New insights into aromaticity, Kekulé structures, Dewar structures of armchair versus zigzag carbon nanotubes through delta, matching and spectral polynomials

Abstract

The topic of aromaticity of polycyclic assembly of hexagons has been of considerable interest over the decades. Polyhex carbon nanotubes in different topologies are especially intriguing from the standpoint of aromaticity, Kekulé structures, Dewar structure counts and various polynomials pertinent to these structures. In this study we juxtapose the various novel aromatic measures of zigzag versus armchair polyhex single-walled carbon nanotubes as a function of their tube lengths and circumference. We have computed the matching, spectral and delta polynomials of the two topologies of these tubes as a function of their lengths and circumferences. Our computations reveal that for a single-walled tube, the armchair is more aromatic than zigzag by all measures, and as the tube length increases aromaticity increases for both configurations. In contrast, as the tube circumference increases the aromaticity increases for the zigzag while a less pronounced opposite trend is exhibited by the armchair. There is a dramatic odd-even alternation in zigzag tubes with even parameter exhibiting zero gap, and for both tubes odd parameters exhibit perfect square constant coefficients in the spectral polynomials correlating with the square of the Kekulé structure counts. The armchair tube exhibits a much greater number of Dewar and Kekulé structures for any given set of parameters of the tube compared to the zigzag tubes confirming a greater aromaticity of the armchair tube. For example, the armchair [5,7] tube exhibits K = 65,445 and DS = 12,001,780 compared to the zigzag[5,7] with K = 128 and DS = 1,071,345. On the other hand, the zigzag nanotubes exhibit greater entropies compared to the armchair nanotubes. Applications of the combinatorial and computational techniques to various parameters related to the aromaticity and stability of different topologies of carbon nanotubes are considered.