Target-oriented design of helical nanotube molecules for rolled incommensurate bilayers

Incommensurate double-wall carbon nanotubes give rise to unique stereochemistry originating from twisted stacks of hexagon arrays. However, atomic-level studies on such unique systems have rarely been performed, even though syntheses of molecular segments of carbon nanotubes have been extensively explored. The design of cylindrical molecules with chirality, particularly, in pairs provides synthetic challenges, because relationships between diameters specified with chiral indices and structures of arylene panels have not been investigated in a systematic manner. Here we show that a molecular version of incommensurate double-wall carbon nanotubes can be designed through the development of an atlas for the top-down design of cylindrical molecules. A large-bore cylindrical molecule with a diameter of 1.77 nm was synthesized using a readily available pigment and encapsulated a small-bore cylindrical molecule with a diameter of 1.04 nm. The large- and small-bore molecules possessed helicity in atomic arrangements, and their coaxial assembly proceeded in nonstereoselective manner to give both heterohelical and homohelical combinations.