Beam to String Transition of Vibrating Carbon Nanotubes Under Axial Tension

Abstract

State‐of‐the‐art nanoelectromechanical systems have been demonstrated in recent years using carbon nanotube (CNT) based devices, where the vibration of CNTs is tuned by tension induced through external electrical fields. However, the vibration properties of CNTs under axial tension have not been quantitatively determined in experiments. Here, a novel in situ method for precise and simultaneous measurement of the resonance frequency, the axial tension applied to individual CNTs and the tube geometry is demonstrated. A gradual beam‐to‐string transition from multi‐walled CNTs to single‐walled CNTs is observed with the crossover from bending rigidity dominant regime to extensional rigidity dominant regime occur much larger than that expected by previous theoretical work. Both the tube resonance frequency under tension and transition of vibration behavior from beam to string are surprisingly well fitted by the continuum beam theory. In the limit of a string, the vibration of a CNT is independent of its own stiffness, and a force sensitivity as large as 0.25 MHz (pN)−1 is demonstrated using a 2.2 nm diameter single‐walled CNT. These results will allow for the designs of CNT resonators with tailored properties.

A Waveguide‐Like Effect Observed in Multiwalled Carbon Nanotube Bundles

“…They were fabricated by a chemical vapor deposition (CVD) technique on Si substrates 33. Their structural, electrical, and mechanical thermoelectric properties have been reported elsewhere 34. Bundles of the MWCNTs tubes were mechanically cut from the original substrates, then one or several pieces of the bundles with the same diameter, ranging from 65 to 230 µm (Table 1), were mounted onto a testing device made from a piece of commercial coaxial copper cable (RG174).…”

Mass and force sensing of an adsorbate on a string resonator

“…(2) is the nth eigenfrequency of a string. Wei et al [39] observed that when T L 2 /EI > 2000, a carbon nanotube vibrates as a string rather than a beam; Unterreithmeier et al [40] also found that when σ > 100 MPa, the stretching energy of a silicon nitride nanowire is dominant and the bending energy becomes negligible, which means the string behavior dominates. Many one-dimensional mechanical resonators are modeled as a string because of the presence of large tension [3, A c c e p t e d M a n u s c r i p t 4,8,25].…”

Mass Detection in Viscous Fluid Utilizing Vibrating Micro- and Nanomechanical Mass Sensors under Applied Axial Tensile Force

“…In this paper, we extend our previous works [ 10 , 16 , 17 ] to report the modified technique capable of mass determination in viscous fluid without the necessity of knowing the surrounding fluid density and viscosity. This technique utilizes the measurement of the fundamental resonant frequencies of the micro-/nanomechanical mass sensor under different values of the intentionally applied axial tensile force, which is created and controlled either via an external electrical/electromagnetic field [ 5 , 17 ] or mechanically [ 18 ]. In addition, due to the importance in real application use, we show that the commonly achievable force measurement errors, e.g., inaccuracy in the estimation of the electrical force, have a negligibly small impact on the extracted mass values.…”