Ion transport in phase-separated single ion conductors

We report an analysis of the applicability of the Nernst-Einstein (N-E) description relating ion conductivity to diffusivity to phase-separated single-ion conductors. We find that two different bases for this description are needed to capture regimes in which the membrane contains high or low amounts of water uptake. The N-E equation requires an ion concentration term. For high water contents, good agreement with the N-E equation is obtained if the concentration is calculated based on the amount of water present. For lower water contents, the concentration must be based on the total membrane volume for the diffusivity/conductivity behavior to comply. The division between these two regimes is roughly water content corresponding to the hydration number of the ion. This has implications for the study of hydrated polymer electrolytes as well as other 'channel' containing ion conductors.