  We report on a computer simulation and integral equation study of a simple
model of patchy spheres, each of whose surfaces is decorated with two opposite
attractive caps, as a function of the fraction $\chi$ of covered attractive
surface. The simple model explored --- the two-patch Kern-Frenkel model ---
interpolates between a square-well and a hard-sphere potential on changing the
coverage $\chi$. We show that integral equation theory provides quantitative
predictions in the entire explored region of temperatures and densities from
the square-well limit $\chi = 1.0$ down to $\chi \approx 0.6$. For smaller
$\chi$, good numerical convergence of the equations is achieved only at
temperatures larger than the gas-liquid critical point, where however integral
equation theory provides a complete description of the angular dependence.
These results are contrasted with those for the one-patch case. We investigate
the remaining region of coverage via numerical simulation and show how the
gas-liquid critical point moves to smaller densities and temperatures on
decreasing $\chi$. Below $\chi \approx 0.3$, crystallization prevents the
possibility of observing the evolution of the line of critical points,
providing the angular analog of the disappearance of the liquid as an
equilibrium phase on decreasing the range for spherical potentials. Finally, we
show that the stable ordered phase evolves on decreasing $\chi$ from a
three-dimensional crystal of interconnected planes to a two-dimensional
independent-planes structure to a one-dimensional fluid of chains when the
one-bond-per-patch limit is eventually reached.
