Phase behavior of an amphiphilic fluid Martin Schoen 1,2 , Stefano Giura 1 , and Sabine H. L. Klapp 3 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, 10623 Berlin, GERMANY 2 Department of Chemical and Biomolecular Engineering, Engineering Building I, Box 7905, North Carolina State University, 911 Partners Way, Raleigh, NC 27695, U.S.A. 3 Institut f¨ ur Theoretische Physik, Fakult¨ at f¨ ur Mathematik und Naturwissenschaften, Technische Universit¨ at Berlin, Hardenbergstr. 36, 10623 Berlin, GERMANY (Dated: December 6, 2013) 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. PACS numbers: 05.20.Jj,64.60.A-,64.60.fd,05.10.Ln I. INTRODUCTION Amphiphiles are chemical compounds consisting of moieties with antithetic properties. An example are sur- factants that are composed of hydrophilic and hydropho- bic parts. Because of the presence of moieties with conflictive properties in the same molecule amphiphiles exhibit a rather rich phase behavior and a large vari- ety of different structures that can form through self- assembly [1]. A special class of amphiphiles are Janus particles which are particles with chemically distinct sur- faces. These surfaces cause an orientation dependence of the interaction potential [2, 3]. Advances in chemical syn- thesis nowadays permit to fabricate Janus particles with sizes all the way down to the nanometer length scale [4]. In a recent study we investigated the formation of or- dered liquid phases in an amphiphilic fluid [5]. Polarity of the ordered phase is promoted by orientation dependent intermolecular interactions resembling those characteris- tic of the interaction between a pair of “spins” in the clas- sical, three-dimensional Heisenberg model (coupling con- stant ε H ) with superimposed “dipolar” interactions (cou- pling constant ε D ). In our model both the “spin-spin” and the “dipole-dipole” interactions are short-range, that is at fixed relative orientation of an amphiphilic pair the intermolecular interaction potential decays proportional to r −6 where r denotes the distance between the cen- ters of mass of the amphiphiles. As was argued earlier by Erdmann et al., who introduced this model, chains of amphiphiles should form under favorable thermodynamic conditions if both ε H and ε D are positive [6]. Ideally, in these chains the North Pole of any given amphiphile would then be facing the South Pole of its neareast neigh- bor along the chain and vice versa (see Fig. 1 and Table 1 of Ref. 6). Employing Landau theory we could show that in our model a line of critical points exists sepa- rating isotropic from polar liquid phases similar to the Curie line in ferroelectrics [5]. However, so far it is not known whether and how these second-order phase tran- sitions interfere with other fluid-fluid transitions such as condensation. In our earlier study we could also demonstrate that the formation of the ordered phase is almost exclusively driven by the Heisenberg contribution to the interac- tion potential whereas the “dipolar” one is negligible [see Eqs. (3.26) and (3.33) of Ref. 5]. This is consistent with the observation that our model pertains to the three- dimensional Heisenberg universality class [7]. The neg- ligible influence of the “dipolar” part of the interaction potential on the formation of a polar liquid phase is also not surprising because of the short-range character of the ”dipolar” interactions. This is in contrast to fluids in which molecules carry true electric or magnetic (point) dipoles where at fixed relative orientation the interaction