Theoretical description of dielectric relaxation of ice with low concentration impurities

•A new model of non-Arrhenius relaxation behavior of ice with impurities is developed.•A temperature dependence of the dielectric relaxation time of ice with impurities is obtained.•It reproduces the observed non-Arrhenius relaxation behavior of ice.•The suppression of the non-Arrhenius behavior of ice relaxation in a water-gelatin mixture with increasing of the gelatin is described.•The theoretical model can be used for monitoring the purity of ice. The impurities in ice generate the orientational defects in the sample that block proton jumps. In this article, we analyze the dielectric relaxation behavior of ice in the presence of impurities in the framework of the trap-controlled proton transport model. We obtain an expression for the dielectric relaxation time, which reproduces the non-Arrhenius behavior and includes the parameters of the ice microstructure. Using the obtained expression for the dielectric relaxation time, we analyze the dielectric relaxation of ice in a water-gelatin mixture with a low gelatin concentration and demonstrate excellent agreement between the developed theoretical approach and experiment. The developed approach discovers new promising possibilities of the method of broadband dielectric spectroscopy in control of the purity of ice.