Helically-coiled nanotubes

Physical modeling with beads is a powerful way to get an intuition about the effect of spatial arrangement on the shapes of nontrivial carbon graphitic surfaces. But, the actual weaving of a beaded molecule is a slow process. We usually only build a few physical models. With these models in hand, it becomes much easier to figure out the general rules for construction. We then write matlab scripts with these rules. Chuang and Fan have worked out a very general algorithm to obtain an arbitrary helically-coiled nanotube that can be derived from a torus generated according to our generalized classification scheme. Here is the homologous series of helices that are derived from T240 (2,2,2,2,0,0). All of these helically-coiled models have the same inner-rim structure (D5d), but with different arrangement of pentagons in the out-rim. Whereas the girth widths of these models are quite close to each other, the pitches and grooves vary significantly for molecules with different arrangements.