Mechanical deformation of carbon nanotube nano-rings on flat substrate

Abstract

We present a numerical analysis of the mechanical deformation of carbon nanotube (CNT) nano-rings on flat graphite substrates, which is motivated by our recent experimental findings on the elastic deformation of CNT nano-rings. Our analysis considers a perfectly circular CNT ring formed by bending a straight individual or bundled single-walled nanotube to connect its two ends. The seamless CNT ring is placed vertically on a flat graphite substrate and its respective deformation curvatures under zero external force, compressive, and tensile forces are determined using a continuum model based on nonlinear elastica theory. Our results show that the van der Waals interaction between the CNT ring and the substrate has profound effects on the deformation of the CNT ring, and that the interfacial binding interaction between the CNT ring and the substrate is strongly modulated by the ring deformation. Our results demonstrate that the CNT ring in force-free conditions has a flat ring segment in contact with the substrate if the ring radius R≥EI2Wvdw, in which EI is the flexural rigidity of the nanotube and Wvdw is the per-unit-length van der Waals energy between the flat ring segment and the substrate. Our results reveal that the load-deformation profiles of the CNT ring under tensile loadings exhibit bifurcation behavior, which is ascribed to its van der Waals interaction with the substrate and is dependent on its relaxed conformation on the substrate. Our work suggests that CNT nano-rings are promising for a number of applications, such as ultrasensitive force sensors and stretchable and flexible structural components in nanoscale mechanical and electromechanical systems.