Chiral interaction in double-wall carbon nanotubes: simple rules deduced from a large sampling of tubes

We study a large sampling of chiral double-wall carbon nanotubes to propose simple formula describing the dependence of the interwall energy, the chiral discrimination energy, and the radial breathing mode frequencies as a function of the main characteristics of the tubes, i.e., their radius, length and chiral angle. It is shown that tube pairs with the same handedness are more stable than enantiomeric pairs, and this discrimination, though small, mainly occurs in the first step of the growth of an inner tube inside an outer one. Chiral splittings of the breathing mode frequencies for the two DWCNT diastereoisomers (n(i),m(i))@(n(o),m(o)) and (m(i),n(i))@(n(o),m(o)) can reach a few wave numbers.