Carbon Nanotube Oscillators Research Articles

Tunable High-Frequency Acoustoelectric Current Oscillations in Fluorine-Doped Single-Walled Carbon Nanotubes

Herein, we report on a fluorine-doped single-walled carbon nanotube (FSWCNT) phenomenon, that yields tunable high-frequency self-sustained acoustoelectric direct current (ADC) oscillations. A tractable analytical method was used in the hypersound domain, to base the calculations on carriers in the lowest miniband. Hypothetically, the energy of interaction between the carriers and the acoustic phonons is less than the energy of the typical carriers. High-order harmonics of the acoustic phonons’ effective field could be disregarded under this supposition. The ADC was observed to exhibit a nonlinearity, that resulted from the carrier distribution function’s distortion as a result of interaction with the acoustic phonons, which had strong nonlinear effects. Theoretically, we demonstrated that the dynamics of space charge instabilities, due to Bragg reflection of Bloch oscillating carriers in the FSWCNT’s miniband, were the only factors which contributed to the creation of radiation in the terahertz (THz) frequency range. The study also investigated the influence of various FSWCNT parameters such as the overlapping integrals (Δs and Δz), ac-field E1, and carrier concentration noon the behaviour of the ADC. The results showed that the intensity of the ADC oscillation Jzzae/Joae could be tuned by adjusting Δs, Δz, E1, and no.This tunability suggests that FSWCNTs could be used as an active device operating at very high frequencies, potentially reaching the submillimeter wavelength range. The study also suggests the possibility of domain suppression and acoustic Bloch gain through dynamic ADC stabilisation.

In English

We investigated influence of multiwalled carbon nanotubes (CNTs) on spectral characteristics of composites “thermo-expanded graphite – carbon nanotubes (TEG–CNTs)”. The introduction of CNTs in an amount of 0-3% by weight of TEG composites results in a significant increase in the strength characteristics and thermal stability of the composites. This result indicates that CNTs is ideal filler for composites based on TEG compositions and structures. Measurements the giant two-polar oscillations with very small half-width 0.5 cm–1 testify the strong interaction of surface polaritons with photons. When frequencies of local oscillations of surface bonds of carbon nanotubes and modes along “nanotube-TEG” boundaries matches, then the light absorption increases 102–105 times. Thus, IR absorption with two-polar oscillations was measured at 0% of nanotubes in TEG at frequency of 2750 cm–1. It is own optical mode in the thermally expanded graphite. 5 peaks with two-polar oscillations were measured in the IR absorption spectra at 1% of carbon nanotubes. And 8 peaks with two-polar oscillations were measured at 3 % of carbon nanotubes at optical mode frequencies along the boundaries of thermally expanded graphite - carbon nanotubes. When frequencies of local oscillations of carbon nanotubes and composite’s modes matches, then the light absorption extremely increases (in 102–105 times), and two-polar IR absorption oscillations with negative components are formed. In general, two-photon interference is a result of quantum entanglement of dipole-active oscillations and splitting of photons according to the Hong-Ou-Mendel (HOM) quantum effect. Two-photon entanglement is built on the basis of the most entanglement states, also known as Bell's states. The HOM–quantum effect on composites “expanded graphite-carbon nanotubes” is promising for the development of highly coherent optical quantum computers.

Quint points lattice and multistability in a damped-driven curved carbon nanotube oscillator model.

Single-walled carbon nanotubes (SWCNTs) can undergo arbitrarily large nonlinear deformations without permanent damage to the atomic structure and mechanical properties. The dynamic response observed in curved SWCNTs under externally driven forces has fundamental implications in science and technology. Therefore, it is interesting to study the nonlinear dynamics of a damped-driven curved SWCNT oscillator model if two control parameters are varied simultaneously, e.g., the external driven strength and damping parameters. For this purpose, we construct high-resolution two-dimensional stability diagrams and, unexpectedly, we identify (i) the existence of a quint points lattice merged in a domain of periodic dynamics, (ii) the coexistence of different stable states for the same parameter combinations and different initial conditions (multistability), and (iii) the existence of infinite self-organized generic stable periodic structures (SPSs) merged into chaotic dynamics domains. The quint points lattice found here is composed of five distinct stability domains that coalesce and are associated with five different periodic attractors. The multistability is characterized by the coexistence of three different multi-attractors combinations for three exemplary parameter sets: two periodic attractors, two chaotic attractors, or one periodic and one chaotic attractor. This study demonstrates how complex the dynamics of a damped-driven curved SWCNT oscillator model can be when parameters and initial conditions are varied. For this reason, it may have a relevant impact on new theoretical and experimental applications of damped-driven curved SWCNTs.

Synchronized oscillations of carbon nanotubes dispersed in solution

Although synchronized oscillations are found in a variety of systems and living organisms in nature, there has been no report on technologically important materials. We have observed by a fluorescence microscope that a large number of carbon nanotubes (CNTs) dispersed in an aqueous mixture of the surfactant and dye execute synchronized oscillations spontaneously. The movement was quantified to give a power spectrum, revealing a single, sharp synchronization peak at 20 Hz. It was found not to be affected nor created by external vibrations. The surfactant concentration dependence demonstrates that the Kuramoto model is applicable to describe the CNT synchronization. It is always associated with the power-law noise, indicating the presence of complex heterogeneous networks. These results suggest a highly cooperative form of the sparse CNT network connected with variable linkages.

Chaotic Dynamics of a Carbon Nanotube Oscillator with Symmetry-Breaking

Chaotic Dynamics of a Carbon Nanotube Oscillator with Symmetry-Breaking

Nonlinear Oscillations of CNT Nano-resonator Based on Nonlocal Elasticity: The Energy Balance Method

This paper deals with investigating the nonlinear oscillation of carbon nanotube manufactured nano-resonator. The governing equation of the nano-resonator is extracted in the context of the nonlocal elasticity. The impact of the Casimir force is also incorporated in the developed model. A closed-form solution based on the energy balance method is presented for investigating the oscillations of the nano-resonator. The proposed closed-form solution is compared with the numerical solution. The impact of influential parameters including applied voltage, Casimir force, geometrical and nonlocal parameters on the nano resonator’s vibration and frequency are investigated. The obtained results demonstrated that the Casimir force reduces the nano-resonator frequency. However, the nonlocal parameter has a hardening effect and enhances the system’s frequency.

Electron scattering by Friedel oscillations in carbon nanotubes

Electron scattering by Friedel oscillations in carbon nanotubes

A CNT based VCO with extremely low phase noise and wide frequency range for PLL application

AbstractVoltage controlled oscillators (VCOs) are used as key components in phase‐locked loop systems for generating stable oscillation signals. Since the digital electronics industry increasingly needs a faster operation, VCOs need to generate signals at higher frequencies. This paper presents a voltage controlled oscillator with a wide frequency range and very low phase noise by using carbon nanotube technology. The Stanford CNTFET model is implemented in Verilog‐A, and the proposed CNTFET VCO is simulated using ADS software. Simultaneous use of forward bulk biasing and an inductor yields a carbon nanotube oscillator with a frequency range of 6‐20 GHz and a phase noise of −123 dBc/Hz.

A detailed parametric study on the operating frequency of chloride ion-electrically charged carbon nanotube oscillators

Fabrication of new types of nanoscale oscillators with enhanced operating frequency has become the focal centre of interest. The aim of this paper is to explore the mechanical oscillatory behaviour of chloride ion tunnelling through carbon nanotubes (CNTs) decorated with identical functional groups at both ends. To this end, our previously proposed analytical expression for total potential energy between an ion and a functionalized CNT is used to derive a new semi-analytical expression for the accurate evaluation of oscillation frequency. With respect to the proposed frequency formula obtained from the conservation of mechanical energy principle, a comprehensive study is conducted to gain an insight into the effects of different parameters such as, sign and magnitude of functional group charge, nanotube length and initial conditions on the operating frequency of chloride ion-electrically charged CNT oscillators. It is revealed that the presence of functional groups, especially ones with the opposite charges to the chloride ion, leads to enhancement of the maximum achievable frequency. It is further observed that optimal frequency is attained when the ion oscillates near the ends of a positively charged nanotube.

Anomalous zero-temperature magnetopolaronic blockade of resonant electron tunneling in Majorana-resonant-level single-electron transistor

The magnetopolaronic generalization of a Majorana-resonant-level (MRL) model is considered for a single-level vibrating quantum dot coupled to two half-infinite $g=1/2$ Tomonaga-Luttinger liquid (TLL) leads. A qualitatively new non-trivial formula for the effective transmission coefficient and differential conductance for resonant magnetopolaron-assisted tunneling is obtained under the assumption about a fermion-boson factorization of corresponding averages. This approach is valid for the case of weak magnetopolaronic coupling in a system. Surprisingly, it is found that despite a supposed weakness of interaction between fermionic and bosonic subsystems in that case, a strongly correlated electron transport in the system reveals features of strong (and, hence, anomalous) magnetopolaronic blockade at zero temperature if the energy of a vibrational quantum is the smallest (but nonzero) energy parameter in the system. Such an effect should be referred to as magnetic phase-coherent magnetopolaron-assisted resonant tunneling of Andreev type, that originates from a special, Majorana-like, symmetry of magnetopolaron-coupled tunnel Hamiltonian. The effect predicted in this paper can be used as an experimental fingerprint of Majorana-resonant level situation in single-electron transistors as well as for detection of ultra-slow zero-point oscillations of suspended carbon nanotubes in the Majorana-resonant level regime of electron tunneling through corresponding single-electron transistors.

Energy dissipation of damping cantilevered single-walled carbon nanotube oscillator

The cantilevered carbon nanotube is a traditional model in the design of some precise nano-oscillators. The sensitivity that is denoted by the quality factor defined as the ratio of the energy stored to the energy dissipated by losses in the oscillator is an important index for the nano-oscillators. In this paper, the small mass impacting on the single-walled carbon nanotube is simplified as an impact load and the governing equation of the transverse oscillation for the nanotube is established firstly. Based on the structure-preserving idea, the generalized multi-symplectic formulations of the governing equation are constructed. The oscillation of the damping nanotube under the transverse impact load with different amplitudes is simulated after the small numerical dissipation and the good convergence of the scheme constructed is verified. From the numerical results, the effects of the induced tension and the energy dissipation are investigated. More importantly, the high precision and the feasibility of the numerical approach proposed in this paper for reproducing the energy dissipation in the carbon nanotube oscillator are illustrated, which gives a new way to investigate the properties of the carbon nanotube oscillators.

Semi-inverse method in nonlinear mechanics: application to couple shell- and beam-type oscillations of single-walled carbon nanotubes

We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the beam and circumferential flexure modes we obtain the dynamical equations, the solutions of which describe the coupled stationary states. The latter are characterized by the non-uniform distribution of the energy along the circumferential coordinate. The non-stationary solutions for obtained equations correspond to the slow change of the energy distribution. It is shown that adequate description of considered resonance processes can be achieved in the domain variables. They are the linear combinations of the shell- and beam-type normal modes. Using such variables we have analyzed not only nonlinear normal modes but also the limiting phase trajectories describing the strongly non-stationary dynamics. The evolution of the considered resonance processes with the oscillation amplitude growth is analyzed by the phase portrait method and verified by the numerical integration of the respective dynamical equations.

Erratum: “Effects of electron exchange-correlation potential on electrostatic oscillations in single-walled carbon nanotubes” [J. Appl. Phys. 115, 204304 (2014)

Erratum: “Effects of electron exchange-correlation potential on electrostatic oscillations in single-walled carbon nanotubes” [J. Appl. Phys. <b>115</b>, 204304 (2014)

Comment on “Effects of electron exchange-correlation potential on electrostatic oscillations in single-walled carbon nanotubes” [J. Appl. Phys. 115, 204304 (2014)

In a recent article, Khan and Hassan [J. Appl. Phys. 115, 204304 (2014)] investigated the dispersion properties of electrostatic electron plasma oscillations on the surface of single-walled carbon nanotubes by considering the exchange-correlation potential. They showed that the surface plasmon energies are blue-shifted by the exchange-correlation effects. Here, we derive the correct form of the dispersion relation and show that the energies of plasmonic modes are red-shifted by the exchange-correlation effects.

Phononic Origins of Friction in Carbon Nanotube Oscillators.

Phononic coupling can have a significant role in friction between nanoscale surfaces. We find frictional dissipation per atom in carbon nanotube (CNT) oscillators to depend significantly on interface features such as contact area, commensurability, and by end-capping of the inner core. We perform large-scale phonon wavepacket MD simulations to study phonon coupling between a 250 nm long (10,10) outer tube and inner cores of four different geometries. Five different phonon polarizations known to have dominant roles in thermal transport are selected, and transmission coefficient plots for a range of phonon energies along with phonon scattering dynamics at specific energies are obtained. We find that the length of interface affects friction only through LA phonon scattering and has a significant nonlinear effect on total frictional force. Incommensurate contact does not always give rise to superlubricity: the net effect of two competing interaction mechanisms shown by longitudinal and transverse phonons decides the role of commensurability. Capping of the core has no effect on acoustic phonons but destroys the coherence of transverse optical phonons and creates diffusive scattering. In contrast, the twisting and radial breathing phonon modes have perfect transmission at all energies and can be deemed as the enablers of ultralow friction in CNT oscillators. Our work suggests that tuning of interface geometries can give rise to desirable friction properties in nanoscale devices.

Chaotic region of elastically restrained single-walled carbon nanotube.

The occurrence of chaos in the transverse oscillation of the carbon nanotube in all of the precise micro-nano mechanical systems has a strong impact on the stability and the precision of the micro-nano systems, the conditions of which are related with the boundary restraints of the carbon nanotube. To generalize some transverse oscillation problems of the carbon nanotube studied in current references, the elastic restraints at both ends of the single-walled carbon nanotube are considered by means of rotational and translational springs to investigate the effects of the boundary restraints on the chaotic properties of the carbon nanotube in this paper. Based on the generalized multi-symplectic theory, both the generalized multi-symplectic formulations for the governing equation describing the transverse oscillation of the single-walled carbon nanotube subjected to the transverse load and the constraint equations resulting from the elastic restraints are presented firstly. Then, the structure-preserving scheme with discrete constraint equations is constructed to simulate the transverse oscillation process of the carbon nanotube. Finally, the chaotic region of the carbon nanotube is captured, and the oscillations of the two extreme cases (including simply supported and cantilever) are investigated in the numerical investigations. From the numerical results, it can be concluded that the relative bending stiffness coefficient and the absolute bending stiffness coefficients at both ends of the carbon nanotube are two important factors that affect the chaotic region of the carbon nanotube, which provides guidance on the design and manufacture of precise micro-nano mechanical systems. In addition, the different routes to the chaos of the carbon nanotube in two extreme cases are revealed.

Telescopic oscillations of double-walled carbon nanotubes in the presence of an inner semi-infinite tube

Telescopic oscillation of nested carbon nanotubes is capable of generating GHz frequency. A main challenge against their practical applications is how to control and tune such oscillations. In this paper, we demonstrate that by displacing the tip of a semi-infinite tube inside a conventional double-walled oscillatory system, we can change the vdW force distribution acting on the oscillating tube. By changing this distribution, the dynamics of the system is altered; hence, the oscillations are retuned. The positioning of the tip can be controlled externally by moving its other end. The proposed mechanism provides a solution to control and tune this type of oscillatory systems during the course of oscillations. Concerning the different system parameters (i.e. geometrical parameters and initial conditions), we perform a thorough study to reveal how the oscillatory frequency will change by moving the tip of the semi-infinite tube.

The influence of external transverse magnetic field in propagation of electrostatic oscillations in single-walled carbon nanotubes

Propagation of an electrostatic oscillation by using the linearized quantum hydrodynamic model in conjunction with Maxwell’s equations was studied. The dispersion relation of a system of electron plasma in single-walled carbon nanotubes in the presence of an external magnetic field B 0 by considering the exchange-correlation effects in 2D cylindrical geometry is derived here. The uniform static magnetic field is assumed to be normal to the cylindrical surface (Voigt configuration). Distribution of the electrons and ions are considered uniformly over the cylindrical surface of a nanotube. It is found that the external magnetic field has significant impact on the wave in the longer wavelength. The influence of variation in azimuthal index and radius of the nanotube on dispersion relation is also discussed. It is tried to plot some schemes and analyze numerically in different limits of cylindrical and planar geometries. The results can be important in the study of collective phenomena in nanostructures.

Effect of bending on the molecular transport along carbon nanotubes

The effect of bending on the molecular transport and oscillation of carbon nanotube–fullerene‐based systems is investigated using molecular dynamics simulations. It is known that single‐walled carbon nanotubes demonstrate gradual buckling phenomenon under bending strain. In this work, we investigate the limit of bending curvature for successful transport of fullerene along a carbon nanotube for nanotube–fullerene‐based systems. We also analyze the behavior of nanotube transport through another nanotube for nanotube–nanotube‐based systems. The dependence of transport characteristics on the atomicity of the inner nanotube is also investigated in this regard. In addition, the effect of the outer nanotube's diameter and surface smoothness on the oscillation stability in relation to the oscillation property of the inner molecules has been studied for both systems.

Characterizing the nonlinear behaviour of double walled carbon nanotube based nano mass sensor

This work deals with the evaluation of nonlinear behaviour of a curved double walled carbon nanotube (DWCNT) when used for mass sensing applications. The DWCNT is considered to be doubly clamped at a source and a drain. To judge the nonlinear behaviour, equations of motion have been derived using Euler beam theory and Hamilton principle, considering nonlinear van der Waals interaction nonlinear oscillations of a double walled carbon nanotube excited harmonically near its primary resonance are considered. The nonlinear free vibration of double-walled carbon nanotubes based on the elasticity theory is studied in this paper. Modelling of the weak van der Waals force of attraction between the inner and outer tubes is represented using a spring element. The equation of motion involves four nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the double walled carbon nanotube based mass sensor is analyzed in the context of the time response, Poincare maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass, inner and outer tubes and the geometric imperfections of double walled carbon nanotube.