Simple bond length dependence: A correspondence between reactive fluid theories

The theory of classical, associating fluids in two different but equivalent methods were examined for a pair of simple reactive models and extract low density limits for two models. The first method is the dissociative system equivalent to assuming a rigid bond at some fixed length that has a trivial, discontinuous dissociation energy characterized by a sticky parameter. The second model is a rigid molecule with no dissociation. In both cases, the theory shows that if the total site density is treated as given and the molecular density solved for in terms of the total density, hard sphere diameter, and dimer bond length, then the limits of short and logn bond lengths for both models are equal.