I am puzzled by a strange frequency dependence of the AC conductivity published for some carbon-filled (e.g. graphite, carbon black or combined carbon fillers) polymer composites above the precolation threshold at high frequencies. See the top curves in figs. 4-7 of the attached paper. I browsed several other publications. In most cases above the percolation threshold one gets either a frequency-independent conductivity (which is expected for Ohmic behavior), or a linearly inceasing conductivity in the log(sigma) - log (frequency) plot, which is expected for the hopping model. I did find some publications which exhibited the behavior shown in the attached file: i.e. a decreasing conductvitiy at teh highest frequencies. So far I did not find a convincing model which would explain this behavior. What is your suggestion? Can it be a testing artefact?