It is well know that a benzene molecule is highly symmetric. The tale of the rings begins with first making a ribbon, which has only one benzene ring for its width. This, however, still preserves the symmetry between the top and bottom. By either substituting hydrogen atoms on one side or replacing carbon with heteroatoms, one can create a further asymmetry.
Electronically, this system has a dipole moment, which forces it to slightly bend forming an arc rather than a straight chain of rings. The result of this subtle asymmetry has been studied for zigzag nanoribbons made from fluorinated graphene, boron nitride and silicon carbide. All of these ribbons have a curvature, mostly in the plane, but the fluorinated graphene also out of plane.
The effect of the subtle curvature disappears in wider ribbons: for ribbons with the width of three rings it is already barely seen.
The electronic properties of these bent ribbons depend on their composition, length and width: some ribbons have a triplet ground state (fluorinated graphene), whereas the HOMO-LUMO gap also varies widely from nearly metallic to semiconductor. A desired gap can be created by modifying the size and composition.
Finally, if one extends a bent ribbon long enough, eventually it closes into a full ring, or one can make an incomplete ring. In order to optimize the geometry of a full BN nanoring having the diameter of 105 nm and composed of 1312 aromatic BN rings, the fragment molecular orbital method was used, which is capable of performing ab initio type of calculations of large molecular systems.The lord of the nanorings forged three rings made of 1311, 1312 and 1313 BN rings, whose geometry was fully optimized to verify that they are not distorted.
The full rings are found to have a nearly zero dipole moment, as follows from symmetry. However, incomplete rings have a huge dipole moment, for example, the ring with a 120 degree opening has a dipole moment of 493 Debye.
These results are obtained from DFT calculations. It the literature one can find many reports on wide ribbons, but no experiment on narrow ribbons has been reported so far to the best of my knowledge.