Horst, R.

"Computation of Unstable Binodals Not Requiring Concentration Derivatives of the Gibbs Energy"

*Journal of Physical Chemistry B* **1998**, *102, 17,*
3243-3248.

**Abstract: **The equilibrium of three liquid phases in a binary
mixture implies the existence of tie lines and binodals that are different from
the normal experimentally observable ones. First of all, there are the metastable
extensions of the binodal built up by S/S tie lines. These S/S tie lines fulfill
the equilibrium condition of the minimum of the Gibbs energy of the entire two-phase
system. Both coexisting phases are located within the meta(stable) region, There
are two additional types of tie lines: U/U (maximum of the Gibbs energy; both
end points within the unstable area) and U/S tie lines (saddle point; one end
point within the (meta)stable, the other within the unstable region). All types
of tie lines fulfill the condition that the chemical potentials of each component
have to be equal in the two phases given by the end points of the tie line.
It is shown how all these tie lines build up the binodal and which rules they
have to obey. A method for the calculation of all types of tie lines is presented
that requires only the knowledge of the Gibbs energy of mixing; there is no
need to calculate the chemical potentials. The method is applied to a Sanchez-Lacombe
lattice fluid, and a polymer solution described by an extended Flory-Huggins
model accounting for nonpolar and polar interactions.

preprint number: 201a