Frederick's transitions for nematics dispersed by nanoparticles with cylindrical–spherical symmetry

In this paper, we obtain the Frederick’s transition parameters for nematic liquid crystal–nanoparticle (NLC–NP) systems. We introduce a new term in Frank's elastic energy expression, which describes the orientational interaction energy between LC molecules and NPs, which have cylindroid-spherical symmetry and some degree of anisotropy. We show that the anchoring angle of LC molecules on the NP surface plays a critical role in determining the sign of the interaction energy density. The latter dictates how the doped NPs affect the material and display parameters of the LC. We use our previously reported experimental data on 6CB nematic dispersed with silver NPs to evaluate the newly introduced critical parameters. The measured elastic parameter data at different temperatures are fitted with theoretical curves, where the anchoring angle and surface energy are used as the fitting parameters. The obtained values of the critical parameters show that the proposed model adequately describes the interaction of NPs with the LC matrix in these studied systems.