Dielectric Relaxation in Nanocrystals: A Scale Effect

Abstract

The study explores a scale effect inherent to the dielectric relaxation in nanocrystals: the dependence of dielectric relaxation parameters on the size of a nanocrystal. We offer a model of the scale effect for the dielectric relaxation caused by thermally activated motion. In this model, a nanocrystal is considered as a physical infinitesimal volume: a region where a local equilibrium exists. We conclude that the thermally activated motion causes the energy fluctuations in a nanocrystal as a whole. A relation between the intensity of these fluctuations and the size of nanocrystals is derived. According to this relation, the intensity of the fluctuations decreases with the decrease of the nanocrystal sizes. Using the relation, a characteristic of a thermally activated motion–the size of the activation zone–can be determined experimentally. We verify the model using experimental data for the complex dielectric permittivity of the composites (silica gel matrix with undecylenic acid nanocrystalline inclusions of various sizes) in the temperature range from −190 to 50 °C at frequencies 5, 10, 20, and 50 kHz. The results of the experiment agree with the predictions of the model.