- Strip algebra
Strip Algebra is a set of elements and operators for the description of
carbon nanotube structures, considered as a subgroup ofpolyhedra , and more precisely, of polyhedra with vertices formed by three edges. This restriction is imposed on the polyhedra because carbon nanotubes are formed of sp2 carbon atoms.Background
Graphitic systems are
molecule s andcrystal s formed ofcarbon atoms in sp2 hybridization. Thus, the atoms are arranged on ahexagon al grid.Graphite , nanotubes, andfullerene s are examples of graphitic systems. All of them share the property that cach atom is bonded to three others (3-valent).The relation between the number of vertices, edges and faces of any finite polyhedron is given by
Euler's polyhedron formula ::e - f - v = 2 (g -1),,
where "e", "f" and "v" are the number of edges, faces and vertices, respectively, and "g" is the genus of the polyhedron, i.e., the number of "holes" in the surface. For example, a
sphere is a surface of genus 0, while atorus is of genus 1.Nomenclature
A substrip is identified by a pair of natural numbers measuring the position of the last ring in parentheses, together with the turns induced by the defect ring. The number of
edge s of the defect can be extracted from these.:n,m) [T_+,T_-]
Elements
A Strip is defined as a set of consecutive rings, that is able to be joined with others, by sharing a side of the first or last ring.
Numerous complex structures can be formed with strips. As said before, strips have both at the beginning and at the end two connections. With strips only, can be formed two of them.
Operators
Given the definition of a strip,
* Addition of two strips: "(upcoming)"
* Turn Operators: "(upcoming)"
* Inversion of a strip: "(upcoming)"Applications
* Strip Algebra has been applied to the construction of nanotube heterojunctions, and was first implemented in the CoNTub v1.0 software, which makes it possible to find the precise position of all the carbon rings needed to produce a heterojunction with arbitrary indices and chirality from two
nanotube s.
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