Modelling dielectric behaviour and anomalous relaxation in chromonic liquid crystals

We discuss the feasibility of applying a frequency-dependent diffusive model to study the dielectric response of complex fluids. The model considers the effect of free and bound particles by solving a non-exponential relaxation behaviour and anomalous diffusion phenomena into a coupled system of differential equations and boundary conditions. To illustrate the potentialities of the model in the data interpretation, we used the experimental results that provide the frequency spectra of a system formed by an aqueous solution of sunset yellow, a chromonic liquid crystal. Our model yields a considerably better adjustment of the experimental data compared to the simple Havriliak-Negami model and provides the relaxation frequency due to the director mode associated with the stack fluctuations about their short axis. Furthermore, we obtained parameters associated with the ion motion nature of the sample, including diffusion coefficient, Debye length and the ionic diffusive regime, which present a similar subdiffusive behaviour found in nematic thermotropic liquid crystals.