  A crystal lattice, when confined to the surface of a cylinder, must have a
periodic structure that is commensurate with the cylinder circumference. This
constraint can frustrate the system, leading to oblique crystal lattices or to
structures with a chiral seam known as a "line slip" phase, neither of which
are stable for isotropic particles in equilibrium on flat surfaces. In this
study, we use molecular dynamics simulations to find the steady-state structure
of spherical particles with short-range repulsion and long-range attraction far
below the melting temperature. We vary the range of attraction using the
Lennard-Jones and Morse potentials and find that a shorter-range attraction
favors the line-slip. We develop a simple model based only on geometry and bond
energy to predict when the crystal or line-slip phases should appear, and find
reasonable agreement with the simulations. The simplicity of this model allows
us to understand the influence of the commensurability constraint, an
understanding that might be extended into the more general problem of
self-assembling particles in strongly confined spaces.
