Non-exponential kohlrausch polarization currents in solid electrolytes

The non-exponential polarization and depolarization current density after a voltage step is investigated in the ion conducting polymer polyethylene oxide yielding a Kohlrausch or Curie-von Schweidler behavior in the long and in the short time range with different exponents respectively. To explain this behavior simulations with a three-dimensional hopping model are performed. Interactions between all charges in the system are considered. A distribution of sites is introduced to construct an amorphous structure. The intrinsic barrier heights between two neighboring sites in a multi-well energy structure depend here on the distance between the sites and the interaction between the charges yielding a distribution of relaxation times. Simulations with this model show a Kohlrausch behavior in the long time range as well as in the short time range. For short times the distribution of relaxation times is responsible for the Kohlrausch behavior. In the long time range a distribution of distances of the sites to the electrodes resulting in a distribution of image forces causes the Kohlrausch current.