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 rationalfunction 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.

A class of binary mixtures of Janus fluids formed by colloidal spheres with the hydrophobic hemispheres constrained to point either up or down are studied by means of Gibbs ensemble Monte Carlo simulations and simple analytical approximations. These fluids can be experimentally realized by the application of an external static electrical field. The gas-liquid and demixing phase transitions in five specific models with different patch-patch affinities are analyzed. It is found that a gas-liquid transition is present in all the models, even if only one of the four possible patch-patch interactions is attractive. Moreover, provided the attraction between like particles is stronger than between unlike particles, the system demixes into two subsystems with different composition at sufficiently low temperatures and high densities.

The equilibrium properties of a Janus fluid confined to a one-dimensional channel are exactly derived. The fluid is made of particles with two faces (active and passive), so that the pair interaction is that of hard spheres, except if the two active faces are in front of each other, in which case the interaction has a square-well attractive tail. Our exact solution refers to quenched systems (i.e., each particle has a fixed face orientation), but we argue by means of statistical–mechanical tools that the results also apply to annealed systems (i.e., each particle can flip its orientation) in the thermodynamic limit. Comparison between theoretical results and Monte Carlo simulations for quenched and annealed systems, respectively, shows an excellent agreement.

The question of whether the known virial coefficients are enough to determine the packing fraction η ∞ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Padé approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that η ∞ is equal to the maximum packing fraction corresponding to an ordered crystalline structure.

The equilibrium properties of a Janus fluid made of two-face particles confined to a one-dimensional channel are revisited. The exact Gibbs free energy for a finite number of particles N is exactly derived for both quenched and annealed realizations. It is proved that the results for both classes of systems tend in the thermodynamic limit (N → ∞) to a common expression recently derived (Maestre and Santos 2020 J. Stat. Mech. 063217). The theoretical finite-size results are particularized to the Kern–Frenkel model and confirmed by Monte Carlo simulations for quenched and (both biased and unbiased) annealed systems.