Diffusion of ionic penetrants in charged disordered media

Abstract

We consider the diffusion of ionic species in technologically relevant materials such as zeolites. These materials are characterized by a disordered density distribution of charged sites that couple with the diffusing species. We present a model for ion diffusion in a specific form of charged disorder. This is a primitive model for ion diffusion in charged or acidic zeolites. The theory relies on a path integral representation of the propagator, and a Gaussian field theory for the effects of the disorder. We use the Feynman–Bogoliubov variational method to treat the model, and calculate the diffusion coefficient for ions in a medium characterized by randomly located charges. Numerical solution of our equations, and asymptotic analyses of the same, show that in our theory there is a crossover from diffusive to subdiffusive behavior beyond a threshold value for the average density of the disorder. This threshold coincides with the actual diffusion changing from processes well approximated by Gaussian paths to those involving escapes from deep potential wells and barrier crossings. These results are discussed in the context of recent field-theoretic and renormalization group approaches to the problem of diffusion in random media. Our approach to diffusion in random media appears reasonably general and should be applicable to many technologically relevant problems, and is not compute intensive.