Janus fluid with fixed patch orientations: Theory and simulations

Abstract

We study thermophysical properties of a Janus fluid with constrained orientations, using analytical techniques and numerical simulations. The Janus character is modeled by means of a Kern-Frenkel potential where each sphere has one hemisphere of square-well and the other of hard-sphere character. The orientational constraint is enforced by assuming that each hemisphere can only point either North or South with equal probability. The analytical approach hinges on a mapping of the above Janus fluid onto a binary mixture interacting via a "quasi" isotropic potential. The anisotropic nature of the original Kern-Frenkel potential is reflected by the asymmetry in the interactions occurring between the unlike components of the mixture. A rationalfunction approximation extending the corresponding symmetric case is obtained in the sticky limit, where the square-well becomes infinitely narrow and deep, and allows a fully analytical approach. Notwithstanding the rather drastic approximations in the analytical theory, this is shown to provide a rather precise estimate of the structural and thermodynamical properties of the original Janus fluid.

Bethe-lattice calculations for the phase diagram of a two-state Janus gas

“…We then make contact with recent simulations for the analogous system of hard spheres with a short-range attractive potential well. The results on the Bethe lattice provide a unified view of the systems represented in a cubic diagram of interactions drawn by Fantoni and collaborators [11,10]. In particular, depending on a combination of energy parameters, which includes the analog of the directional Kern-Frenkel potential, we show the existence of a critical line separating disordered and cycle-2 modulated phases, which have been found in some of the simulations for equal concentrations.…”

“…[8,9,4,6]). In particular, a simplified two-state version of the Kern-Frenkel model, which is reminiscent of the Zwanzig approximation for liquid-crystalline models, and can be experimentally realised by the application of an electric field, has been extensively studied in [10,11].…”

From the Liouville to the Smoluchowski equation for a colloidal solute particle in a solvent

“…An interesting progress that could be made at the level of the Fokker-Planck description is to derive the expression for the friction coefficient for a colloidal patchy sticky hard sphere in a solvent of isotropic sticky hard spheres, in the spirit of Refs. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] or in a solvent of penetrable square well particles, in the spirit of Refs. [37][38][39][40][41][42] or fluid mixtures adsorbed in porous disordered materials, as in Ref.…”

Playing with Marbles: Structural and Thermodynamic Properties of Hard-Sphere Systems

“…6.3, left panel) [111,112,113], the square-shoulder potential (see Fig. 9.3, left panel) [114], piece-wise constant potentials with more than one step [115,116], nonadditive hardsphere mixtures [117,118], and Janus particles with constrained orientations [119]. In those cases, the simplest rational-function approximation is already quite accurate, generally improving on the (numerical) solution of the Percus-Yevick equation.…”