Crystallographic models of ribbons and ribbon-based J-aggregate nanotubes from the geometry of tube ends.

Self-assembly into tubular structures typically proceeds by helical winding of ribbon intermediates, however, only the central parts of the tubes, that retain no information on the ribbon geometry, have received attention so far. We propose the procedure of establishing the crystal structure of ribbons and ribbon-based tubes on the basis of crystallographic analysis of the tube-end geometry, where the terminal parts of the ribbons fold and form characteristic mono/bilayer polygonal shapes. The terminal parts of flattened J-aggregate nanotubes of trimethine cyanine dye were clearly resolved in electron microscopy and atomic force microscopy images, and the original parallelogram shape of ribbons was reconstructed and interpreted as a two-dimensional [1-10]/[010] facetted crystal with inclined molecular π-stacks parallel to the long ribbon side. The back-reconstructed molecular orientations in a tube wall tend to be close to the tube normal. A two-stage "nucleation and growth" type model of the ribbon to tube transition is proposed that takes into account the established ribbon mechanical asymmetry. The model includes closure of the single ribbon loop as a nucleation event and explains, mostly observed in experiments, nearly rectangular shapes of tubes by the transition kinetics. Due to its universal character, the suggested approach can be applied to any ribbon-based tubes, regardless of their chemical composition.