Enhancement in electrical response of liquid crystals with carbon nanotubes doping

The Freedericksz transition threshold is investigated in a homogeneously aligned carbon nanotube (CNT) doped liquid crystal (LC) planar cell. By neglecting the aggregate and bundle formation of CNTs in a low concentration of CNT doped LC cell, the reduction in the Freedericksz transition threshold is calculated theoretically. Flexoelectric polarisation tensorial expansion in terms of the order parameter and the generalised Helfrich theory is used to estimate the flexoelectric coefficients in the mixture. Dipolar and quadrupolar polarisations are studied in the flexoelectric coefficients of the mixture. It is shown that doping CNTs changes the flexoelectric coefficients through the order parameter of LCs. According to these calculations, for the LC molecules with a dipole moment parallel to their molecular axis, up to 4-fold increase in flexoelectric coefficient is expected, which is in good accordance with experimental reports. Also, it is shown that in the absence of dipolar flexoelectricity, the quadrupolar polarisation is responsible for the changes of the flexoelectric coefficients.