Oscillatory characteristics of carbon nanotubes inside carbon nanotube bundles

Abstract

This article presents a comprehensive study on the mechanics of carbon nanotubes (CNTs) oscillating in CNT bundles. Using the continuum approximation along with Lennard-Jones (LJ) potential function, new semi-analytical expressions in terms of double integrals are presented to evaluate van der Waals (vdW) potential energy and interaction force upon which the equation of motion is directly solved. The obtained potential expression enables one to arrive at a new semi-analytical formula for the exact evaluation of oscillation frequency. Also, an algebraic frequency formula is extracted on the basis of the simplifying assumption of constant vdW force. Based on the present expressions, a thorough study on various aspects of operating frequencies under different system parameters is given, which permits fresh insight into the problem. The strong dependence of oscillation frequency on system parameters, such as the extrusion distance and initial velocity of the core as initial conditions for the motion is indicated. Interestingly, a specific initial velocity is found at which the oscillation frequency is independent of the core length. In addition, a relation between this specific initial velocity and the escape velocity is disclosed.

Molecular dynamics investigation into the electric charge effect on the operation of ion-based carbon nanotube oscillators

“…These special characteristics sparked the scientist's interest to explore the mechanical oscillatory behavior of different types of nano-oscillators. Up until now, various types of these devices including nested CNTs, spherical fullerenes-CNT, ellipsoidal fullerene-CNT, nanotori-CNT and CNT/C 60 -CNT bundle oscillators have been recommended in the published literature [11][12][13][14][15][16][17]. For theoretically modeling of nanoscale oscillators, two basically different approaches, namely continuum mechanics [18,19] and atomistic approaches such as molecular dynamics (MD) simulations [20,21] are available.…”

Encapsulation of monocyclic carbon clusters into carbon nanotubes: A continuum modeling approach

“…Continuum approaches are often employed for modeling structures that are highly symmetrical in nature and CNTs are ideal structures for implementing such approaches in view of their cylindrical symmetry. 35–50 Besides, there are also reports in the literature wherein continuum approaches are adopted for describing interactions involving graphene, graphene oxide, carbon nanotubes and fullerenes. 41–44 The total interaction energies between carbon nanostructures in the continuum approximation are evaluated by summing over the contributions (in reality, evaluating the line, surface and the volume integrals depending on the dimensionalities of the interacting systems) from pairs of tiny elements on the interacting systems.…”

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

“…The oscillation frequencies of such nano-oscillators were obtained based on the simplifying assumption of vdW interaction force. To accurately model the dynamics of such nanodevices, however, Ansari et al [49][50][51][52] abandoned this assumption and proposed semi-analytical frequency statements using the conservation of mechanical energy principle. Based on their proposed frequency expressions, which were dependent on the system parameters, some new features of such oscillatory systems were revealed.…”