Multifractal nature of heterogeneous dynamics and structures in glass forming ionic liquids

Complex dynamics and structures of ionic liquids exemplified in 1-ethyl-3-methylimidazolium nitrate (EMIM-NO₃) are examined by molecular dynamics simulations. Correlation length of the radial charge distribution function and density distribution function show different temperature dependence. Density profiles are obtained from the accumulated positions visited by ions during the MD runs. The profile originating from the coexistence of layered structures of density (density wave) and those of charges (charge density wave), shows complicated heterogeneity, which is proven to be multifractal in nature. Thus, present is more than one characteristic length scale together with their mixing. The multifractal density profiles are formed by the multifractal walks with fast and slow ions. Generally, the coexistence of different length scales due to the different species or the different local structures can be the mechanism to form similar multifractal dynamics and structures.