A van der Waals-type equation of state for fluids with associating molecules

The basic assumptions of van der Waals theory are contained in two well-known concepts: excluded volume (repulsive forces) and a homogeneous, isotropic field potential (attractive forces). We have superimposed on these, one more well-known concept: the existence of dimers, trimers, etc., at chemical equilibrium. With reasonable simplifying assumptions, we obtain a closed-form equation of state, applicable to all fluid densities, and potentially useful for fluids containing strongly polar or hydrogen-bonded molecules. At all temperatures and at high densities, the equation of state suggests a phase transition where, because of extensive association, a new (solid-like) phase is in equilibrium with a "normal" fluid phase. The boundary between these phases has no critical point.