Binormal nanohelices
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Binormal nanohelices A. F. da Fonseca1, D. S. Galvao2* and C. P. Malta1 1 Institute of Physics, University of Sao Paulo, 05508-900 Sao Paulo, Brazil 2 Applied Physics , State University of Campinas, 13083-970 Campinas, São Paulo, Brazil ABSTRACT Helical structures can be classified in accordance with the orientation of its cross-section with respect to the normal or binormal vectors. We investigate the geometric features of several nanosprings verifying the non-existence of normal nanohelices. In this work, using the VLS growth model, we explain not only the absence of normal nanosprings but also the growing process of binormal nanosprings. The dynamical stability of crystalline ZnO binormal nanohelices is also addressed. * Corresponding author: [email protected] FAX: +551937885376 INTRODUCTION Helical nanowires and nanobelts are promising nanostructures due to their great potential applications in nanoelectronics, nanomechanics and nanoelectromechanical systems[1-4]. Amorphous and crystalline nanosprings of different materials have been synthesized using different methods[4]. It is known[5] that the synthesis of amorphous nanowires requires the presence of a metallic catalyst. Following the vapor-liquid-solid (VLS) growth model, known since 1964[5], a liquid droplet of a metal absorbs the building block material for the growth of the nanowire from the surrounding vapor and, after supersaturation of the absorbed material within the droplet, the excess material precipitates at the liquid/solid interface forming the wire beneath the metallic droplet. In contrast to the formation of straight nanowires, the synthesis of helical nanostructures requires either the existence of anisotropy at some level of the growing process or the existence of external forces holding the nanowire in a helical shape. Both cases have been reported in the literature. In the case of helical structures, mechanisms for helical growth have been recently proposed. Amelinckx et al. [6] introduced the concept of a spatial-velocity hodograph to describe the helical growth of nanotubes of carbon, where the asymmetry arises from variations in the velocity of the growth in the perimeter of the carbon nanotube. In the case of amorphous nanosprings, McIlroy et al.[4,7] developed a modified VLS growth model to explain the formation of helical nanosprings based on the interactions between the metallic catalyst and the nanowire. They showed that the anisotropy in the contact angle between the catalyst and the nanowire induces the helical growth. The interesting feature in this case is that the structure of the nanospring is amorphous[7] and the modified VLS growth model can, therefore, be applied to nanosprings of different materials[7-9]. In the case of crystalline nanosprings, Kong and Wang[10] reported the formation of nanohelices of zinc oxide (ZnO) and showed that the electrostatic interaction between the nanowire and the substrate where it is grown holds the ZnO nanowires in a helical shape. In this work, we analyze several recent r
