A model is presented in which the bonds of a honeycomb lattice are covered by rodlike molecules of types $AA$ and $BB$, molecular ends near a common site having both three-body interactions and orientation-dependent bonding between two $A$ molecular ends and between an $A$ and a $B$ molecular end. Phase diagrams corresponding to the separation into $AA$-rich and $BB$-rich phases are calculated exactly. Depending on the relative strengths of the interactions, one of several qualitatively different types of phase diagrams can result, including diagrams containing phenomena such as a double critical point or two separate asymmetric closed loops. The model is essentially a limiting case of a previously considered ternary solution model, and it is equivalent to a two-component system of interacting $A$ and $B$ molecules on the sites of a kagomé lattice.

• Received 5 February 2005
• Accepted 31 October 2005

DOI:https://doi.org/10.1103/PhysRevE.73.021508