LATTICE STATISTICS FOR SIZE, CLUSTERING AND DISSOCIATION WITH EXAMPLEAPPLICATIONS IN VAPOR-LIQUID-EQUILIBRIA

An expression for the configurational degeneracy OMEGA of chain-like m olecules that undergo clustering and dissociation in a lattice is deve loped for the first time. Molecules are allowed to completely or parti ally dissociate and or cluster. The average number of molecules in a c luster and the average number of segments that a molecules dissociated into can be functions of both temperature and volume fraction. OMEGA is shown to reduce to Flory's expression for the configurational entro py of a system consisting of N polymer and M-rN solvent molecules when clustering and dissociation do not occur and when a vacant cell play the role of a solvent molecule. A Bragg-Williams-type approximation is used to model the effects of interaction energy. Two example applicat ions in vapor liquid equilibrium are presented. The first application is in the near ideal mixture of toluene and ethylbenzene. The method u sed to correlate the pure component vapor pressure data is demonstrate d. The molar volume and enthalpy of vaporization at various temperatur es are predicted. The binary x-y and T-x phase diagrams at P = 1 bar a re predicted and compared with measured data. The second application i s in the binary mixture of n-octane and propionic acid. Propionic acid completely dimerizes in the mixture. Predictions of the activity coef ficients of propionic acid are shown to be generally more representati ve of the actual behavior than predictions from the chemical theory of solutions.