Flexoelectric coefficients enhancement via doping carbon nanotubes in nematic liquid crystal host

Flexoelectric coefficients of carbon nanotube (CNT) doped nematic liquid crystals (NLCs) are studied based on the Helfrich theory. Weak and hard anchoring conditions between the NLC molecules and CNTs are considered. The volume fraction of the CNTs in nematic host is assumed to be low, which makes nanotubes aggregation phenomena negligible. Also, the length of doped CNTs is assumed to be lower than 10μm, so these rigid rods with low concentration cannot possess any flexoelectric polarization by themselves, only their presence modifies the flexoelectric coefficients of the NLC system. The Landau-de Gennes theory is used to calculate the order parameter changes in the medium. Also, the numerical density definition is renewed in the presence of nanotubes. It is shown that in the nematic phase the flexoelectric coefficients increase along with the increase of the coupling strength and temperature. The enhancement in flexoelectric coefficients is more significant in hard anchoring conditions than in the weak anchoring case. The flexoelectric coefficients increase up to 5-fold is calculated near the phase transition temperature, which is in good accordance with the experimental reported data.