Entanglement and the Nonlinear Elastic Behavior of Forests of Coiled Carbon Nanotubes
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Entanglement and the Nonlinear Elastic Behavior of Forests of Coiled Carbon Nanotubes Vitor R. Coluci1, Alexandre F. Fonseca2, Douglas S. Galvao1, and Chiara Daraio3 1 Applied Physics, State University of Campinas, DFA-IFGW-UNICAMP, Campinas-SP, 13081-970, Brazil 2 Alan G. McDiarmid NanoTech Institute, University of Texas at Dallas, Richardson, TX, 5083-0688 3 Aeronautics and Applied Physics, California Institute of Technology, Pasadena, CA, 91125 ABSTRACT A model for the elastic response of a foamlike forest of coiled carbon nanotubes under mechanical impact is proposed according to recent experiments reported in the literature. A force vs. displacement relation is derived for different geometries of the impacting object (sphere, cube and circular cone). In the model, entanglement among neighboring coils in the superior part of the forest is explicitly taken into account and we show that it allows the full description of the strongly nonlinear elastic behavior of the forest. * Corresponding author: [email protected] FAX: +551935215376 INTRODUCTION The interesting mechanical properties of helical and coiled nanostructures has motivated intense basic and applied researches 1,2,3,4. Coiled carbon nanotubes (CCNTs), first predicted to exist in the early 1990s by Dunlap5 and Ihara et al.6,7,8, and experimentally observed in 1994 by Zhang et al.9, are of particular interest because of their capability to serve as nanoscale mechanical springs10 and electrical inductors11, as well as for their potential applications in nanocomposites12. Recently, the dynamical response of a foamlike forest of CCNTs [Fig. 1(a)] under impact of a drop ball has been reported13. The experiment consisted of producing arrays of bundles of CCNTs, letting a stainless steel bead fall down on the forest of CCNTs, and measuring the dynamic force at the wall below the forest during the stages of penetration and restitution. The analysis of the forest’s morphology after impact has shown no trace of plastic deformation and a full recovery of the foamlike layer of CCNTs under various impact velocities was observed. The contact force, F, exhibits a strongly nonlinear dependence on displacement, δ , (according to Ref. 13, F ∝ δ 2.2 ) and the obtained results have been compared to the Hertz elastic model14 of a solid sphere and a planar surface in contact (where F ∝ δ 1.5 ). It has been hypothesized that sideways interactions of the compressed CCNTs can be associated with the strong nonlinear behavior in CCNT. Here, we present a model15 for the force vs. displacement behavior of CCNT forests under mechanical impact of a spherical object, taking into account the formation of an entanglement among neighboring coils in the superior part of the forest. We have expanded our previous work15 to include the cases where the impacting objects have other than spherical geometries.
ELASTIC MODEL OF THE FOREST OF CCNTS Fig. 1 presents a scheme used to derive the present model. Fig. 1(a) shows the forest of CCNTs; Fig. 1(b) shows the geometry of the im
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