A modified free-volume model: correlation of ion-conduction in strongly associating polymeric materials

Ions tend to aggregate in media of low dielectric constant, and this tenden cy to form strong associations causes small amounts of ionic functionality to have a significant influence on the properties of ionic polymers. As a c onsequence of ionic functionality and strong interactions ionomers exhibit unique transport characteristics compared to conventional polymers. While i t has been observed that ion mobility is related to viscosity, a comprehens ive theory like the existing theories for non-associating systems has not b een developed for associating systems. In this work, free-volume expressions are developed for self-diffusion of i ons in ionomers by treating the polymer chain as a two-component system. Th e ion-counterion pair and the non-ionic part that is involved in ion transp ort are treated as species 1 while the remaining non-ionic part of the poly mer is treated as species 2. The free-volume of the system is obtained by f itting the viscosity-temperature relationship using the Williams-Landel-Fer ry (WLF) equation [Viscoelastic Properties of Polymers, Wiley, New York, 19 70]. However, since the flow behavior of the ionomer consists of contributi ons from both the ionic and non-ionic parts, the definitions of the free-vo lume parameters have been modified. The expressions developed are then used to evaluate data for polymer systems with different molecular weights, and type and size of cation in the ionic group. The results of the correlation are generally consistent with the free-volume concepts and assumptions emp loyed to describe ion-conduction. Using the approach developed, an estimate of the relative size, of the jumping units responsible for conduction and diffusion in polymeric materials can be obtained. The free-volume expressio ns demonstrate that the size of the jumping unit is a complex function of t he ionomer composition and the size of the ion-counter ion pair; a finding consistent with the values obtained from correlation of experimental data. The relatively large size of the ionic jumping units compared to convention al polymeric materials agrees with the ion-hopping mechanism used to descri be mobility in ionic polymers. (C) 2001 Elsevier Science B.V. All rights re served.