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

Abstract

We use a simple lattice statistical model to analyze the effects of directional interactions on the phase diagram of a fluid of two-state Janus particles. The problem is formulated in terms of nonlinear recursion relations along the branches of a Cayley tree. Directional interactions are taken into account by the geometry of this graph. Physical solutions on the Bethe lattice (the deep interior of a Cayley tree) come from the analysis of the attractors of the recursion relations. We investigate a number of situations, depending on the concentrations of the types of Janus particles and the parameters of the potential, and make contact with results from recent numerical simulations.

Bottom-Up Construction of the Interaction between Janus Particles

“…Recent advances in mesoscale fabrication have allowed for the construction of anisotropic colloidal particles that are anticipated to self-assemble into novel structure so as to unlock new material properties. − One example is the prediction of richer phase behavior for anisotropic colloidal materials ,− as can exist in gas, liquid, crystalline, or amorphous phases due to the order between particles in analogy with atomic materials. The Janus structurewherein spherical particles have two chemically distinct hemispheresis one such anisotropic colloid particle structure that has warranted much attention through experiment, ,,− theory, − and simulation. ,− …”