contact and in the channel region. Comparing our experimental data with simulations allows extracting the coupling strength between metal and graphene and also estimating the magnitude of the metal-induced doping concentration in the case of palladium contacts. In contrast to conventional metal-semiconductor contacts, our simulations predict a decreased on-current for increased coupling strength in graphene field-effect transistors.

Effect of topology on the critical charge in graphene

We show that the critical charge for the Dirac excitations in gapless graphene depends on the spatial topology of the sample. In particular, for graphene cones, the effective value of the critical charge can tend towards zero for a suitable angle of the conical sample. We discuss the nature of the scattering phase shifts, quasi-bound state energies and local density of states for a gapless graphene cone and determine the dependence of these physical quantities on the sample topology.

Fullerenes, zero-modes and self-adjoint extensions

We consider the low-energy electronic properties of graphene cones in the presence of a global Fries–Kekulé Peierls distortion. Such cones occur in fullerenes as the geometric response to the disclination associated with pentagon rings. It is well known that the long-range effect of the disclination deficit-angle can be modelled in the continuum Dirac-equation approximation by a spin connection and a non-Abelian gauge field. We show here that to understand the bound states localized in the vicinity of a pair of pentagons one must, in addition to the long-range topological effects of the curvature and gauge flux, consider the effect of the short-range lattice disruption near the defect. In particular, the radial Dirac equation for the lowest angular-momentum channel sees the defect as a singular endpoint at the origin, and the resulting operator possesses deficiency indices (2, 2). The radial equation therefore admits a four-parameter set of self-adjoint boundary conditions. The values of the four parameters depend on how the pentagons are distributed and determine whether or not there are zero modes or other bound states.

Antiaromatic holes in graphene and related graphite defects

New examples of polycyclic alternant hydrocarbon (PAH) series having doubly degenerate zero eigenvalues (NBMOs) are presented and their electronic and topological characteristics studied. The lowest singlet-states of these PAHs have exceptionally large macrocyclic antiaromatic contributions. Antiaromatic holes in graphene cones and saddles are defined as those holes with inner perimeters corresponding to 4annulene-, 8annulene-, and 12annulene-shaped polygons in which the corresponding molecule has doubly degenerate zero eigenvalues.

Theory of Carbon Nanocones: Mechanical Chiral Inversion of a Micron-Scale Three-Dimensional Object

Graphene cones have two degenerate configurations: their original shape and its inverse. When the apex is depressed by an external probe, the simulated mechanical response is highly nonlinear, with a broad constant-force mode appearing after a short initial Hooke's law regime. For chiral cones, the final state is an atomically exact chiral invert of the original system. If the local reflection symmetry of the graphene sheet is broken by the chemisorption of just five hydrogen atoms to the apex, then the maximal yield strength of the cone increases by approximately 40%. The high symmetry of the conical geometry can concentrate micron-scale mechanical work with atomic precision, providing a way to activate specific chemical bonds.

Graphene cones: Classification by fictitious flux and electronic properties

Multiple five- and seven-membered rings in graphene surfaces have long-range effects which are very sensitive to their relative placement. The sensitivity is described by an $\mathrm{``}n\ensuremath{-}m\mathrm{''}$ combination rule derived here. This rule classifies graphene cones by the localized fictitious gauge flux through their apices, leading to two classes of graphene cones with two apical pentagons. The local density of states vanishes at the Fermi energy in one class, but in the other, it is nonzero and decreases inversely with distance from the apex. Fictitious apical flux also affects the response of electrons to a magnetic field, leading to position dependent local degeneracy of Landau levels as well as anomalous Landau levels which are semiclassically linked to cyclotron orbits which encircle the apex multiple times before closing. We derive these results in a continuum theory, but confront them with numerical tight-binding computations, finding good agreement. We also discuss an intrinsic Aharonov-Bohm effect which persists in the ray-optics limit, and possibilities for producing different inhomogeneous effective fields by exploiting the conical shape.

Graphitic cones in carbon nanofibres

High yields of graphitic conical nanofibres (5-70nm OD; <5 μm in length) are produced by pyrolysing various palladium precursors under an Ar atmosphere at 850-1000°C. The fibres exhibit diamond-shaped Pd particles at their tips, which are responsible for the carbon aggregation and its subsequent diffusion. This carbon replication phenomenon on the Pd particles results in the formation of stacked graphene cones, which grow aligned along a common axis, thus creating graphitic nanofibres. The cones within the fibres can be either open (lamp-shade type) or closed. The material has been analysed using sophisticated electron microscopy (HRTEM, SEM, ED) and spectroscopic techniques (Raman, EELS, EDX). Due to the large number of open edges, we envisage that these novel nanofibres may find important applications in the fabrication of field emitters, gas storage devices and composites.