DENSITY FUNCTIONAL THEORY OF THE ELASTIC-CONSTANTS OF A NEMATIC LIQUID-CRYSTAL

We present a derivation of the microscopic expressions for the elastic constants of nematic liquid crystals within the density functional formalism. We recover the expressions of Poniewierski and Stecki for molecules with three planes of symmetry, but our general expression includes the effects of the relaxation in the angular distribution function of the deformed nematic, which, for asymmetric molecules, may reduce the values of the elastic constants. The connection with the flexoelectric effect is also analysed.