Molecular dynamics studies of ionically conducting glasses and ionic liquids: wave number dependence of intermediate scattering function.

Dynamical heterogeneity is a key feature to characterize both acceleration and slowing down of the dynamics in interacting disordered materials. In the present work, the heterogeneous ion dynamics in both ionically conducting glass and in room temperature ionic liquids are characterized by the combination of the concepts of Lévy distribution and multifractality. Molecular dynamics simulation data of both systems are analyzed to obtain the fractional power law of the k-dependence of the dynamics, which implies the Lévy distribution of length scale. The multifractality of the motion and structures makes the system more complex. Both contributions in the dynamics become separable by using g(k,t) derived from the intermediate scattering function, F(s)(k,t). When the Lévy index obtained from F(s)(k,t) is combined with fractal dimension analysis of random walks and multifractal analysis, all the spatial exponent controlling both fast and slow dynamics are clarified. This analysis is generally applicable to other complex interacting systems and is deemed beneficial for understanding their dynamics.