We have carried out experimental and theoretical studies of the electric field-dependent ion transport in disordered materials and in disordered potential landscapes, respectively. In our experiments, we work in an electric field range up to 100 kV cm(-1), which is characterised by a weak nonlinear response of the mobile ions. We detect remarkable differences between different ion-conducting glasses regarding the temperature dependence of the nonlinear response. Theoretically, we study one-dimensional hopping models and continuous disordered potential models, respectively. When comparing theoretical and experimental data, we find both analogies and discrepancies.

Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of positive or negative nonlinear effects, respectively. Analytical results are obtained in the limit of high but finite dimensions. They are compared with the numerical results for 3D up to 6D systems. A very good agreement can be found, in particular for higher dimensions. The results can also be used to rationalize previous numerical simulations. The implications for the interpretation of nonlinear conductivity experiments on inorganic ion conductors are discussed.

The modelling of the ion conduction in disordered systems is analysed from two different perspectives. First, molecular dynamics simulations are employed to extract some basic properties of the hopping dynamics. It turns out that the dynamical processes can be described to a very good approximation as vacancy hopping processes. Second, the information content of nonlinear conductivity experiments, using high electric fields, is elucidated. For this purpose the single-particle dynamics on 1D and 2D model energy landscapes is elucidated numerically and partly analytically. The approaches encompass discrete as well as continuous energy landscapes, yielding complementary results about the dynamics. The impact for the interpretation of experimental data is discussed.