  We study thermophysical properties of a Janus fluid with constrained
orientations, using analytical techniques and numerical simulations. The Janus
character is modeled by means of a Kern-Frenkel potential where each sphere has
one hemisphere of square-well and the other of hard-sphere character. The
orientational constraint is enforced by assuming that each hemisphere can only
point either North or South with equal probability. The analytical approach
hinges on a mapping of the above Janus fluid onto a binary mixture interacting
via a "quasi" isotropic potential. The anisotropic nature of the original
Kern-Frenkel potential is reflected by the asymmetry in the interactions
occurring between the unlike components of the mixture. A rational-function
approximation extending the corresponding symmetric case is obtained in the
sticky limit, where the square-well becomes infinitely narrow and deep, and
allows a fully analytical approach. Notwithstanding the rather drastic
approximations in the analytical theory, this is shown to provide a rather
precise estimate of the structural and thermodynamical properties of the
original Janus fluid.
