Isotropic-polar phase transitions in an amphiphilic fluid: density functional theory versus computer simulations

We investigate the critical line separating isotropic from polar phases in an amphiphilic bulk fluid by means of density functional theory (DFT) and Monte Carlo (MC) simulations in the isothermal-isobaric ensemble. The intermolecular interactions are described by a Lennard-Jones potential in which the attractive contribution is modified by an orientation-dependent function. The latter consists of two terms: The first one has the orientation dependence of a classical three-dimensional Heisenberg interaction, whereas, the second one has the orientation dependence of a classical dipole-dipole interaction. However, both contributions are short range. Employing DFT together with a modified mean-field (MMF) approximation for the orientation-dependent pair correlation function, we derive an analytical expression for the critical line separating isotropic from polar liquidlike phases. In parallel MC simulations, we locate the line of critical points through an analysis of Binder's second-order cumulant of the polar-order parameter. Comparison with DFT shows that the dipolelike contribution is irrelevant for the isotropic-polar phase transition. As far as the Heisenberg contribution is concerned, the MC data are in semiquantitative agreement with the DFT predictions for sufficiently strong coupling between molecular orientations. For weaker coupling, the variation in the ratio of critical density and temperature ρ(c)/T(c) with the Heisenberg coupling constant ε(H) is underestimated by the MMF treatment. The MC results suggest that this is because ρ(c) increases with decreasing ε(H) such that the assumption on which the MMF approach rests becomes less applicable in the weaker-coupling limit.