Metastable States of a Fluid Inside a Binodal in the Context of Cluster Variation

The behavior of the isotherm and molecular distributions inside the binodal is analyzed to solving an Ising model obtained on the basis of cluster variation for planar lattices with coordination numbers 3, 4, 6. It is found that the microscopic approach gives a probabilistic interpretation of the Maxwell macroscopic rule and explains how the isotherm a secant appears between the regions of coexistence of two phases. A region of no solutions (the region of degeneracy) is found inside the binodal, and the critical temperatures of degeneracy at which the nontrivial solution to the equations disappears are calculated for this region. The region of degeneracy inside the binodal expands and approaches the binodal curve as the temperature falls, so the degeneracy curve and the binodal become indistinguishable. Numerical iterative calculations are used to study the dependence of the region of no solution inside the binodal as a cluster grows. The critical temperature of degeneracy asymptotically approaches that of the binodal as the cluster grows. Existing ways of interpreting metastable states are discussed, along with as the correspondence between the new results and previously known mean-field (ignoring correlations) and quasi-chemical (considering only direct correlations) approximations, and an exact result of the Yang–Lee condensation theory.