Theoretical understanding of stability of mechanically interlocked carbon nanotubes and their precursors.

Dispersion-corrected DFT calculations were performed on ( a , a ) nanotubes ( a = 5-10) attached by a U-shaped functional group consisting of p -xylene-linked double 9,10-di(1,3-dithiol-2-ylidene)-9,10-dihydro anthracene terminated by C n H 2 n chains ( n = 6, 8, and 9), and their ring-closing macrocycles containing tubes. The reactant precursors and macrocycles are denoted by UP- n -( a , a ) and ( a , a )@Cycle- n , respectively. We found that UP- n -( a , a ) are energetically preferable relative to the dissociation limit toward a U-shaped functional group (UP- n ) and a tube (initial state) due to the attractive CH-π and π-π interactions. The attractive interactions are enhanced by increasing the tube diameters and C n H 2 n chain lengths because UP- n structures can be easily adjusted to interact with the tubes. The stability of ( a , a )@Cycle- n and related ( a , b )@Cycle- n is sensitive to tube diameters due to the restriction of ring structures. When diameter differences between a Cycle- n and a tube ( D - d ) are larger than 5 Å, ( a , a )@Cycle- n plus C 2 H 4 are energetically preferable relative to the initial state. However, the ( a , a )@Cycle- n plus C 2 H 4 byproduct is always energetically unstable relative to UP- n -( a , a ). The DFT calculations found that the energy differences were low at D - d values ranging from 7 to 8 Å, explaining the tube-diameter-selective formation of the mechanically-interlocked tubes, observed experimentally.