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We present a theoretical study of the orientational and electrical behaviors of a cholesteric liquid crystal dispersed with ferroelectric nanoparticles. We assume a soft planar coupling between the liquid crystal molecules and the nanoparticles. We consider two spiral structures in the ferroelectric nano-dispersed system under an external electric field. This assumption is due to the fact that the director and the polarization vector would have different pitches of spiral structure. We study the behavior of the average polarization and the pitch of the helical structure as a function of the field strength. The impact of ferroelectric nanoparticles on cholesteric-nematic phase transition is investigated by calculating the critical electric field. The influence of field strength and material parameters on the phase transition is also discussed. The calculations are based on a developed continuum theory and a modified form of free energy for the helical supramolecular structure. The influence of nanoparticle volume fraction on the helix unwinding of both spiral structures is studied. It is found that an electric field with a sufficiently high strength causes an increase in the pitch of the helical structure of polarization. We obtain a critical volume fraction of nanoparticles, after which the pitch of the polarization helical structure differs from the director pitch.

Structural transition in a ferroelectric nano-dispersed cholesteric liquid crystal