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By means of Diffusion Monte Carlo calculations, we obtained the completephase diagrams of H$_2$ adsorbed on the outer surface of isolated armchaircarbon nanotubes of radii ranging from 3.42 to 10.85 \AA. We only considereddensity ranges corresponding to the filling of the first adsorption layer inthese curved structures. In all cases, the zero-temperature ground state wasfound to be an incommensurate solid, except in the widest tube, in which thestructure with lowest energy is an analogous of the $\sqrt{3} \times \sqrt{3}$phase found in planar substrates. Those incommensurate solids result form thearrangement of the hydrogen molecules in circumferences whose plane isperpendicular to the main axis of the carbon nanotube. For each tube, there isonly one of such phases stable in the density range considered, except in thecase of the (5,5) and (6,6) tubes, in which two of these incommensurate solidsare separated by novel first order phase transitions.

Phase transitions of H2 adsorbed on the surface of single carbon nanotubes