Mechanical resonances of helically coiled carbon nanowires

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.