Analytical expressions of Helmholtz function of mixing for Ising model

Accurate analytical expressions for the internal energy of mixing and the Helmholtz function of mixing for an Ising lattice have been derived. Non-randomness factors are defined which are shown to have a linear composition dependence from the computer-simulation results. On the other hand, non-randomness factors at infinite dilution can be obtained from the statistical mechanics. Expressions for those mixing properties are then derived by the combination of the statistical mechanics with the computer simulation. The expressions have been tested by comparisons with computer simulation results of the internal energy of mixing, chemical potential and liquid–liquid coexistence curve. The agreement is near perfect.