Lattice theory of solvation and dissociation in macromolecular fluids. II. Quasichemical approximation

Solvation and association of ions in polymer solvents used for polymer electrolytes is studied in the framework of the Guggenheim quasichemical approximation using a lattice model. The pure solvent is described using the mean-field approximation of Sanchez and Lacombe. The model accounts for the short range part of the ion-polymer interaction, in particular at specific interaction sites (such as the cation-oxygen attraction in polymer hosts), while long range dieletric effects are added as in the Born theory of solvation. We obtain expressions which relate thermodynamic quantities of solvation (free energy, entropy, enthalpy, and volume) to properties of the pure solvent. From these, the equilibrium constant for the ion pairing can be obtained as a function of temperature, pressure, and solvent properties. A consistent fit to the experimental data in polypropylene oxide) (PPO) can be obtained if specific interaction sites for the cations are assumed. Dependence of the solvation and the equilibrium constant on the polymer chain length which is seen in the short chain limit saturates and disappears beyond a few monomer sizes. The relative roles of short range and of dielectric interactions is discussed.