The incompressible lattice-gas model by ten Brinke and Karasz is adopt
ed to introduce the effect of specific interactions into a recently-pr
esented Monte-Carlo-based lattice expression for the Helmholtz energy
of nonrandom mixing. While the lattice remains incompressible, intermo
lecular forces consist of two types: London dispersion forces and spec
ific (chemical) forces. The specific interactions between similar comp
onents, as well as those between dissimilar components, are incorporat
ed in a systematic manner. Closed-loop temperature-composition phase d
iagrams are obtained. The theory is compared with experimental data fo
r several binary systems, including polymer solutions, which exhibit c
losed-loop coexistence curves. Theoretical and experimental results ar
e in good agreement.