Nematic ordering in a cell with modulated surface anchoring: Effects of flexoelectricity

We have analyzed molecular ordering in a nematic sample sandwiched between two parallel substrates, characterized by a periodically varying anchoring easy axis. If the periodicity lambda is smaller than the Debye screening le ngth l(D) and the nematic material possesses flexoelectric properties, it i s necessary to take into account also the electrostatic and flexoelectric c ontributions in the thermodynamical potential when the actual director held is determined. In this framework, for small deviations from the homeotropi c alignment we have derived analytical expressions for the tilt angle (thet a) and the electrical potential To establish a connection with experimental ly observable quantities, we have related the theta profile to the average [theta(2)] and investigated its behavior for different values of lambda, th e flexoelectric coefficient, and the anchoring strength w. Our results indi cate that in a nematic with Pronounced flexoelectric properties for small e nough lambda, a kind of subsurface deformation appears, which substantially decreases [theta(2)]. Therefore, effects of flexoelectricity cannot be neg lected in treating nematic cells with modulated anchoring which allows bist able ordering. [S1063-651X(99)07807-1].