FLORY AND GUGGENHEIM LATTICE STATISTICS REINTERPRETED AND EXTENDED TOINCLUDE MOLECULAR CLUSTERING AND CHEMICAL-DISSOCIATION

A new method is presented for counting the number of distinguishable a rrangements available to a mixture of molecules in a lattice model. Ch ain molecules are used and these are allowed to undergo molecular clus tering and chemical dissociation. The resulting equation for the confi gurational degeneracy is shown to reduce to, the equations of Flory an d Guggenheim in the appropriate limits. The Guggenheim equation is sho wn to be exact in one dimension; extension to higher dimensions requir es allowing the lattice coordination number to increase beyond 2. The Flory equation is shown to be the low volume fraction approximation of the Guggenheim equation. The counting method developed can be used to model entropy effects associated with chemical reactions. The equatio n of state derived using the new configurational degeneracy term is sh own to reduce to a number of well known equations. Comparison to van d er Waals equation of state shows that the improved ability of the new equation to model observed behavior, results from a redefinition of th e van der Waals free volume. (C) 1995 American Institute of Physics.