Spontaneous breaking of molecular identity and phase diagrams of thermally reversible association systems with alternating molecules

The global phase behavior of a mixture of molecules $A_f$ and $B_f$, each containing $f$ functional groups of, respectively, types $A$ and $B$ capable of forming thermally reversible chemical bonds, is considered. Contrary to the traditional approach based on the consideration of an infinite cluster of labile bonds that appears in such systems on the Bethe lattice (i.e., in the Cayley tree approximation) under certain conditions, we additionally take into account the contribution to the thermodynamics from the cluster fragments forming mesoscopic cycles. It is shown, within the framework of the suggested mesoscopic cyclization approximation, which is based on the concept of spontaneous breaking of molecular identity upon the formation of an infinite cluster, that this contribution is finite. Phase diagrams are constructed for the systems considered. The presence of a point of equal concentrations, where two liquid phases coexist and one of them contains an infinite cluster of thermally reversible bonds, is the specific feature of the phase diagrams in the approximation suggested.