Nanoribbon Length Research Articles

Finding Stable Graphene Conformations from Pull and Release Experiments with Molecular Dynamics

Here, we demonstrate that stable conformations of graphene nanoribbons can be identified using pull and release experiments, when the stretching force applied to a single-layer graphene nanoribbon is suddenly removed. As it is follows from our numerical experiments performed by means of molecular dynamics simulations, in such experiments, favorable conditions for the creation of folded structures exist. Importantly, at finite temperatures, the process of folding is probabilistic. We have calculated the transition probabilities to folded conformations for a graphene nanoribbon of a selected size. Moreover, the ground state conformation has been identified and it is shown that its type is dependent on the nanoribbon length. We anticipate that the suggested pull and release approach to graphene folding may find applications in the theoretical studies and fabrication of emergent materials and their structures.

Thermal characteristics of graphene nanoribbons endorsed by surface functionalization

In this paper, the thermal characteristics of graphene nanoribbons with surface hydrogenation are investigated using Reverse Non-Equilibrium Molecular Dynamics (RNEMD) simulations. Thermal conductivity of graphene nanoribbons with fully hydrogenated domain (graphane) are studied by calculating the Kapitza conductance across the graphene-graphane interface. Thermal conductivity of hybrid nanoribbon is revealed to depend on the length as well as charity and initial temperature, and been systematically interpreted from the perspectives of morphology and phonon vibrational spectra. More interestingly, remarkable thermal rectification is noticed for hybrid nanoribbon with graphene-graphane interface. The thermal conductivity under heat flux from graphane to graphene is higher than that under opposite heat flux. Such thermal rectification decays with the length of nanoribbon and a critical length of 10 nm is identified for single layer nanoribbon beyond which the thermal rectification disappeared. We also studied the thermal properties of graphene nanoribbon with gradient hydrogen arrangement at the surface. Gradient hydrogenation can provide graphene nanoribbon with similar thermal rectification while eliminating the dependency on chirality and length. The proposed gradient hydrogenation can be used for length-insensitive thermal diode with practical application. Our work reveals detailed thermal characteristics of hydrogenated graphene nanoribbons, and provides a possible design of carbon-based thermal diodes.

Symmetric scrolled packings of multilayered carbon nanoribbons

Scrolled packings of single-layer and multilayer graphene can be used for the creation of supercapacitors, nanopumps, nanofilters, and other nanodevices. The full atomistic simulation of graphene scrolls is restricted to consideration of relatively small systems in small time intervals. To overcome this difficulty, a two-dimensional chain model making possible an efficient calculation of static and dynamic characteristics of nanoribbon scrolls with allowance for the longitudinal and bending stiffness of nanoribbons is proposed. The model is extended to the case of scrolls of multilayer graphene. Possible equilibrium states of symmetric scrolls of multilayer carbon nanotribbons rolled up so that all nanoribbons in the scroll are equivalent are found. Dependences of the number of coils, the inner and outer radii, lowest vibrational eigenfrequencies of rolled packages on the length L of nanoribbons are obtained. It is shown that the lowest vibrational eigenfrequency of a symmetric scroll decreases with a nanoribbon length proportionally to L –1. It is energetically unfavorable for too short nanoribbons to roll up, and their ground state is a stack of plane nanoribbons. With an increasing number k of layers, the nanoribbon length L necessary for creation of symmetric scrolls increases. For a sufficiently small number of layers k and a sufficiently large nanoribbon length L, the scrolled packing has the lowest energy as compared to that of stack of plane nanoribbons and folded structures. The results can be used for development of nanomaterials and nanodevices on the basis of graphene scrolled packings.

Length-dependent thermal transport in one-dimensional self-assembly of planar π-conjugated molecules.

This work reports a thermal transport study in quasi-one-dimensional organic nanostructures self-assembled from conjugated planar molecules via π-π interactions. Thermal resistances of single crystalline copper phthalocyanine (CuPc) and perylenetetracarboxylic diimide (PTCDI) nanoribbons are measured via a suspended thermal bridge method. We experimentally observed the deviation from the linear length dependence for the thermal resistance of single crystalline β-phase CuPc nanoribbons, indicating possible subdiffusion thermal transport. Interestingly, a gradual transition to the linear length dependence is observed with the increase of the lateral dimensions of CuPc nanoribbons. The measured thermal resistance of single crystalline CuPc nanoribbons shows an increasing trend with temperature. However, the trend of temperature dependence of thermal resistance is reversed after electron irradiation, i.e., decreasing with temperature, indicating that the single crystalline CuPc nanoribbons become 'amorphous'. Similar behavior is also observed for PTCDI nanoribbons after electron irradiation, proving that the electron beam can induce amorphization of single crystalline self-assembled nanostructures of planar π-conjugated molecules. The measured thermal resistance of the 'amorphous' CuPc nanoribbon demonstrates a roughly linear dependence on the nanoribbon length, suggesting that normal diffusion dominates thermal transport.

Highly stretchable MoS2 kirigami.

We report the results of classical molecular dynamics simulations focused on studying the mechanical properties of MoS2 kirigami. Several different kirigami structures were studied based upon two simple non-dimensional parameters, which are related to the density of cuts, as well as the ratio of the overlapping cut length to the nanoribbon length. Our key findings are significant enhancements in tensile yield (by a factor of four) and fracture strains (by a factor of six) as compared to pristine MoS2 nanoribbons. These results, in conjunction with recent results on graphene, suggest that the kirigami approach may be generally useful for enhancing the ductility of two-dimensional nanomaterials.

Simulation of folded and scrolled packings of carbon nanoribbons

A simple model of a molecular chain on the plane, which allows the description of folded and scrolled packings of graphene nanoribbons, has been proposed. Using this model, possible steady states of single-walled graphene nanoribbons have been obtained, their stability has been shown, and their energy has been calculated as a function of the nanoribbon length L. The results obtained have been easily interpreted taking into account that the formation of van der Waals bonds results in an energy gain, while the bending of the nanoribbon leads to an energy loss. It has been shown that, at L > 13.39 nm, the minimum energy among the studied conformations is inherent in the scrolled packing, which is possible for nanoribbons with length L ⩾ 5.77 nm. For shorter nanoribbons, only the plane form exists. The simplicity of the proposed model allows the consideration of the dynamics of longer graphene nanoribbon rolls at rather long time intervals.

Scroll configurations of carbon nanoribbons

Carbon nanoscroll is a unique topologically open configuration of graphene nanoribbon possessing outstanding properties and application perspectives due to its morphology. However molecular dynamics study of nanoscrolls with more than a few coils is limited by computational power. Here, we propose a simple model of the molecular chain moving in the plane, allowing to describe the folded and rolled packaging of long graphene nanoribbons. The model is used to describe a set of possible stationary states and the low-frequency oscillation modes of isolated single-layer nanoribbon scrolls as the function of the nanoribbon length. Possible conformational changes of scrolls due to thermal fluctuations are analyzed and their thermal stability is examined. Using the full-atomic model, frequency spectrum of thermal vibrations is calculated for the scroll and compared to that of the flat nanoribbon. It is shown that the density of phonon states of the scroll differs from the one of the flat nanoribbon only in the low (omega<100 cm-1) and high (omega>1450 cm-1) frequency ranges. Finally, the linear thermal expansion coefficient for the scroll outer radius is calculated from the long-term dynamics with the help of the developed planar chain model. The scrolls demonstrate anomalously high coefficient of thermal expansion and this property can find new applications.

Random vacancy effect on the electronic transport of zigzag graphene nanoribbon using recursive Green’s function

The electrical conductance of zigzag graphene nanoribbons (ZGNRs) is numerically investigated in the presence of different percentages of edge and middle vacancies. The vacancies are randomly distributed in the edge or innermost of ZGNRs. We take advantage of recursive Green’s function under tight-binding model to study the electrical conductance. It is found that in the both vacancy types, and all widths and lengths of our samples, the conductance degrades as the vacancy concentration increases. In addition, we illustrate how transport properties are sensitive to the width and length of nanoribbon. At fixed defect concentration, the length growth leads to exponential decrease, and the width growth leads to power law increase in the conductance of ZGNRs, respectively. Under the same numerical framework, we have also studied transition from metal to insulator and vice versa.

The defect location effect on thermal conductivity of graphene nanoribbons based on molecular dynamics

Abstract The defect location effect on thermal conductivity of single-layer graphene nanoribbons is investigated. The length and width of pristine graphene nanoribbons are 12.3 nm and 5.112 nm in this paper. The results show the defect location has different levels of influence on thermal conductivity in horizontal and vertical directions. In vertical direction, the change of thermal conductivity is smaller than that in horizontal direction. The thermal conductivity of graphene nanoribbons shows some nonlinearity such as periodic trend when changing the defect location. It implies the chirality of zigzag graphene nanoribbons. In addition, phonon spectrum of atoms on the sides of the model is calculated. The results suggest the effect is greatly influenced by boundary scattering.

Self-reconstruction and predictability of bonds disruption in twisted graphene nanoribbons

Graphene nanoribbons are of great interest due to their applications in nanosized circuitry, where the former can undergo several mechanical deformations, as for example strains and twists. Although there are many investigations about twisted graphene nanoribbons, no density functional calculations are presented concerning their structural integrity when these ribbons are twisted by large angles. In order to investigate this, here are reported first principles calculations on twisted graphene nanoribbons. The results show that for most structures, the system undergoes a transition where it self-reconstructs to the original nanoribbon after twisting beyond a specific angle. This twist angle depends linearly on the nanoribbon length and has a non-linear behavior with the width. Also one finds that it is easier to twist an armchair graphene nanoribbon than a zigzag one when both have the same width and length. In addition, it was performed a simple classical model by applying tensile strain where its agreement with the density functional calculations becomes better for wider graphene nanoribbons, indicating that it is possible to estimate the maximum twist angle knowing only geometric data. This information could be used in prevention ruptures due to twists of the graphene nanoribbons present in nanosized circuitry with flexible shape.

Millimeter-long multilayer graphene nanoribbons prepared by wet chemical processing

Millimeter long multilayer graphene nanoribbons were prepared by a chemical treatment of graphite oxide (GO). To our knowledge, this is the very first report to harvest ultralong graphene ribbons with length dimension >1mm using a wet chemical process. Scanning electron microscope (SEM) images reveal the nanoribbon length larger than 1mm and width ∼10μm. X-ray photoelectron spectroscopy (XPS) analysis shows that oxygen-containing functional groups decreased as the extent of the chemical treatment increased. X-ray diffraction (XRD) and Raman spectroscopy studies confirmed the XPS result and unveil more graphitic sheet like structure formed as GO was reduced by more concentrated NaOH. It is found that by adjusting NaOH/GO mass ratio during the chemical treatment, we can produce >1mm long multilayer graphene nanoribbons and achieve controllable degree of reduction to the GO material. It is expected that this technique will make ultralong graphene nanoribbons readily available for research and applications.

Effects of External Field and Nanoribbon Length on the Electronic Structure and Properties of Graphene Nanoribbons

National Natural Science Foundation of China [21103001]; Research Fund for the Doctoral Program of Higher Education of China [20113401120004]

Synthesis of graphene nanoribbons with various widths and its application to thin-film transistor

Novel precursor polymers containing phenylene, naphthalene and anthracene units were synthesized for fabrication of graphene nanoribbons (GNRs) by the Suzuki coupling reaction between dibrominated monomers and diboronic ester monomers. The precursor polymers were converted into GNRs by intramolecular cyclodehydrogenation using FeCl3 as a catalyst. The degree of cyclodehydrogenation was determined by analysis of nuclear magnetic resonance spectra. All GNR films show ambipolar charge transport behavior in thin-film transistor (TFT). The GNR film prepared from anthracene-based polymer exhibits the highest TFT performance due to its longer conjugation length and larger width of nanoribbon than GNRs prepared from phenylene and naphthalene-based polymers.

Termini of Bottom-Up Fabricated Graphene Nanoribbons

Atomically precise graphene nanoribbons (GNRs) can be obtained via thermally induced polymerization of suitable precursor molecules on a metal surface. This communication discusses the atomic structure found at the termini of armchair GNRs obtained via this bottom-up approach. The short zigzag edge at the termini of the GNRs under study gives rise to a localized midgap state with a characteristic signature in scanning tunneling microscopy (STM). By combining STM experiments with large-scale density functional theory calculations, we demonstrate that the termini are passivated by hydrogen. Our results suggest that the length of nanoribbons grown by this protocol may be limited by hydrogen passivation during the polymerization step.

Analytical modeling of trilayer graphene nanoribbon Schottky-barrier FET for high-speed switching applications

Recent development of trilayer graphene nanoribbon Schottky-barrier field-effect transistors (FETs) will be governed by transistor electrostatics and quantum effects that impose scaling limits like those of Si metal-oxide-semiconductor field-effect transistors. The current–voltage characteristic of a Schottky-barrier FET has been studied as a function of physical parameters such as effective mass, graphene nanoribbon length, gate insulator thickness, and electrical parameters such as Schottky barrier height and applied bias voltage. In this paper, the scaling behaviors of a Schottky-barrier FET using trilayer graphene nanoribbon are studied and analytically modeled. A novel analytical method is also presented for describing a switch in a Schottky-contact double-gate trilayer graphene nanoribbon FET. In the proposed model, different stacking arrangements of trilayer graphene nanoribbon are assumed as metal and semiconductor contacts to form a Schottky transistor. Based on this assumption, an analytical model and numerical solution of the junction current–voltage are presented in which the applied bias voltage and channel length dependence characteristics are highlighted. The model is then compared with other types of transistors. The developed model can assist in comprehending experiments involving graphene nanoribbon Schottky-barrier FETs. It is demonstrated that the proposed structure exhibits negligible short-channel effects, an improved on-current, realistic threshold voltage, and opposite subthreshold slope and meets the International Technology Roadmap for Semiconductors near-term guidelines. Finally, the results showed that there is a fast transient between on-off states. In other words, the suggested model can be used as a high-speed switch where the value of subthreshold slope is small and thus leads to less power consumption.

Anomalous length dependence of the conductance of graphene nanoribbons with zigzag edges

Charge transport through two sets of symmetric graphene nanoribbons with zigzag shaped edges in a two-terminal device has been investigated, using density functional theory combined with the non-equilibrium Green's function method. The conductance has been explored as a function of nanoribbon length, bias voltage, and the strength of terminal coupling. The set of narrower nanoribbons, in the form of thiolated linear acenes, shows an anomalous length dependence of the conductance, which at first exhibits a drop and a minimum, followed by an evident rise. The length trend is shown to arise because of a gradual transformation in the transport mechanism, which changes from being governed by a continuum of out-of-plane π type and in-plane state channels to being fully controlled by a single, increasingly more resonant, occupied π state channel. For the set of nanoribbons with a wider profile, a steady increase is observed across the whole length range, owing to the absence of the former transport mechanism. The predicted trends are confirmed by the inclusion of self-interaction correction in the calculations. For both sets of nanoribbons the replacement of the strongly coupling thiol groups by weakly bonding phenathroline has been found to cause a strong attenuation with the length and a generally low conductance.

Phonon limited transport in graphene nanoribbon field effect transistors using full three dimensional quantum mechanical simulation

This paper present a study of carrier transport in graphene nanoribbon (GNR) transistors using three-dimensional quantum mechanical simulations based on a real-space approach of the non-equilibrium Green's function formalism in the ballistic and dissipative limit. The carrier transport parameters are determined in the presence of electron-phonon scattering, and its influence on carrier mobility including both optical phonons (OPs) and acoustic phonons (APs). The performances of GNR field effect transistors (GNRFETs) are investigated in detail considering the third nearest neighbour tight-binding approximation. The low-field mobility is extracted in the presence of AP and OP as a function of nanoribbon width and length, from which the diffusive/ballistic limit of operation in GNRFETs is determined.

Graphene Nanoribbons with End- and Side-Contacted Electrodes

This contribution reports on theoretical studies of electronic transport through graphene nanoribbons in the two-terminal geometry. The method combines the Landauer-type formalism with Green's function technique within the framework of the standard tight-binding model. The aim of this study is to gain some insight on how fundamental electric current characteristics (conductance and shot noise) depend on interface conditions imposed by graphene nanoribbon/metal-electrode contact details. Calculations have been carried out for both endand side-contact geometries, and metallic (zigzag-edge) as well as semiconducting (armchair-edge) graphene nanoribbons. It turns out that results for side-contacted systems depend on the ratio between the free-standing graphene nanoribbon length to that covered by the electrode. For su ciently long nanoribbons the results start converging when this ratio exceeds 0.5. In the case of ferromagnetic contacts, the giant magnetoresistance coe cient is also discussed.

Synthesis of Graphene Nanoribbons Encapsulated in Single-Walled Carbon Nanotubes

A novel material, graphene nanoribbons encapsulated in single-walled carbon nanotubes (GNR@SWNT), was synthesized using confined polymerization and fusion of polycyclic aromatic hydrocarbon (PAH) molecules. Formation of the GNR is possible due to confinement effects provided by the one-dimensional space inside nanotubes, which helps to align coronene or perylene molecules edge to edge to achieve dimerization and oligomerization of the molecules into long nanoribbons. Almost 100% filling of SWNT with GNR is achieved while nanoribbon length is limited only by the length of the encapsulating nanotube. The PAH fusion reaction provides a very simple and easily scalable method to synthesize GNR@SWNT in macroscopic amounts. First-principle simulations indicate that encapsulation of the GNRs is energetically favorable and that the electronic structure of the encapsulated GNRs is the same as for the free-standing ones, pointing to possible applications of the GNR@SWNT structures in photonics and nanoelectronics.

Conductance quantization and transport gaps in disordered graphene nanoribbons

We study numerically the effects of edge and bulk disorder on the conductance of graphene nanoribbons. We compute the conductance suppression due to Anderson localization induced by edge scattering and find that even for weak edge roughness, conductance steps are suppressed and transport gaps are induced. These gaps are approximately inversely proportional to the nanoribbon width. On/off conductance ratios grow exponentially with the nanoribbon length. Our results impose severe limitations to the use of graphene in ballistic nanowires.