An exactly solvable model ternary solution with strong three-body interactions

We consider a three-component model of rodlike molecules AA, BB, and AB, co nfined to the bonds of the honeycomb or three-coordinated Bethe lattice, an d with three-body interactions between the molecular ends near a common lat tice site, The model is equivalent to an Ising model on an associated latti ce and has been previously transformed first to an Ising model on an interm ediate lattice then to a standard Ising model on the original honeycomb or Bethe lattice. The exact coexistence curves for phase separation have been previously calculated for weak three-body interactions. In the present pape r the same transformations are used for the case of strong three-body inter actions, the difference being that in this case the Ising parameters on the intermediate lattice are complex, Exact, closed-form expressions are obtai ned for the two-phase coexistence surface in temperature-composition space. The exact coexistence curves are drawn for various values of a reduced thr ee-body coupling constant and the reduced temperature. It is proved there i s no phase separation in the model on these lattices if the reduced three-b ody coupling constant is sufficiently large. (C) 2001 Elsevier Science BY. All rights reserved.