Description of mechanical properties of carbon nanotubes. Tube wall thickness problem. Size effect. Part 1

R V Goldstein,G E Norman,V A Gorodtsov,A V Chentsov,S V Starikov,V V Stegailov

doi:10.22226/2410-3535-2011-4-185-189

Abstract

The classical theory of elasticity is used to describe the mechanical properties of nanotubes in many publications. However, necessary for applicability of the theory of elasticity conditions are not fulfilled in the case of single-walled carbon nanotubes (SWCNTs) and tubes with a small number of atomic layers in their walls. Therefore, in the first part of this article, we introduce the method of molecular dynamics and general energy analysis for the description of the generalized Young's modulus (with the dimension of the surface stiffness) and Poisson's ratio characterizing the uniaxial tension of SWCNTs. The strong dependence of the generalized characteristics of the studied nanoscales is their distinctive feature (size effect) as in the contrast to the similar concepts of the elasticity theory. <br /> Here in Part 1 we discussed features of the basic approach and the using of the semi-empirical Tersoff-Brenner-Stewart potential. The main findings will be presented in Part 2.<br /> <br />

Highlights

Nanotubes, including carbon and non-carbon nanotubes, have already been intensively studied for almost two decades
In the first part of this article, we introduce the method of molecular dynamics and general energy analysis for the description of the generalized Young’s modulus and Poisson’s ratio characterizing the uniaxial tension of SWCNTs
It is common that the description of nanotubes mechanical properties is based on macroscopic ideas

Summary

Introduction

Nanotubes, including carbon and non-carbon nanotubes, have already been intensively studied for almost two decades (the starting articles [1,2]). The conditions of classical elasticity theory concepts applicability are fulfilled and the sense of nanotube thickness is clear In this case the surface stiffness becomes the traditional in-plane stiffness proportional to Young’s modulus multiplied by thickness of a nanotube Es0≈Eh. The thickness of a nanotube h is equal to N·a≈N·0.35 nm, where N is number of layers and a is the distance between the graphene plates for graphite. At first sight it seems possible to calculate independently the thickness h and Young’s modulus computing other elastic characteristics (e.g., bending or torsion stiffness) This formal method gives the non-physical results for SWCNTs [60]. The subjects of simulations are the mechanical properties of SWCNTs under tension and compression This standard method (including the effects for nonzero temperatures and the remarks on some restrictions for the description of the large deformations) is briefly written . The boundaries of instability and existence of various stable forms of nanotubes are established for axial compression

Modeling of atomic interactions in SWCNTs

WkTi j l

WT kijl term is an explicit