Molecular-dynamics simulations of carbon nanotubes as gigahertz oscillators

On the Oscillation Frequency of Ellipsoidal Fullerene–Carbon Nanotube Oscillators

There are many new nanomechanical devices created based on carbon nanostructures among which gigahertz oscillators have generated considerable interest to many researchers. In the present paper, the oscillatory behavior of ellipsoidal fullerenes inside single-walled carbon nanotubes is studied comprehensively. Utilizing the continuum approximation along with Lennard–Jones potential, new semi-analytical expressions are presented to evaluate the potential energy and van der Waals interaction force of such systems. Neglecting the frictional effects, the equation of motion is directly solved on the basis of the actual force distribution between the interacting molecules. In addition, a semi-analytical expression is given to determine the oscillation frequency into which the influence of initial conditions is incorporated. Based on the newly derived expression, a thorough study on the various aspects of operating frequencies under different system variables such as geometrical parameters and initial conditions is conducted. Based on the present study, some new aspects of such nano-oscillators have been disclosed.

FORCE DISTRIBUTION AND OFFSET CONFIGURATION FOR CARBON NANOTUBES

In this study, a novel semi-analytical approach is presented to evaluate the preferred position of an offset inner single-walled carbon nanotube (SWCNT) with reference to the cross-section of outer one. Moreover, on the basis of the continuum method utilized together with Lennard-Jones potential function, suction energy and acceptance condition for a SWCNT entering the outer one are investigated. Using netting analysis, the optimum configuration is determined to minimize the potential energy. To obtain the nature of interaction force, a universal potential curve is presented for an offset inner tube entering various semi-infinite outer ones. Lastly, based on the direct method, the mechanics of multi-walled carbon nanotubes (MWCNT) is investigated.

MOLECULAR DYNAMICS SIMULATIONS OF CARBON NANOTUBE-BASED OSCILLATORS HAVING TOPOLOGICAL DEFECTS

Effect of vacancy and Stone–Wales defects on the oscillatory behavior of (5,5)/(10,10) carbon nanotube-based oscillator are studied using NVE molecular dynamics simulations. Results show that defects reduce stability of the oscillators. Effect of single vacancy defect on stability is very small, whereas Stone–Wales defect considerably reduces the stability thereby damping the oscillations quickly. Further increase in density of vacancy defects causes a monotonic decrease of stability of oscillator. In all cases the initial temperature (1 and 300 K) had almost no effect on the oscillation stability.

SPIN IN CARBON NANOTUBE-BASED OSCILLATORS

In this paper, molecular dynamics simulations are performed on a [10, 10]/[5, 5] carbon nanotube-based oscillator. In our work, we observed a spin phenomenon of the inner tube when it oscillated in an isolated oscillator system. If there exist a rocking motion when the inner tube started to oscillate, an axial torque would be observed, and it would drive the inner tube to spin. When the oscillation became stable, the torque almost vanished, and the spin was stabilized with a constant frequency of 21.78 GHz. Such a spin phenomenon was also observed when the oscillator system was at a room temperature of 300 K. However, both magnitude and direction of the spin angular velocity varied from time to time, even after the oscillation of the inner tube stopped due to the energy dissipation.

Ordered phases of encapsulated diamondoids into carbon nanotubes

Diamondoids are hydrogen-terminated nanosized diamond fragments that are present in petroleum crude oil at low concentrations. These fragments are found as oligomers of the smallest diamondoid, adamantane (C(10)H(16)). Due to their small size, diamondoids can be encapsulated into carbon nanotubes to form linear arrangements. We have investigated the encapsulation of diamondoids into single walled carbon nanotubes with diameters between 1.0 and 2.2 nm using fully atomistic simulations. We performed classical molecular dynamics and energy minimizations calculations to determine the most stable configurations. We observed molecular ordered phases (e.g. double, triple, 4- and 5-stranded helices) for the encapsulation of adamantane, diamantane, and dihydroxy diamantane. Our results also indicate that the functionalization of diamantane with hydroxyl groups can lead to an improvement on the molecular packing factor when compared to non-functionalized compounds. Comparisons to hard-sphere models revealed differences, especially when more asymmetrical diamondoids were considered. For larger diamondoids (i.e., adamantane tetramers), we have not observed long-range ordering but only a tendency to form incomplete helical structures. Our calculations predict that thermally stable (at least up to room temperature) complex ordered phases of diamondoids can be formed through encapsulation into carbon nanotubes.

Ultrafast nano-oscillators based on interlayer-bridged carbon nanoscrolls

We demonstrate a viable approach to fabricating ultrafast axial nano-oscillators based on carbon nanoscrolls (CNSs) using molecular dynamics simulations. Initiated by a single-walled carbon nanotube (CNT), a monolayer graphene can continuously scroll into a CNS with the CNT housed inside. The CNT inside the CNS can oscillate along axial direction at a natural frequency of tens of gigahertz. We demonstrate an effective strategy to reduce the dissipation of the CNS-based nano-oscillator by covalently bridging the carbon layers in the CNS. We further demonstrate that such a CNS-based nano-oscillator can be excited and driven by an external AC electric field, and oscillate at more than 100 GHz. The CNS-based nano-oscillators not only offer a feasible pathway toward ultrafast nano-devices but also hold promise to enable nanoscale energy transduction, harnessing, and storage (e.g., from electric to mechanical).

Defect-related hysteresis in nanotube-based nano-electromechanical systems

The electronic properties of multi-walled carbon nanotubes (MWCNTs) depend on the positions of their walls with respect to neighboring shells. This fact can enable several applications of MWCNTs as nano-electromechanical systems (NEMS). In this article, we report the findings of a first-principles study on the stability and dynamics of point defects in double-walled carbon nanotubes (DWCNTs) and their role in the response of the host systems under inter-tube displacement. Key defect-related effects, namely, sudden energy changes and hysteresis, are identified, and their relevance to a host of MWCNT-based NEMS is highlighted. The results also demonstrate the dependence of these effects on defect clustering and chirality of DWCNT shells.

Double-walled carbon nanotubes: challenges and opportunities

Double-walled carbon nanotubes are coaxial nanostructures composed of exactly two single-walled carbon nanotubes, one nested in another. This unique structure offers advantages and opportunities for extending our knowledge and application of the carbon nanomaterials family. This review seeks to comprehensively discuss the synthesis, purification and characterization methods of this novel class of carbon nanomaterials. An emphasis is placed on the double wall physics that contributes to these structures' complex inter-wall coupling of electronic and optical properties. The debate over the inner-tube photoluminescence provides an interesting illustration of the rich photophysics and challenges associated with the myriad combinations of the inner and outerwall chiralities. Outerwall selective covalent chemistry will be discussed as a potential solution to the unattractive tradeoff between solubility and functionality that has limited some applications of single-walled carbon nanotubes. Finally, we will review the many different uses of double-walled carbon nanotubes and provide an overview of several promising research directions in this new and emerging field.

Adsorption configuration effects on the surface diffusion of large organic molecules: the case of Violet Lander

Violet Lander (C(108)H(104)) is a large organic molecule that when deposited on Cu(110) surface exhibits lock-and-key like behavior [Otero et al., Nature Mater. 3, 779 (2004)]. In this work, we report a detailed fully atomistic molecular mechanics and molecular dynamics study of this phenomenon. Our results show that it has its physical basis on the interplay of the molecular hydrogens and the Cu(110) atomic spacing, which is a direct consequence of the matching between molecule and surface dimensions. This information could be used to find new molecules capable of displaying lock-and-key behavior with new potential applications in nanotechnology.

Sustained smooth dynamics in short-sleeved nanobearings based on double-walled carbon nanotubes

We carry out a molecular dynamics study of nanobearings based on double-walled carbon nanotubes with a short rotating outer tube. A (4, 4)/(9, 9) bearing configuration shows peculiar stabilization of rotational motion at certain values of angular velocities. The observed trend is found at those values of initial angular velocities (in the current context, 0.8-1.5 rad ps(-1)) which denote a transitional regime between nearly frictionless operation at low initial angular speeds and decaying performance at high initial angular velocities. With the use of detailed 'principal components analysis', we find that the energy dissipation occurs mainly due to the excitation of wavy modes in the inner tube of the bearing. It is also proposed that wavy deformation is facilitated by the actuation of axial translation of the outer tube, which acts as an energy channelling mode. Hence, we find that the absence of dissipative wavy modes results in sustained smooth rotational dynamics of the nanobearing at low temperature.

An oscillator in a carbon peapod controllable by an external electric field: a molecular dynamics study

We investigate the peapod structure of C(59)N(+)@(10, 10) single-walled carbon nanotubes by simulation, and discover that the ball initial velocity could be controlled by the external impulse electric field, then becoming an oscillator, of which the period could be tuned in a relatively large range of 80-18 ps by adjusting the ball motion in the initial stage. The SWNT length could also be used to tune the period of the oscillator. Based on these results, two potential devices, controllable period and constant period systems are proposed. For the first device, the ball motion is adjusted step by step and the period decreases from 80-100 ps to 18-20 ps or increases from 18-20 ps to 80-100 ps. For the second one, a relatively high constant period within 20-25 ps could be controlled by applying a much longer period signal generator (1 ns) from the external electric field, indicating a robust signal magnification.

Stability and analysis of configuration-tunable bi-directional MWNT bearings

We report on the energetic and structural stability of configuration-tunable, bi-directional linear bearings based on cap-less, partial segments engineered within individual multi-walled carbon nanotubes (MWNTs). Using computational models, we show that an externally applied excitation force can be used to select an operating bearing configuration with a desired stiffness and operating frequency. Our models also demonstrate the possibility of simultaneous, independent operation of multiple bearings within a single NT segment, paving the way towards ultra-high device densities with molecular-scale footprints.

Coaxial nanocables of codoped double-walled carbon nanotubes

The electronic and optical properties of codoped double-walled carbon nanotubes (DWNTs), in which nucleophilic atoms (potassium) are adsorbed outside the outer tube and electrophilic molecules (NO(2)) are adsorbed inside the inner tube, are investigated by density functional theory. It is found that the inner core tube is p-type doped and the outer shell tube is n-type doped, forming a radial p-n junction of DWNTs. A type-II band energy alignment is formed at the interface of two constituting walls of codoped DWNTs. Moreover, optical calculations show that the band edge absorption is zero for pristine DWNTs, while it is pronounced for the codoped DWNTs. This absorption of codoped DWNTs leads to charge separation in the interface of two walls of DWNTs with holes located on core tube while electrons located on shell one. The properties of DWNT coaxial nanocables demonstrated here can find future applications in electronic and optoelectronic devices.

The structure and dynamics of boron nitride nanoscrolls

Carbon nanoscrolls (CNSs) are structures formed by rolling up graphene layers into a scroll-like shape. CNNs have been experimentally produced by different groups. Boron nitride nanoscrolls (BNNSs) are similar structures using boron nitride instead of graphene layers. In this paper we report molecular mechanics and molecular dynamics results for the structural and dynamical aspects of BNNS formation. Similarly to CNS, BNNS formation is dominated by two major energy contributions, the increase in the elastic energy and the energetic gain due to van der Waals interactions of the overlapping surface of the rolled layers. The armchair scrolls are the most stable configuration while zigzag scrolls are metastable structures which can be thermally converted to armchairs. Chiral scrolls are unstable and tend to evolve into zigzag or armchair configurations depending on their initial geometries. The possible experimental routes to produce BNNSs are also addressed.

Oscillation of carbon molecules inside carbon nanotube bundles

In this paper, we investigate the mechanics of a nanoscaled gigahertz oscillator comprising a carbon molecule oscillating within the centre of a uniform concentric ring or bundle of carbon nanotubes. Two kinds of oscillating molecules are considered, which are a carbon nanotube and a C(60) fullerene. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the nanotube-bundle and the C(60)-bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques, which provides considerable insight into the underlying mechanisms of the nanoscaled oscillators. The paper presents a synopsis of the major results derived in detail by the present authors (Cox et al 2007 Proc. R. Soc. A 464 691-710 and Cox et al 2007 J. Phys. A: Math. Theor. 40 13197-208).

Application of coupled nanoscale resonators for spectral sensing

In this paper we propose a method to perform tunable spectral sensing using globally inhibitory coupled oscillators. The suggested system may operate in the analog radio frequency (RF) domain without high speed ADC and heavy digital signal processing. Oscillator arrays may be made of imprecise elements such as nanoresonators. Provided there is a proper coupling, the system dynamics can be made stable despite the imprecision of the components. Global coupling could be implemented using a common load and controlled by digital means to tune the bandwidth. This method may be used for spectral sensing in cognitive radio terminals.

Dissipation and fluctuations in nanoelectromechanical systems based on carbon nanotubes

The tribological characteristics of nanotube-based nanoelectromechanical systems (NEMS) exemplified by a gigahertz oscillator are studied. Various factors that influence the tribological properties of nanotube-based NEMS are quantitatively analyzed with the use of molecular dynamics calculations of the quality factor (Q-factor) of the gigahertz oscillator. We demonstrate that commensurability of the nanotube walls can increase the dissipation rate, while the structure of the wall ends and the nanotube length do not influence the Q-factor. It is shown that the dissipation rate depends on the interwall distance and the way of fixation of the outer wall, and is significant in the case of a poor fixation for nanotubes with a large interwall distance. Defects are found to strongly decrease the Q-factor due to the excitation of low-frequency vibrational modes. No universal correlation between the static friction forces and the energy dissipation rate is established. We propose an explanation of the obtained results on the basis of the classical theory of vibrational-translational relaxation. Significant thermodynamics fluctuations are revealed in the gigahertz oscillator by molecular dynamics simulations and they are analyzed in the framework of the fluctuation-dissipation theorem. The possibility of designing NEMS with a desirable Q-factor and their applications are discussed on the basis of the above results.

A carbon nanotube oscillator as a surface profiling device

A double wall carbon nanotube oscillator near an infinite surface with the nanotube axis perpendicular to the surface is investigated. The oscillatory motion is governed in part by the van der Waals forces in the system, and we use the Lennard-Jones approximation for their calculation. In addition, friction losses due to the proximity of the oscillating nanotube near the infinite surface are taken into account using a phenomenological model. Newton's equation is solved and the oscillatory motion is studied as a function of the nanotube-surface distance, the nanotube length, and the initial extrusion of the moving nanotube. A practical device for surface profiling is also proposed.

Design and Analysis of Nanotube-Based Memory Cells

In this paper, we proposed a nanoelectromechanical design as memory cells. A simple design contains a double-walled nanotube-based oscillator. Atomistic materials are deposed on the outer nanotube as electrodes. Once the WRITE voltages are applied on electrodes, the induced electromagnetic force can overcome the interlayer friction between the inner and outer tubes so that the oscillator can provide stable oscillations. The READ voltages are employed to indicate logic 0/1 states based on the position of the inner tube. A new continuum modeling is developed in this paper to analyze large models of the proposed nanoelectromechanical design. Our simulations demonstrate the mechanisms of the proposed design as both static and dynamic random memory cells.

Frequency characteristics of triple-walled carbon nanotube gigahertz devices

We explore the frequency characteristics of triple-walled carbon nanotube (TWCNT) oscillators using molecular dynamics simulations. The fast Fourier transform results of the TWCNT oscillators show both primary (f(1)) and minor (f(2)) peaks. The frequency characteristics of TWCNT oscillators are closely related to the amplitude (A(1)) of the primary peak. Both f(1) and f(2) linearly increase as a function of A(1) for A(1)(-0.5)<0.45, whereas f(1) and f(2) slightly decrease as a function of A(1) for A(1)(-0.5)>0.45. f(1) for all TWCNT oscillators is always less than the frequency of the double-walled CNT oscillators, while f(2) is less than the operating frequencies of double-walled CNT oscillators for A(1)(-0.5)<0.3. As a function of A(1)(-0.5), f(2) was almost two times higher than f(1).

Trans-phonon effects in ultra-fast nanodevices

We report a novel phenomenon in carbon nanotube based ultra-fast mechanical devices, the trans-phonon effect, which resembles the transonic effects in aerodynamics. It is caused by dissipative resonance of nanotube phonons similar to the radial breathing mode, and subsequent drastic surge of the dragging force on the sliding tube, and multiple phonon barriers are encountered as the intertube sliding velocity reaches critical values. It is found that the trans-phonon effects can be tuned by applying geometric constraints or varying chirality combinations of the nanotubes.

Atomically resolved mechanical response of individual metallofullerene molecules confined inside carbon nanotubes

The hollow core inside a carbon nanotube can be used to confine single molecules and it is now possible to image the movement of such molecules inside nanotubes. To date, however, it has not been possible to control this motion, nor to detect the forces moving the molecules, despite experimental and theoretical evidence suggesting that almost friction-free motion might be possible inside the nanotubes. Here, we report on precise measurements of the mechanical responses of individual metallofullerene molecules (Dy@C82) confined inside single-walled carbon nanotubes to the atom at the tip of an atomic force microscope operated in dynamic mode. Using three-dimensional force mapping with atomic resolution, we addressed the molecules from the exterior of the nanotube and measured their elastic and inelastic behaviour by simultaneously detecting the attractive forces and energy losses with three-dimensional, atomic-scale resolution.

Developing nanoscale inertial measurement systems with carbon nanotube oscillators

We have developed a conceptual design for an inertial measurement system using the oscillatory characteristics of carbon nanotube (CNT) oscillators with or without fillings, and performed molecular dynamics (MD) simulations to investigate its dynamic operations. In the operations, the instantaneous equilibrium position, which is uniquely related to the rotation, is traced by monitoring the variations of the tip-surface capacitance, i.e., the capacitance between a spherical cap of the oscillating CNT and an adjacent metallic plate. The MD simulations for the three model systems: the (5, 5)&(10, 10) CNT system, and the (10, 10)&(15, 15) CNT system with copper and gold fillings, respectively, show that the induced variations of the tip-surface capacitance can be significantly enhanced by increasing the size and the weight of the oscillating core of such an inertial measurement system.

Self-retracting motion of graphite microflakes

We report the observation of a novel phenomenon, the self-retracting motion of graphite, in which tiny flakes of graphite, after being displaced to various suspended positions from islands of highly orientated pyrolytic graphite, retract back onto the islands under no external influences. Reports of this phenomenon have not been found in the literature for single crystals of any kind. Models that include the van der Waals force, electrostatic force, and shear strengths were considered to explain the observed phenomenon. These findings may conduce to create nanoelectromechanical systems with a wide range of mechanical frequency from megahertz to gigahertz.

Characterization and air pressure sensing of doubly clamped multi-walled carbon nanotubes

We report the fabrication and characterization of doubly clamped multi-walled carbon nanotubes (MWNTs). The devices were assembled by applying an electric field while the MWNTs were firmly clamped and suspended at both ends of a thick metal trench electrode in solution. The contacts were further processed using a focused ion beam. Final dimensions ranged from 100 to 150 nm in diameter and 1.5-4 µm in length. The fabricated devices were characterized by I-V curves, impedance measurements, and their mechanical deformation under a high pressure airflow. In the latter case, the resistance of a MWNT device varied linearly with the magnitude of the air pressure. These characteristics strongly suggest potential applications in fields such as nanoelectronics and sensors.

Mechanics of nanotubes oscillating in carbon nanotube bundles

Carbon nanotubes are nanostructures that promise much in the area of constructing nanoscale devices due to their enhanced mechanical, electrical and thermal properties. In this paper, we examine a gigahertz oscillator that comprises a carbon nanotube oscillating in a uniform concentric ring or bundle of carbon nanotubes. A number of existing results for nanotube oscillators are employed to analyse the design considerations of optimizing such a device, and significant new results are also derived. These include a new analytical expression for the interaction per unit length of two parallel carbon nanotubes involving the Appell hypergeometric functions. This expression is employed to precisely determine the relationship between the bundle radius and the radii of the nanotubes forming the bundle. Furthermore, several pragmatic approximations are also given, including the relationships between the bundle radius and the constituent nanotube radius and the oscillating tube radius and the bundle nanotube radius. We also present a simplified analysis of the force and energy for a nanotube oscillating in a nanotube bundle leading to an expression for the oscillating frequency and the maximum oscillating frequency, including constraints on configurations under which this maximum is possible.

Continuum modelling for carbon and boron nitride nanostructures

Continuum based models are presented here for certain boron nitride and carbon nanostructures. In particular, certain fullerene interactions, C(60)-C(60), B(36)N(36)-B(36)N(36) and C(60)-B(36)N(36), and fullerene-nanotube oscillator interactions, C(60)-boron nitride nanotube, C(60)-carbon nanotube, B(36)N(36)-boron nitride nanotube and B(36)N(36)-carbon nanotube, are studied using the Lennard-Jones potential and the continuum approach, which assumes a uniform distribution of atoms on the surface of each molecule. Issues regarding the encapsulation of a fullerene into a nanotube are also addressed, including acceptance and suction energies of the fullerenes, preferred position of the fullerenes inside the nanotube and the gigahertz frequency oscillation of the inner molecule inside the outer nanotube. Our primary purpose here is to extend a number of established results for carbon to the boron nitride nanostructures.

Selective tuning of the electronic properties of coaxial nanocables through exohedral doping

The electronic properties of exohedrally doped double-walled carbon nanotubes (DWNTs) have been investigated using density functional theory and resonance Raman spectroscopy (RRS) measurements. First-principles calculations elucidate the effects of exohedral doping on the M@S and S@M systems, where a metallic (M) tube is either inside or outside a semiconducting (S) one. The results demonstrate that metallic nanotubes are extremely sensitive to doping even when they are inner tubes, in sharp contrast to semiconducting nanotubes, which are not affected by doping when the outer shell is a metallic nanotube (screening effects). The theoretical predictions are in agreement with RRS data on Br2- and H2SO4-doped DWNTs. These results pave the way to novel nanoscale electronics via exohedral doping.

Synthetic molecular motors and mechanical machines

The widespread use of controlled molecular-level motion in key natural processes suggests that great rewards could come from bridging the gap between the present generation of synthetic molecular systems, which by and large rely upon electronic and chemical effects to carry out their functions, and the machines of the macroscopic world, which utilize the synchronized movements of smaller parts to perform specific tasks. This is a scientific area of great contemporary interest and extraordinary recent growth, yet the notion of molecular-level machines dates back to a time when the ideas surrounding the statistical nature of matter and the laws of thermodynamics were first being formulated. Here we outline the exciting successes in taming molecular-level movement thus far, the underlying principles that all experimental designs must follow, and the early progress made towards utilizing synthetic molecular structures to perform tasks using mechanical motion. We also highlight some of the issues and challenges that still need to be overcome.

Batch fabrication of carbon nanotube bearings

Relative displacements between the atomically smooth, nested shells in multiwalled carbon nanotubes (MWNTs) can be used as a robust nanoscale motion enabling mechanism. Here, we report on a novel method suited for structuring large arrays of MWNTs into such nanobearings in a parallel fashion. By creating MWNT nanostructures with nearly identical electrical circuit resistance and heat transport conditions, uniform Joule heating across the array is used to simultaneously engineer the shell geometry via electric breakdown. The biasing approach used optimizes process metrics such as yield and cycle-time. We also present the parallel and piecewise shell engineering at different segments of a single nanotube to construct multiple, but independent, high density bearings. We anticipate this method for constructing electromechanical building blocks to be a fundamental unit process for manufacturing future nanoelectromechanical systems (NEMS) with sophisticated architectures and to drive several nanoscale transduction applications such as GHz-oscillators, shuttles, memories, syringes and actuators.

Mechanics of atoms and fullerenes in single-walled carbon nanotubes. II. Oscillatory behaviour

The discovery of carbon nanotubes and C 60 fullerenes has created an enormous impact on possible new nanomechanical devices. Owing to their unique mechanical and electronic properties, such as low weight, high strength, flexibility and thermal stability, carbon nanotubes and C 60 fullerenes are of considerable interest to researchers from many scientific areas. One aspect that has attracted much attention is the creation of high-frequency nanoscale oscillators, or the so-called gigahertz oscillators, for applications such as ultrafast optical filters and nano-antennae. While there are difficulties for micromechanical oscillators, or resonators, to reach a frequency in the gigahertz range, it is possible for nanomechanical systems to achieve this. This study focuses on C 60 –single-walled carbon nanotube oscillators, which generate high frequencies owing to the oscillatory motion of the C 60 molecule inside the single-walled carbon nanotube. Using the Lennard-Jones potential, the interaction energy of an offset C 60 molecule inside a carbon nanotube is determined, so as to predict its position with reference to the cross-section of the carbon nanotube. By considering the interaction force between the C 60 fullerene and the carbon nanotube, this paper provides a simple mathematical model, involving two Dirac delta functions, which can be used to capture the essential mechanisms underlying such gigahertz oscillators. As a preliminary to the calculation, the oscillatory behaviour of an isolated atom is examined. The new element of this study is the use of elementary mechanics and applied mathematical modelling in a scientific context previously dominated by molecular dynamical simulation.

Oscillatory Behavior of Rare-gas Atoms in SWCNT

In this paper, we have investigated both the process of rare-gas atoms (He, Ne, Ar, Kr, Xe) injected into single-wall carbon nanotube (SWNT) and the mechanical oscillatory behavior of rare-gas atoms sliding in a SWCNT by using molecular dynamics simulations. The minimal diameters of SWCNT to encapsulate rare-gas atoms are obtained, which are from 6.246 to 7.828 A. The threshold energies to encapsulate rare-gas atoms in SWCNT are also presented, which are less than 0.15 eV/atom. The oscillatory frequencies of the encapsulated atoms in zigzag SWCNT have been studied. The oscillatory frequencies are insensitive to the initial kinetic energy, but they are sensitive to the lengths and the radius of the tube, and they decrease as the length and the radius of the tube increases.

Carbon nanotube linear bearing nanoswitches

We exploit the remarkable low-friction bearing capabilities of multiwalled carbon nanotubes (MWNTs) to realize nanoelectromechanical switches. Our switches consist of two open-ended MWNT segments separated by a nanometer-scale gap. Switching occurs through electrostatically actuated sliding of the inner nanotube shells to close the gap, producing a conducting ON state. For double-walled nanotubes in particular, a gate voltage can restore the insulating OFF state. Acting as a nonvolatile memory element capable of several switching cycles, our devices are straightforward to implement, self-aligned, and do not require complex fabrication or geometries, allowing for convenient scalability.

Molecular dynamics study of carbon nanotube oscillators revisited

We performed molecular dynamics simulation of double walled carbon nanotube (DWCNT) oscillators under constant energy and constant temperatures with various commensurations and nanotube lengths. We clarify and resolve questions and differences raised by previous simulation results of similar systems. At constant energy, sustained oscillation is available for a wide range of initial temperatures. But low initial temperature is advantageous for DWCNTs to sustain oscillation under constant energy. We observed sustained oscillation at constant energy for both commensurate and incommensurate DWCNTs. On the other hand, under constant temperatures, both high and low temperatures are disadvantageous to sustain DWCNT oscillations. At constant low temperature, neither commensurate nor incommensurate DWCNTs can maintain oscillation. At appropriate constant temperatures, the oscillatory behavior of incommensurate nanotubes is much more sustained than that of commensurate tubes. The oscillatory frequency of DWCNTs depends significantly on the length of tubes. The initial oscillatory frequency is inversely proportional to the DWCNT lengths. The oscillation frequency of DWCNTs is insensitive to the initial temperatures at constant energy, but slightly dependent on the temperature at constant temperatures.

Self-assembly of single-walled carbon nanotubes into multiwalled carbon nanotubes in water: molecular dynamics simulations

We report discoveries from a series of molecular dynamics simulations that single-walled carbon nanotubes, with different diameters, lengths, and chiralities, can coaxially self-assemble into multiwalled carbon nanotubes in water via spontaneous insertion of smaller tubes into larger ones. The assembly process is tube-size-dependent, and the driving force is primarily the intertube van der Waals interactions. The simulations also suggest that a multiwalled carbon nanotube may be separated into single-walled carbon nanotubes under appropriate solvent conditions. This study suggests possible bottom-up self-assembly routes for the fabrication of novel nanodevices and systems.

Energy exchanges in carbon nanotube oscillators

Energy exchanges between orderly intertube axial motion and vibrational modes are studied for isolated systems of two coaxial carbon nanotubes at temperatures ranging from 300 to 500 K. It is found that the excess intertube van der Waals energy, depleted from the intertube axial motion, is primarily stored in low-frequency mechanical modes of the oscillator for an extended period of time. This constitutes the first computer simulation of a nanomechanical device that exhibits negative friction.

A theoretical study for mechanical contact between carbon nanotubes

We have theoretically investigated motions of single-walled carbon nanotubes (SWNTs) which are mounted on a flat substrate layer of SWNTs by tight-binding molecular dynamics simulations. One of the most interesting motions is the conversion of force and torque, where the force and torque acting initially on the mounted tube finally results in the lateral motion and rolling of the supporting tubes in the substrate. This motion is well understood in terms of the total energy surface of the SWNT/SWNT system. It is suggested that an undulation of the total energy surface plays a role as an atomic-scale gear tooth in the field of nanomechanics, in spite of the atomically smooth surface of SWNT.

The oscillatory damped behaviour of incommensurate double-walled carbon nanotubes

The mechanical properties of sliding carbon nanotubes have been investigated by classical molecular dynamics simulations in the canonical ensemble. In particular we have studied damped oscillations in the separation between the centres of mass of the inner and outer tubes of double-walled carbon nanotubes (DWCN). Incommensurate DWCNs forming (7, 0)@(9, 9) structures were simulated for systems at 298.15 K with axial lengths from 12.21 to 98.24 nm. The oscillations exhibited frequencies in the range of gigahertz with the frequency decreasing as the length of the system increases. The time until oscillations become negligible exhibited a nearly linear dependence on the length of the system. Two macroscopic models were developed in order to understand the forces involved in terms of macroscopic properties like friction and shear. The first model considered constant restoring forces during the whole event, while in the second the value of these constant restoring forces depended on the initial conditions of each oscillation. Both models reproduced the oscillations quite well, while the second model allows us to predict the dynamic shear strength in terms of the axial length of the system for tubes with the same diameters. The calculated dynamic shear strength exhibited monotonic behaviour with an inverse dependence on the length of the system. For systems with unequal axial lengths, the restoring force, which drives the oscillation, is reduced compared to the system with equal lengths, regardless of whether the outer nanotube is longer or shorter.