  We consider orientational transitions of lamellar phases under the influence
of a spatially nonuniform electric field. The transition between parallel and
perpendicular lamellar stackings with respect to the substrate is investigated
as a function of the system parameters. The dielectrophoretic energy and the
energy penalty for having dielectric interfaces perpendicular to the field's
direction are identified as linear and quadratic terms in a free energy
expansion in the dielectric constant mismatch. We find that if the dielectric
constant mismatch $\Delta\eps$ is smaller than some critical value
$\Delta\eps_c$, parallel lamellar stacking will be realized, no matter how
large the voltage difference between electrodes is. At
$\Delta\eps>\Delta\eps_c$, perpendicular stacking will appear if the voltage is
high enough. Nonuniform fields remove the in-plane degeneracy present in the
more common uniform fields. We therefore calculate the energy of grains of
different orientations. The torque acting on the grains leads to the preference
of only one orientation. The results have direct implications to block
copolymer orientation and to surface patterning on the nanometer scale.
