Topics in Applied Physics Volume 111, 2008, pp 605-629

Single-Wall Carbon Nanohorns and Nanocones

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In addition to sheet structures with purely hexagonal carbon rings, whichnaturally form surfaces of zero Gaussian curvature such as sheets and tubes, agraphenic membrane can also assume a conical shape whose apex is defined by one ormore disclinations taking the form of fivefold (or possibly smaller) rings.Geometrically, just as a sheet of paper with a wedge removed can be resealed to forma conical hat, a graphene sheet with a wedge removed (i.e., a disclination) can beresealed, notionally, to form a cone or horn. The single-wall carbon nanohorns(SWNH) form one class of such conical structures, with a particularly sharp apicalangle, a well-characterized high-yield synthesis route, and a distinct aggregatemicrostructure. Conical graphenic structures with wider opening angles,corresponding to fewer pentagonal disclinations at the apex, also form, sometimes asmultilayered structures. The pentagonal defects in carbon nanocones perturb thelow-energy electronic structure both locally and globally, defining both a localregion of enhanced reactivity and a global geometric phase relation withprofound consequences for electron transport around the apex. The rapidvariation in local sheet orientation around the cone and the two-dimensionalnature of the electronic states within imply that uniform laboratory fields cangenerate highly nonuniform effective local fields for states in the cone.