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

Abstract

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.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. II. The interplay between molecular packing and orientational order

“…Depending on the thermodynamic conditions, this model fluid is capable of forming an ordered polar phase in addition to the more conventional gas and isotropic liquid phases in the bulk. [5][6][7][8][9][10]35 There is a threefold reason to adopt this simple yet sufficiently complex model. First, on account of the short-range nature of the attractive interactions, the phase boundaries of (isotropic or polar) liquid phases are shifted to lower densities that would make this model easily amenable to computer simulation approaches involving, for example, grand canonical Monte Carlo techniques.…”

“…This allows us to conclude that there is a line of critical points described by the expression ρ = 2π/u( β); the critical line ends at the cep at which the critical line joins the remainder of the phase diagram. The expression for the critical line, which is the analog of the Curie line in ferroelectrics, is wellknown for the Heisenberg fluid 35 and for dipolar fluids 1,4 in the bulk.…”

Molecular theory of proper ferroelectricity in bent-core liquid crystals

“…In principle, ferroelectric ordering may occur spontaneously also in isotropic and nematic phases composed of strongly polar molecules. Such a transition into the ferroelectric isotropic and/or nematic phase is indeed predicted by simple mean-field theories [3][4][5][6]. On the other a e-mail: grzegorz@th.if.uj.edu.pl hand, polar phases of this kind have never been observed experimentally (at least the spontaneous polarization has not been measured directly) except for more complicated columnar systems.…”

“…Recently steric polar interactions of V-shaped molecules have been considered in detail by Bisi et al [21,22]. At the same time, in the existing molecular-statistical theory [3][4][5][6] the dipole-dipole interaction is considered to be responsible for ferroelectric ordering in isotropic fluids composed of strongly polar but weakly anisometric molecules. However, as discussed in the Introduction, there is no direct experimental evidence if favor of ferroelectricity in isotropic fluids.…”

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring

“…(32) (namely, homogeneity of the density of the confined fluid), g depends only on r 12 . We approximate g at the so-called modified mean-field level 4,8,14,23,24,26,33,34 as…”