"Pure-Polyhex" π-Networks: Topo-Combinatorics

Douglas J. Klein, Bholanath Mandal
2021 Croatica Chemica Acta  
Structural possibilities are considered for what arguably is the most general class of connected "pure-polyhex" π-networks (of carbon atoms). These are viewed as hexagonal-network coverings (i.e., a tiling by hexagons) of a connected locally Euclidean surface S possibly with holes which can be simple cycles of sizes other than 6. The surface S can curve around to connect to itself in different ways, e.g., with handles of different sorts. This then includes ordinary benzenoids, coronoids, carbon
more » ... nanotubes, bucky-tori, carbon nano-cones, carbon nano-belts, certain fullerenes & fulleroids, various benzenoid polymers, a great diversity of defected (disclinational or dislocational) graphene flakes, and many other novel pure-polyhexes. A topological classification is made, and several combinatorial conditions on chemical sub-structure counts are identified. These counts include that of "combinatorial curvature", such as is related to curvature stresses, as also relate to the Gaussian curvatures of the embedding surface.
doi:10.5562/cca3790 fatcat:e2svrumekva7vk5puqnj3yryn4