Lattice Theory Predictions of Nonrandom Behavior in Square-Well Fluids

A new attractive term for the equation of state (EOS) of square-well fluids has been developed by using an off-lattice mean-field term in an approximate solution for the lattice gas. van der Waals theory predicts that the attractive contribution to the compressibility factor is proportional to the inverse of temperature and volume. However, there are deviations from van der Waals behavior due to both molecular repulsions and molecular attractions. Here, deviations due to repulsions are predicted by first-order perturbation theory and deviations due to attractions are predicted by an approximation to the Ising model. It is shown that this new EOS shows very good agreement with simulation data for square-well fluids. The derivation of the lattice term allows rigorous extension of the EOS to mixtures without using empirical mixing rules. The EOS is applied to mixtures with an extreme difference in the attractive potentials (i.e., mixtures of hard-sphere and square-well molecules of the same core size). This exaggerates the deviations from random mixing. Mixtures of equal-sized, square-well molecules with different well depths are discussed also. Agreement with perturbation theory and computer simulations is very good.