Frederiks transition in ferroelectric liquid-crystal nanosuspensions

We construct a theoretical model of the dielectric properties of a ferroelectric LC nanosuspension (FLCNS), using a generalized Maxwell-Garnett picture. The theory supposes that an FLCNS may as a first approximation be considered as a complex homogeneous dielectric ceramic, thus neglecting positional correlations of the colloidal particles. The FLCNS then consists of an anisotropic matrix with a very low concentration (<1% by volume) of impurity particles. The impurity particles possess both shape and dielectric anisotropy, as well as a permanent electric polarization and strong liquid-crystal director anchoring on the particle surface. We show that the effective dielectric properties for capacitance properties and for effective liquid-crystal free energies do not coincide. We calculate the effect of doping a liquid crystal with ferroelectric impurities on the Frederiks transition. The theory takes account of inclusion shape, dielectric susceptibility, and local field effects. We neglect the possibility of dielectric particle chaining, which appears experimentally not to occur in general. Our calculations suggest, in qualitative agreement with experiment, that doping a nematic liquid crystal with ferroelectric particles, even at very low particle concentration, can in some cases significantly decrease the electric Frederiks threshold field.