Structure and formation energy of carbon nanotube caps

Abstract

We present a detailed study of the geometry, structure and energetics of carbon nanotube caps. We show that the structure of a cap uniquely determines the chirality of the nanotube that can be attached to it. The structure of the cap is specified in a geometrical way by defining the position of six pentagons on a hexagonal lattice. Moving one (or more) pentagons systematically creates caps for other nanotube chiralities. For the example of the (10,0) tube we study the formation energy of different nanotube caps using ab-initio calculations. The caps with isolated pentagons have an average formation energy 0.29+/-0.01eV/atom. A pair of adjacent pentagons requires a much larger formation energy of 1.5eV. We show that the formation energy of adjacent pentagon pairs explains the diameter distribution in small-diameter nanotube samples grown by chemical vapor deposition.Comment: 8 pages, 8 figures (gray scale only due to space); submitted to Phys. Rev.

Constructing tensegrity structures from one-bar elementary cells

“…Following the two rules in §5a, the two modes of adding bars in figure 5a can be implemented. Such graphene-like planar structure can be rolled up into tensegrity structures having the shape of a capped carbon nanotube (Reich et al 2005), as shown in figure 6b.…”

“…According to the definition of tensegrity (Pugh 1976), the structure shall have no node shared by two bars. Therefore, it is convenient to set the connectivity matrix of the bars as…”

“…In his patent, tensegrity was described as 'Islands of compression inside an ocean of tension'. Later, Pugh (1976) proposed a widely accepted definition: 'A tensegrity system is established when a set of discontinuous compression components interacts with a set of continuous tensile components to define a stable volume in space'. In practice, tensegrity structures are usually modelled as a set of weightless discontinuous bars (or struts) and continuous strings (or cables) connected by frictionless ball joints.…”

Indirect-Direct Band Transformation of Few-Layer BiOCl under Biaxial Strain

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