Elastic Properties of Normal and Binormal Helical Nanowires
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0963-Q20-27
Elastic Properties of Normal and Binormal Helical Nanowires Alexandre F. da Fonseca1, C. P. Malta1, and Douglas S. Galvão2 1 Departamento de Física Matemática, Universidade de São Paulo, Rua do Matão, Travessa R, 187. CEP 05508-090 Cidade Universitaria, Caixa Postal 66318, Sao Paulo, 05508-090, Brazil 2 Departamento de Física Aplicada, UNICAMP, Universidade Estadual de Campinas, Unicamp, Campinas, 13083-970, Brazil ABSTRACT A helical nanowire can be defined as being a nanoscopic rod whose axis follows a helical curve in space. In the case of a nanowire with asymmetric cross section, the helical nanostructure can be classified as normal or binormal helix, according to the orientation of the cross section with respect to the helical axis of the structure. In this work, we present a simple model to study the elastic properties of a helical nanowire with asymmetric cross section. We use the framework of the Kirchhoff rod model to obtain an expression relating the Hooke’s constant, h, of normal and binormal nanohelices to their geometric features. We also obtain the Young’s modulus values. These relations can be used by experimentalists to evaluate the elastic properties of helical nanostructures. We showed that the Hooke’s constant of a normal nanohelix is higher than that of a binormal one. We illustrate our results using experimentally obtained nanohelices reported in the literature. INTRODUCTION Nanostructures (nanotubes, nanowires, etc.) have been object of intense theoretical and experimental investigations in the last years. Among these structures, helical nanowires or nanocoils have attracted particular interest due to their special mechanical properties. In particular, piezoelectric nanosprings combine electric and mechanical properties to form nanoelectromechanical systems (NEMS) with great potential in applications to nano-engineering1,2,3,4. Amorphous and crystalline nanosprings of different materials have been synthesized using different approaches4,5,6. Volodin et al7, using a circular beam approximation, have obtained an expression relating the transversal Hooke’s constant of helical nanostructures to the elastic properties of the material. Using the Kirchhoff rod model, we have recently developed8,9 a model for measuring the Young’s modulus and Poisson’s ratio of nanosprings by measuring the geometric parameters of the helical nanostructures and measuring the axial Hooke’s constant of the nanospring. One advantage of our model is that we can obtain all elastic parameters of the nanospring material without resorting to values of the bulk material. Another important advantage for mechanical applications is that one of our expressions relates the elastic properties and geometric features of the nanospring to its axial Hooke’s constant. In this work, we give and analyze expressions for the axial Hooke’s constant of nanosprings whose nanowire asymmetric cross sections are elliptic or rectangular. We also rewrite the expressions in terms of the radius, R, and the pitch, P, of the helical nanostruct
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