A Hybrid Atomic/Continuum Model for Mechanical Behavior of Multiwalled Carbon Nanotubes

University Of California-Riverside, Riverside CA

Investigators

Abstract

ABSTRACT Carbon nanotubes have long been expected to be the ultimate fibers because of the theoretical predictions that their elastic modulus along the tube axis is about five times larger than that of steel. These fibers are not only expected for applications as constituents in composite materials but also as components in nanoscale instruments, such as the GHz molecular oscillator recently predicted by the PI and reported by the Scientific American (<http://www.sciam.com/news/012302/2.html>). These expected applications have led to numerous investigations, both experimental and theoretical, on determination of the mechanical properties of carbon nanotubes. The experimentally determined values of the elastic modulus of carbon nanotubes are not only often inconsistent with theoretical predictions but also scattered in a wide range. All the experimental measurements to date are indirect because the difficulties associated with handling such samples of extremely small diameters have prevented researchers from obtaining reliable data through direct measurements. The primary causes for the wide scattering of measured values of mechanical properties and the inconsistency with theoretical predictions are the quality variations of experimental samples and the inaccuracy of the mechanics theory used in deriving these values from the measurements. The carbon nanotube samples usually contain defects, which inevitably affect the mechanical properties, and there have been intensive efforts towards further understanding and improving the current synthesis methods and developing new methods, which are expected to lead to nanotubes of increasingly superior quality. Most theoretical studies to date are computer simulations based on either molecular dynamics or atomistic modeling. These studies have provided many insights into some experimentally observed fascinating phenomena, such as super-flexibility of carbon nanotubes in bending, but they are severely limited by the system complexity of multiwalled carbon nanotubes. Physicists have recently turned to the continuum theories of beams, shells and columns for effective modeling, and the predictions based on the continuum theories and the molecule dynamics are compared amazingly well for a few mechanical phenomena, namely buckling instabilities and bending instabilities. However, the general applicability of the continuum theories of mechanics to multiwalled carbon nanotubes is not possible because of the strong evidence that the intermolecular interactions between adjacent walls in multiwalled carbon nanotubes have a crucial effect on the mechanical behavior of these nanotubes. The primary objective of this investigation is to develop a hybrid atomic/continuum inter-length-scale model to characterize the mechanical behavior of multiwalled carbon nanotubes. In this model, each wall is modeled as a continuum with their mechanical behavior being characterized by their effective mechanical properties determined by the atomistic and molecular models, and the interactions between adjacent walls are characterized using the existing theories of intermolecular interactions. A detailed analysis for a multiwalled carbon nanotube, subject to tension/compression, torsion and bending as well as their combinations, will be carried out and comparisons with experimental measurements will be made using the available data in the literature and through a collaborative experimental program.