PHYSICAL REVIEW E 87, 012313 (2013) Isotropic-polar phase transitions in an amphiphilic fluid: Density functional theory versus computer simulations Stefano Giura, 1 Bence G. M´ arkus, 2 Sabine H. L. Klapp, 3 and Martin Schoen 1,4,* 1 Stranski-Laboratorium f¨ ur Physikalische und Theoretische Chemie, Fakult¨ at f ¨ ur Mathematik und Naturwissenschaften, Technische Universit¨ at Berlin, Straße des 17. Juni 115, Berlin 10623, Germany 2 Institute of Physics, E ¨ otv¨ os University, P ´ azm´ any P´ eter s´ et´ any 1/A, H-1117, Hungary 3 Institut f ¨ ur Theoretische Physik, Fakult¨ at f ¨ ur Mathematik und Naturwissenschaften, Technische Universit¨ at Berlin, Hardenbergstrasse 36, Berlin 10623, Germany 4 Department of Chemical and Biomolecular Engineering, Engineering Building I, Box 7905, North Carolina State University, 911 Partners Way, Raleigh, North Carolina 27695, USA (Received 7 December 2012; published 31 January 2013) 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. DOI: 10.1103/PhysRevE.87.012313 PACS number(s): 61.25.Em, 05.20.Jj, 64.60.A−, 64.60.fd I. INTRODUCTION To study structure and phase behavior of amphiphilic molecules, Erdmann et al. suggested a simple model, involving spherical particles with an internal degree of freedom, a classical “spin” [1]. The particles interact via the well- known Lennard-Jones potential in which the attractive term is properly modified to account for the orientation dependence of the interaction between a pair of amphiphiles. The anisotropic part of the potential introduced by these authors consists of two contributions. The first one describes the orientation dependence of the intermolecular interactions in a classical three-dimensional (3D) Heisenberg fluid (coupling constant ε H ); the other one resembles that of the interactions between a pair of point dipoles (coupling constant ε D ). However, for fixed molecular orientations, both contributions are short range and decay in proportion to r −6 , where r denotes the distance between the centers of mass of a pair of molecules. For ε H > 0 and ε D < 0, the model is capable of producing micellar and lamellar phases characteristic of amphiphilic molecules [2]. For sufficiently large absolute values of ε H and ε D , the amphiphilic fluid exhibits a bulk phase characterized by long-range ordering of the spins [1,3,4]. In a previous paper, we investigated the isotropic-polar (IP) phase transition by means * Corresponding author: martin.schoen@tu-berlin.de of Monte Carlo (MC) simulations in the isothermal-isobaric ensemble and within the framework of Landau’s mean-field theory [3]. The MC simulations are analyzed by applying finite-size scaling theory based upon Binder’s second-order cumulant. The two main observations made in this earlier paper are that the IP phase transition is continuous over the range of thermodynamic states considered and that a critical line exists similar to the Curie line in ferroelectrics despite the short-range character of our model potential [3]. In a later paper [4], we determined the critical exponents governing the IP phase transition from which we concluded that our model pertains to the universality class of the classical 3D Heisenberg fluid similar to what has been observed for hard spheres with true (i.e., long-range) dipolar interactions [5,6]. This conclusion is based upon a comparison of the critical exponents β, γ , and ν with data published earlier by Campostrini et al. [7]. However, in view of the fact that our model potential consists of superimposed Heisenberg and dipolar terms, it is not immediately clear what is the respective role of both contributions in the formation of polar phases. For models containing either one of the two separately, IP phase transitions have been investigated in a number of previous papers. For example, Ayton et al. have studied ferroelectric and dipolar glass phases in randomly frozen and dynamically disordered dipolar soft-sphere systems [8,9]. Dipolar fluids with a hard-core prolate or oblate ellipsoidal shape have 012313-1 1539-3755/2013/87(1)/012313(13) ©2013 American Physical Society