Density-functional theory of the flexoelectric effect in nematic liquids

A molecular theory of the flexoelectric (FE) effect in nematic liquids is developed. Expressions are derived for both the dipole and quadrupole contributions to the FE coefficients. The dipole contribution is expressed in terms of direct correlation functions of the isotropic liquid having a number density equal to that of the ordered medium. The quadrupole contribution is, however, found to be independent of the direct correlation functions and depends only on the anisotropic part of the molecular quadrupole tensor. The two contributions are found to be nearly equal in magnitude. While the dipole contribution is found to be proportional to both P<SUP>&#8722;</SUP><SUB>2</SUB> and P¯<SUB>2</SUB><SUP>2</SUP>, where P<SUP>&#8722;</SUP><SUB>2</SUB> is the order parameter of the nematic phase, the quadrupole contribution is proportional to P<SUP>&#8722;</SUP><SUB>2</SUB>. The transverse component of the molecular dipole moment contributes significantly more than the longitudinal component. The difference between the two FE coefficients is primarily due to the transverse dipole. It is shown that with increased knowledge of the molecular parameters, such as electric multipole moments, asymmetry in molecular shape, length-width ratio, etc., one can calculate accurate values of the FE coefficients of any given system