Modeling the Effects of Ion Association on Alternating Current Impedance of Solid Polymer Electrolytes

This work presents a rigorous continuum model describing the transport of ions and assocd. ion pairs in solid polymer electrolytes subjected to small amplitude a.c. (ac) excitation. The model treats ion assocn. as a reversible reaction among ions and ion pairs. Dimensionless governing equations are developed from component mass balances, flux equations based on dil. soln. theory, and the Poisson equation. Assuming reversible electrode reactions and electroneutrality, the model equations have an anal. soln. Further simplifications are possible in limiting cases (weak and strong assocn., zero and infinite frequency excitation), giving expressions consistent with previously published models. We use the model to explore the effect of assocn./dissocn. reaction rates, ion pair diffusivity, and fractional dissocn. on ac impedance behavior. We present a scheme for establishing component diffusivities and fractional dissocn. from independent exptl. data for lithium perchlorate in poly(ethylene oxide). With no addnl. adjusted parameters, satisfactory agreement exists between calcd. and exptl. ac impedance data