EXACT THERMODYNAMIC FORMULATION OF CHEMICAL ASSOCIATION

The thermodynamics of interacting systems of two species of particles, A and B, may be specified in ''physical'' terms using only the two de nsities rho(a) and rho(b) or, alternatively, in a ''chemical picture'' using three densities rho(a), rho(b), and rho(c) related by a mass-ac tion law corresponding to the ''reaction'' A+B reversible arrow C, whe re C denotes a ''compound,'' ''complex,'' ''cluster,'' or ''associated pair.'' We present exact methods for generating associative or ''chem ical'' thermodynamics from an arbitrary physical specification. Both e xplicit order by-order matching conditions and a variety of thermodyna mically stable, closed-form solutions are derived. The analysis elucid ates precisely the freedom available to choose the association constan t, the definition of a cluster, and the interactions of a cluster (or ''pair'') with other clusters and with unpaired (i.e., dissociated, or ''free'') species. A single-species system of, say, X particles descr ibed chemically by 2X reversible arrow Y is analyzed similarly. Variou s examples, including purely hard-core liquids and the van der Waals f luid, demonstrate applications of the theory, which should aid in impr oving approximate treatments for electrolytes and other systems. The p recautions necessary in selecting a physically acceptable association constant are discussed. (C) 1998 American Institute of Physics. [S0021 -9606(98)51442-0]