Thermodynamics of ion-containing polymer blends and block copolymers

We develop a theory for the thermodynamics of ion-containing polymer blends and diblock copolymers, taking polyethylene oxide (PEO), polystyrene and lithium salts as an example. We account for the tight binding of Li^{+} ions to the PEO, the preferential solvation energy of anions in the PEO domain, the translational entropy of anions, and the ion-pair equilibrium between EO-complexed Li^{+} and anion. Our theory is able to predict many features observed in experiments, particularly the systematic dependence in the effective χ parameter on the size of the anions. Furthermore, comparison with the observed linear dependence in the effective χ on salt concentration yields an upper limit for the binding constant of the ion pair.