Graphene edge from A to Z - and the origins of nanotube chirality

The energy of arbitrary graphene edge is derived in analytical form. It contains a “chemical phase shift”, determined by the chemical conditions at the edge. Direct atomistic computations support the universal nature of the relationship. Definitive for graphene formation, shapes of the voids or ribbons, this has further important implications for nanotube chirality selection and control by chemical means, at the nucleation stage.