Theoretical Description of Ion Conduction in Disordered Systems: From Linear to Nonlinear Response

Abstract

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.

Physical mechanisms of nonlinear conductivity: A model analysis

“…For single-particle hopping models on a lattice it is has been shown numerically that one obtains σ r < 0 for a broad box-type distribution of energies whereas a broad Gaussian energy distribution gives rise to σ r 1, in agreement with the experimental results 32 .…”

“…In previous simulations also the box-type distribution was analysed somewhat closer. It was shown that in this case one observes σ r < 1 32 . When mapping this distribution on a bimodal distribution an appropriate choice is α ≈ 1/2.…”

“…As outlined in the Introduction hopping models constitute a reasonable approach for the real-world situation in inorganic ion conductors. The previous numerical results indicated that the experimental observation σ r > 1 suggests a very broad distribution of the site energies such that there exist a few sites with very low energies 32 . However, in the previous work no physical picture for this observation could be supplied.…”

Nonlinear ion transport in the supercooled ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide: Frequency dependence of third-order and fifth-order conductivity coefficients

“…[14][15][16][17][18] Other models predict positive third-order a) Email: laxminar@chemie.uni-marburg.de dc conductivity coefficients, which are, however, much smaller than those found in experiments. 19,20 The frequency dependence of the third-order conductivity spectra of solid ion conductors differs clearly from the universal dynamic response observed in the linear spectra. At low frequencies, a dc plateau regime is detectable in the third-order spectra.…”

The frequency dependence of nonlinear conductivity in non-homogeneous systems: An analytically solvable model

“…Interestingly, for periodic boundary conditions the conductivity displays nonanalytic behavior at zero field in the thermodynamic limit [7,24]. From studying a disordered discrete 3D-energy landscape via computer simulations it turned out that for a Gaussian distribution of site energies the experimental relation a app a hopp can be recovered [25].…”