Electrical conductivity and an approximate mean square displacement

Measurements of electrical properties of materials are of interest in diffusion experiments, where the mean square displacement of charge carriers plays a distinctive role. Here, an approximation of the mean square displacement is explored as a route to investigate dynamical aspects of systems from electrical conductivity, independently of the number of types of charge carriers. Within this framework, based on Kubo’s linear response theory, we focus on the variance of the center of charges displacement. As an application of this approach, firstly we considered the impedance spectroscopy of a liquid crystal sample at specific experimental conditions. In a second employment of the approach, we discussed the use of the approximate (effective) mean square displacement in relation to an equivalent circuit modeling. Our analysis highlighted the sensitivity of the method in different situations. In addition, these situations are discussed in connection with anomalous diffusion. From a theoretical point of view, the results obtained here offer a basis for making use of effective models that assume the presence of anomalous diffusion.