林磊
理论物理通讯. 1982, 1(6): 691-697.
The elastic energy density of Iiquid crystal under the action of external electric field E is given by F=F(ni,ni,j,Ei,Ei,j……)where n is the director and ni,j,,Ei,j the gradients. By a systematic expansion of F in polynomials and the use of material symmetries, we obtain macroscopically for nematics and cholesterics all the possible external field-effects. In addition to the well-known dielectric interaction (n · n)and the flexoelec-tric effects of Meyer,-e1(E · n)(∇ · n)-e3 E · (n ∇ ·)n,we find a new term e0n · (n · ∇)E which corresponds to the flexoelectric effect related to electric quadrupoles introduced microscopically by related to electric quadrupoles introduced microscopically by Prost and Marcerou, This new term is not equivalent to the previous two terms of Meyer. An experiment to measure this new flexoelectric constant eo is proposed. Previous experiments measuring fIexoelectric constants are compared and discussed in the light of our theory, which also applies to other cases of external vector fields.