Adsorption on Nanotubes With Repulsive First Neighbors

We consider adsorption on nanotube lattices with zigzag triangular geometry. In Langmuir, Vol.\ 24, pp.\ 11722-11727 (2008), we studied such adsorptions with first- and second-neighbor interactions and attractive first-neighbors. The nanotube energy phase diagram is independent of $M$, the number of atoms in the nanotube circumference, and holds for infinite $M$, reproducing the infinite width limit of a triangular terrace [Langmuir, Vol. 24, pp. 124-134 (2008)]. Here, we consider repulsive first-neighbors. The phase characteristics, \{$\theta_0$, $\theta$, $\beta$\}, are the coverage, and the numbers per site of first and second neighbors, respectively. Particle-hole symmetry holds for all nanotube diameters and the energy phase diagram is $M$ dependent. In the infinite-$M$ limit, the non-trivial phases with their complements are: \{1/4, 0, 0\}, or ($2 \times 2$), and \{3/4, 3/2, 3/2\}; \{1/3, 1/3, 0\}, or ($3 \times 1$), and \{2/3, 4/3, 1\}; \{1/3, 0, 1\}, or ($\sqrt{3} \times \sqrt{3}$) R30$^\circ$, and \{2/3, 1, 2\}; and \{1/2, 1/2, 1/2\}, which is its own complement. This infinite-$M$ limit should be the same as the infinite width limit of a triangular terrace. We found that we had missed the \{2/3, 4/3, 1\}-phase in Langmuir, Vol.\ 23, pp.\ 1928-1936 (2007).