We invoke mean-field density functional theory (DFT) to investigate the phase behavior of an amphiphilic fluid composed of a hard-sphere core plus a superimposed anisometric Lennard-Jones perturbation. The orientation dependence of the interactions consists of a contribution analogous to the interaction potential between a pair of "spins" in the classical, three-dimensional Heisenberg fluid and another one reminiscent of the interaction between (electric or magnetic) point dipoles. At fixed orientation both contributions are short-range in nature decaying as r-6 (r being the separation between the centers of mass of a pair of amphiphiles). Based upon two mean-field-like approximations for the pair correlation function that differ in the degree of sophistication we derive expressions for the phase boundaries between various isotropic and polar phases that we solve numerically by the Newton-Raphson method. For sufficiently strong coupling between the Heisenberg "spins" both mean-field approximations generate three topologically different and generic types of phase diagrams that are observed in agreement with earlier work [see, for example, Tavares et al., Phys. Rev. E 52, 1915 (1995)]. Whereas the dipolar contribution alone is incapable of stabilizing polar phases on account of its short-range nature it is nevertheless important for details of the phase diagram such as location of the gas-isotropic liquid critical point, triple, and tricritical points. By tuning the dipolar coupling constant suitably one may, in fact, switch between topologically different phase diagrams. Employing also Monte Carlo simulations in the isothermal-isobaric ensemble the general topology of the DFT phase diagrams is confirmed.
We consider the phase behavior of a simple model of a liquid crystal by means of modified mean-field density-functional theory (MMF DFT) and Monte Carlo simulations in the grand canonical ensemble (GCEMC). The pairwise additive interactions between liquid-crystal molecules are modeled via a Lennard-Jones potential in which the attractive contribution depends on the orientation of the molecules. We derive the form of this orientation dependence through an expansion in terms of rotational invariants. Our MMF DFT predicts two topologically different phase diagrams. At weak to intermediate coupling of the orientation dependent attraction, there is a discontinuous isotropic-nematic liquid-liquid phase transition in addition to the gas-isotropic liquid one. In the limit of strong coupling, the gas-isotropic liquid critical point is suppressed in favor of a fluid- (gas- or isotropic-) nematic phase transition which is always discontinuous. By considering three representative isotherms in parallel GCEMC simulations, we confirm the general topology of the phase diagram predicted by MMF DFT at intermediate coupling strength. From the combined MMF DFT-GCEMC approach, we conclude that the isotropic-nematic phase transition is very weakly first order, thus confirming earlier computer simulation results for the same model [see M. Greschek and M. Schoen, Phys. Rev. E 83, 011704 (2011)].
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.
We present Monte Carlo simulations of the isotropic-polar (IP) phase transition in an amphiphilic fluid carried out in the isothermal-isobaric ensemble. Our model consists of Lennard-Jones spheres where the attractive part of the potential is modified by an orientation-dependent function. This function gives rise to an angle dependence of the intermolecular attractions corresponding to that characteristic of point dipoles. Our data show a substantial system-size dependence of the dipolar order parameter. We analyze the system-size dependence in terms of the order-parameter distribution and a cumulant involving its first and second moments. The order parameter, its distribution, and susceptibility observe the scaling behavior characteristic of the 3D Ising universality class. Because of this scaling behavior and because all cumulants have a common intersection irrespective of system size we conclude that the IP phase transition is continuous. Considering pressures 1.3 ≤ P ≤ 3.0 we demonstrate that a line of continuous phase transitions exists which is analogous to the Curie line in systems exhibiting a ferroelectric transition. Our results are qualitatively consistent with Landau's theory of continuous phase transitions.
The isotropic-polar phase transition of a model amphiphilic fluid was studied by us by assuming that the model pertains to the universality class of a 3D Ising magnet (Melle et al 2012 J. Phys.: Condens. Matter 24 035103). In this addendum we reanalyze our model in a more sophisticated way by measuring directly the critical exponents in Monte Carlo simulations performed in the isothermal-isobaric ensemble. Using standard notation for the critical exponents we obtain β = 0.371, γ = 1.400, and ν = 0.714, in excellent agreement with literature data for the classical 3D Heisenberg fluid (Campostrini et al 2002 Phys. Rev. B 65 144520).
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