Effective Dielectric, Magnetic and Optical Properties of Isotropic and Anisotropic Suspensions of Ferroic Nano-Particles

The present project focuses on the theoretical study of suspensions of nano-particles of different nature ferroelectric, ferromagnetic, multiferroic with size of 10-100nm in isotropic and anisotropic host. We shall investigate the effect of the dispersed nano-particles on the dielectric, magnetic and optical both linear and non-linear properties of the suspensions depending on the nano-particles nature, size, structure and shape. To describe the electric response of suspension of ferroelectric nanoparticles in insulating non-polar isotropic fluid we use a theory which is based on the Fokker-Planck Smoluchowski equation for a rotator with electric dipole under the external electric field. We also use the dynamic equation for reorientation of ferroelectric nano-particles in the isotropic suspension under the external electric field. We developed the generalized Maxwell-Garnett type theory to study dielectric properties of a dilute suspension of ferroelectric particles in a nematic liquid crystal host. It is supposed that submicron particles do not disturb the LC alignment and the suspension macroscopically appears similar to a pure LC. We propose theoretical model for effective dielectric function of ferroelectric LC suspension. It is found that particles permanent polarisation may significantly increase the effective value of suspension dielectric function in comparison with pure LC. For more elongated particles depolarisation factor is smaller and respectively the contribution of induced polarisation of particles to the effective dielectric function is higher. We show that there are two sets of the effective permittivity tensors. One of these can be used to derive the dielectric properties like capacitances. A second set must be used in free-energy calculations to predict director profile in the cells where, for example, director field is inhomogeneous.