  A theoretical study of a dielectrophoretic force, i.e. the force acting on an
electrically neutral particle in the inhomogeneous electric field, which is
produced by a ferroelectric domain pattern, is presented. It has been shown by
several researchers that artificially prepared domain patterns with given
geometry in ferroelectric single crystals represent an easy and flexible method
for patterning dielectric nanoobjects using dielectrophoretic forces. The
source of the dielectrophoretic force is a strong and highly inhomogeneous
(stray) electric field, which exists in the vicinity of the ferroelectric
domain walls at the surface of the ferroelectric film. We analyzed
dielectrophoretic forces in the model of a ferroelectric film of a given
thickness with a lamellar 180${}^\circ$ domain pattern. The analytical formula
for the spatial distribution of the stray field in the ionic liquid above the
top surface of the film is calculated including the effect of free charge
screening. The spatial distribution of the dielectrophoretic force produced by
the domain pattern is presented. The numerical simulations indicate that the
intersection of the ferroelectric domain wall and the surface of the
ferroelectric film represents a trap for dielectric nanoparticles in the case
of so called positive dielectrophoresis. The effects of electrical neutrality
of dielectric nanoparticles, free charge screening due to the ionic nature of
the liquid, domain pattern geometry, and the Brownian motion on the mechanism
of nanoparticle deposition and the stability of the deposited pattern are
discussed.
