Mechanical Resonances of Helically Coiled Carbon Nanowires

Abstract

Despite their wide spread applications, the mechanical behavior of helically coiled structures has evaded an accurate understanding at any length scale (nano to macro) mainly due to their geometrical complexity. The advent of helically coiled micro/nanoscale structures in nano-robotics, nano-inductors, and impact protection coatings has necessitated the development of new methodologies for determining their shear and tensile properties. Accordingly, we developed a synergistic protocol which (i) integrates analytical, numerical (i.e., finite element using COMSOL®) and experimental (harmonic detection of resonance; HDR) methods to obtain an empirically validated closed form expression for the shear modulus and resonance frequency of a singly clamped helically coiled carbon nanowire (HCNW), and (ii) circumvents the need for solving 12th order differential equations. From the experimental standpoint, a visual detection of resonances (using in situ scanning electron microscopy) combined with HDR revealed intriguing non-planar resonance modes at much lower driving forces relative to those needed for linear carbon nanotube cantilevers. Interestingly, despite the presence of mechanical and geometrical nonlinearities in the HCNW resonance behavior the ratio of the first two transverse modes f2/f1 was found to be similar to the ratio predicted by the Euler-Bernoulli theorem for linear cantilevers.

Mechanics of Helical Carbon Nanomaterials

“…A similar transverse resonance has been observed in nanoscopic counterparts too. It was demonstrated by Saini et al [69] in 2014 for a few HN-Fibers with different coil geometries.…”

“…The peak at 90 kHz corresponds to an in-plane transverse resonance that occurs before the onset of the circular mode (peak at 93.5 kHz). Source: Saini et al [69]. Reproduced with permission of Nature Publishing Group…”

One-Dimensional Carbon Nanostructures—From Synthesis to Nano-electromechanical Systems Sensing Applications—

“…8). (92) Liquidprecursor-based thermal CVD was used to synthesize a forest of randomly oriented HCNWs. For HDR measurements, an isolated HCNW mounted on an electrochemically etched tungsten tip (W-tip) was used as the cantilever.…”

Architectured helically coiled scaffolds from elastomeric poly(butylene succinate) (PBS) copolyester via wet electrospinning

“…as well as high stretchability and mechanical stability. 2,3 The techniques employed to fabricate such nanoscale helical structures include sol-gel, selective etching, and self-organization. [4][5][6] For example, manganese oxide helical structures have been produced from the contraction of a sol-gel in a capillary tube upon solvent evaporation, 5 while Kong et al 7 obtained zinc oxide nano-helical structures by induced spontaneous polarization.…”