  Confinement can have a dramatic effect on the behavior of all sorts of
particulate systems and it therefore is an important phenomenon in many
different areas of physics and technology. Here, we investigate the role played
by the softness of the confining potential. Using grand canonical Monte Carlo
simulations, we determine the phase diagram of three-dimensional hard spheres
that in one dimension are constrained to a plane by a harmonic potential. The
phase behavior depends strongly on the density and on the stiffness of the
harmonic confinement. Whilst we find the familiar sequence of confined
hexagonal and square-symmetric packings, we do not observe any of the usual
intervening ordered phases. Instead, the system phase separates under strong
confinement, or forms a layered re-entrant liquid phase under weaker
confinement. It is plausible that this behavior is due to the larger positional
freedom in a soft confining potential and to the contribution that the
confinement energy makes to the total free energy. The fact that specific
structures can be induced or suppressed by simply changing the confinement
conditions (e.g. in a dielectrophoretic trap) is important for applications
that involve self-assembled structures of colloidal particles.
