A Formation Mechanism for Catalytically Grown Helix-Shaped Graphite Nanotubes

• Published in: Science (American Association for the Advancement of Science) Vol. 265; no. 5172; pp. 635 - 639
• Main Authors: Amelinckx, S., Zhang, X. B., Bernaerts, D., Zhang, X. F., Ivanov, V., Nagy, J. B.
• Format: Journal Article
• Language: English
• Published: Washington, DC American Society for the Advancement of Science 29.07.1994; American Association for the Advancement of Science
• Subjects: 990200 > Mathematics & Computers; BODY; Carbon; Carbon allotropes; Chemistry; Compressive stress; Curvature; Exact sciences and technology; EXTRUSION; FABRICATION; GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Geometric planes; Graphite; Hodographs; Inorganic chemistry and origins of life; INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; KIDNEYS; Kinetics and mechanism of reactions; Lead; MATERIALS WORKING; MATHEMATICAL MODELS; Molecular structure; Nanotubes; ORGANS 400201 > Chemical & Physicochemical Properties; Particle diffusion; SYNTHESIS; TUBULES; Velocity vector; Particle; Reaction mechanism; Tubular shape; Catalytic reaction; Graphite
• ISSN: 0036-8075; 1095-9203
• DOI: 10.1126/science.265.5172.635

The concept of a spatial-velocity hodograph is introduced to describe quantitatively the extrusion of a carbon tubule from a catalytic particle. The conditions under which a continuous tubular surface can be generated are discussed in terms of this hodograph, the shape of which determines the geometry of the initial nanotube. The model is consistent with all observed tubular shapes and explains why the formation process induces stresses that may lead to "spontaneous" plastic deformation of the tubule. This result is due to the violation of the continuity condition, that is, to the mismatch between the extrusion velocity by the catalytic particle, required to generate a continuous tubular surface, and the rate of carbon deposition.