When Small is Different: The Case of Membranes Inside Tubes
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When Small is Different: The Case of Membranes Inside Tubes Eric Perim1, Alexandre F. Fonseca2 and Douglas S. Galvão1 1
Applied Physics Department, State University of Campinas, Campinas-SP, Sao Paulo, Brazil ² UNESP – Sao Paulo State University, Department of Physics, Bauru, Sao Paulo, Brazil. ABSTRACT Recently, classical elasticity theory for thin sheets was used to demonstrate the existence of a universal structural behavior describing the confinement of sheets inside cylindrical tubes. However, this kind of formalism was derived to describe macroscopic systems. A natural question is whether this behavior still holds at nanoscale. In this work, we have investigated through molecular dynamics simulations the structural behavior of graphene and boron nitride single layers confined into nanotubes. Our results show that the class of universality observed at macroscale is no longer observed at nanoscale. The origin of this discrepancy is addressed in terms of the relative importance of forces and energies at macro and nano scales. INTRODUCTION Systems exhibiting classes of universalities (similar behavior not dependent on materials and/or scales) are of great interest, as it is possible to reliably predict and generalize the properties for a large number of structures. With the advent of nanotechnology, we have been faced with many systems which behave, sometimes, in a counter-intuitive way and expose the limitations of macroscopic models. Great efforts have been devoted towards adapting well established macroscale models to nanoscale. Examples of these systems are buckypapers[1], forests of carbon coiled nanotubes [2] and suspended atomic chains [3] formed from nanocontacts [4]. Recently, Romero et al. [5] published a detailed work on the morphology of coiled elastic sheets inside cylinders, including experimental validation. The geometry and mechanical properties of the sheets were described by means of classical continuous mechanics and it was proposed that, as long as some conditions were satisfied, that behavior should be universal. However, as the study was derived for macroscale systems, it neglected some effects which become very important at nanoscale, like the attractive components of the van der Waals forces and some structural atomistic features (such as, the chirality). A natural question is whether this so-called "universal behavior" observed at macroscale still holds at nanoscale. In order to address this important question we have carried out molecular dynamics simulations for nanoscale structural models. As corresponding structures for sheets and tubes we considered graphene (G) [6] and boron nitride (BN) [7] layers, and carbon nanotubes (CNTs), respectively. G and BN layers share the same bi-dimensional honeycomb structure and an almost equivalent lattice parameter value. The main difference between theses analogous structures is their electronic behavior, G being a semi-metal while BN is a wide band gap structure. Similarly to G, BN monolayers were already experimentally obtained [8,9], while BN na
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