Modeling the Effects of Ion Association on Direct-Current Polarization of Solid Polymer Electrolytes

Abstract

Considerable experimental evidence indicates that ion association occurs in solid polymer electrolytes. This work provides a thorough theoretical analysis of the effect of ion association on the conductivity, general current-potential behavior, and limiting current density in a solid polymer electrolyte. The model employs dilute solution theory to describe the fluxes of cations, anions, and ion pairs in a motionless continuum but neglects higher order association. The predictions of the model highlight the effects of the relative diffusion coefficients and dimensionless association constant on concentration distributions of simple ions and ion pairs, the limiting current density, and the potential drop required to drive a specified current density. If ion pairs have a diffusivity comparable to those of cations and anions, increasing ion association leads to a continuous decrease in molar conductivity and current density at constant applied potential. If the ion pairs have a diffusivity that is large compared to cations, the situation is quite different. In this case, ion association increases the limiting current density to values that may be several times that found in the case of full dissociation. Furthermore, the model predicts maxima in the molar conductivity and current density at fixed potential drop as the degree of ion association increases.

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

“…In general, both the real and imaginary components of the impedance decrease with increasing ⌸ p values. The trend at low frequencies is similar to that seen previously 8 for dc polarization. In effect, ion pairs provide a parallel mechanism for transporting cations; increasing ⌸ p promotes this mechanism, reduces concentration polarization, and therefore decreases the impedance ͑at fixed frequency and fractional dissocia- tion͒.…”

“…As discussed previously, 8 the ion pair diffusivity may be greater than that of cations or anions due to attractive interactions between free ions and the polymer electrolyte. Thus, ⌸ p ϵ D p /D s may be either larger or smaller than 1.0.…”

“…For example, the dc model 8 can be used with a measurement of limiting current density to provide one data point involving D p and ␣. One ac impedance spectrum provides three additional data points: the zero and infinite frequency limits ͑for which we have analytical expressions͒, and the breakpoint frequency ͑i.e., max͓ϪIm(Z )͔͒, for which an analytical expression could also be derived ͑although we have not done so͒.…”

“…We were unable to obtain a corresponding analytical expression from our previous dc polarization model. 8 After appropriate translation of dimensionless groups, we find that the zero frequency conductivity derived from Eq. 28 agrees perfectly with the numerical dc conductivity results shown in Fig.…”

Mathematical Model of Electrodiffusion, Dissociation and Recombination in the Diffusive Layer

“…Simultaneously the cation-anion interactions prove to be also very strong. It leads to significant ion association [1,2,4,5]. Experimental data from [4,5] suggest that the neutral ion pairs greatly outnumber single ions.…”