Analytical Analysis of Self-Folded Carbon Nanotube Structures

Abstract

Carbon nanotubes (CNT) are allotropes of carbon with a cylindrical nanostructure, which exhibit excellent mechanical properties such as high strength and resilience. They are promising material for many areas. Due to computational limitations of full atomic simulations of CNT systems, one has to use a mesoscopic (coarse-grained) models, that are much more computationally efficient, but still able to capture the important features of the mechanical behavior of CNT systems. The big scope of the project we will research is to see if DEM can be effectively used for modeling CNT systems. Distinct element method (DEM) is a technique currently used for large scale simulations in granular and discontinuous materials such as granular flows, powder mechanics, and rock mechanics. DEM allows the use of particles with complex geometries rather than simply considering point masses and thousands of particles can be considered in a model with a relatively low computational cost. For the UROP I am doing, I did some basic jobs to do the analytical analysis for two configurations (nanoring and nanoracket) to find the critical length when is potential energy reaches the minimum value. The critical length for the nanoring is found to be 2 π √(EI/ η). E is the Young’s modulus of the carbon nanotube; I is the moment inertia for a hollow circular cross section; η is the cohesive energy. For the critical length for the nanoracket, the results varied because the different assumptions of the shape. The most accurate is found to be 12√(EI/ η). The results have been verified using the DEM in PFC3D, which means the DEM to model the carbon nanotube is acceptable.