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