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Carbon-nanotube geometries as optimal configurations. (English) Zbl 1394.82028
Carbon nanotubes show remarkable strength and, depending on the topology, high electrical conductivity or semiconductivity. Such exceptional properties make carbon nanotubes interesting for the development of innovative technologies. Carbon nanotubes are presently used in the production of composite materials, coatings, microelectronics, energy-storage devices and biotechnologies. The fine geometry of nanotubes is presently still debated, and different models are available. The most nanotube models are geometrical in nature, they reside on sets of geometrical postulates. Here, an approach to investigate carbon nanotube geometries within the frame of molecular mechanics is proposed instead of a variational approach. Atom configurations are modeled as a collection of particle positions, to which a configurational energy is associated. Specific carbon nanotubes geometries are singled out by focusing on their stability. This concept is central with respect to the process of molecular structuring, since among the many theoretically possible geometries, only those showing some suitable stability can be expected to be realized. This concept is formalized here by interpreting stability as minimality of the configurational energy with respect to small perturbations. Some analytical justification of this fact is provided. In particular, stability with respect to a large class of small perturbations including tractions and diameter dilations, among many others, is proved.

MSC:
82D80 Statistical mechanical studies of nanostructures and nanoparticles
82D25 Statistical mechanical studies of crystals
Software:
CHARMM; GROMOS
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