Nanotubes: number of Kekulé structures and aromaticity

Carbon nanotubes (CNTs) are composed of cylindrical graphite sheets consisting of sp(2) carbons. Due to their structure CNTs are considered to be aromatic systems. In this work the number of Kekulé structures (K) in "armchair" CNTs was estimated by using the transfer matrix technique. All Kekulé structures of the cyclic variants of naphthalene and benzo[c]phenanthrene have been generated and the basic patterns have been obtained. From this information the elements of the transfer matrix were derived. The results obtained indicate that K (and the resonance energy) is greater if tubulenes are extended in the vertical than in the horizontal direction. Tubulenes are therefore more stabile than cyclic strips. An illustration, obtained by using scanning probe microscope, has been attached to affirm the existence of thin CNTs.