27 research outputs found
High order elastic terms, boojums and general paradigm of the elastic interaction between colloidal particles in the nematic liquid crystals
Theoretical description of the elastic interaction between colloidal
particles in NLC with incorporation of the higher order elastic terms beyond
the limit of dipole and qudrupole interactions is proposed. The expression for
the elastic interaction potential between axially symmetric colloidal
particles, taking into account of the high order elastic terms, is obtained.
The general paradigm of the elastic interaction between colloidal particles in
NLC is proposed so that every particle with strong anchoring and radius has
three zones surrounding itself. The first zone for is the
zone of topological defects; the second zone at the approximate distance range
is the zone where crossover from
topological defects to the main multipole moment takes place. The higher order
elastic terms are essential nere (from 10% to 60% of the total deformation).
The third zone is the zone of the main multipole moment, where higher order
terms make a contribution of less than 10%. This zone extends to distances
.
The case of spherical particles with planar anchoring conditions and boojums
at the poles is considered as an example. It is found that boojums can be
described analitically via multipole expansion with accuracy up to
and the whole spherical particle can be effectively considered as the multipole
of the order 6 with multipolarity equal . The correspondent elastic
interaction with higher order elastic terms gives the angle
of minimum energy between two contact beads which
is close to the experimental value of .Comment: 9 pages, 13 figure
Elastic interaction between colloidal particles in confined nematic liquid crystals
The theory of elastic interaction of micron size axially symmetric colloidal
particles immersed into confined nematic liquid crystal has been proposed.
General formulas are obtained for the self energy of one colloidal particle and
interaction energy between two particles in arbitrary confined NLC with strong
anchoring condition on the bounding surface. Particular cases of dipole-dipole
interaction in the homeotropic and planar nematic cell with thickness are
considered and found to be exponentially screened on far distances with decay
length . It is predicted that bounding surfaces in
the planar cell crucially change the attraction and repulsion zones of usual
dipole-dipole interaction. As well it is predicted that \textit{the decay
length} in quadrupolar interaction is \textit{two times smaller} than for the
dipolar case.Comment: 4 pages,2 figure
Theory of elastic interaction between colloidal particles in the nematic cell in the presence of the external electric or magnetic field
The Green function method developed in Ref.[S. B. Chernyshuk and B. I. Lev,
Phys. Rev. E \textbf{81}, 041707 (2010)] is used to describe elastic
interactions between axially symmetric colloidal particles in the nematic cell
in the presence of the external electric or magnetic field. General formulas
for dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions in
the homeotropic and planar nematic cells with parallel and perpendicular field
orientations are obtained. A set of new results has been predicted: 1)
\textit{Deconfinement effect} for dipole particles in the homeotropic nematic
cell with negative dielectric anisotropy and perpendicular
to the cell electric field, when electric field is approaching it's Frederiks
threshold value . This means cancellation of the
confinement effect found in Ref. [M.Vilfan et al. Phys.Rev.Lett. {\bf 101},
237801, (2008)] for dipole particles near the Frederiks transition while it
remains for quadrupole particles. 2) New effect of \textit{attraction and
stabilization} of the particles along the electric field parallel to the cell
planes in the homeotropic nematic cell with . The minimun
distance between two particles depends on the strength of the field and can be
ordinary for . 3) Attraction and repulsion zones for all elastic interactions
are changed dramatically under the action of the external field.Comment: 15 pages, 17 figure
Theory of Elastic Interaction of the Colloidal Particles in the Nematic Liquid Crystal Near One Wall and in the Nematic Cell
We apply the method developed in Ref. [S.B.Chernyshuk and B.I.Lev,
Phys.Rev.E, \textbf{81}, 041701 (2010)] for theoretical investigation of
colloidal elastic interactions between axially symmetric particles in the
confined nematic liquid crystal (NLC) near one wall and in the nematic cell
with thickness . Both cases of homeotropic and planar director orientations
are considered. Particularly dipole-dipole, dipole-quadrupole and
quadrupole-quadrupole interactions of the \textit{one} particle with the wall
and within the nematic cell are found as well as corresponding \textit{two
particle} elastic interactions. A set of new results has been predicted: the
effective power of repulsion between two dipole particles at height near
the homeotropic wall is reduced gradually from inverse 3 to 5 with an increase
of dimensionless distance ; near the planar wall - the effect of
dipole-dipole \textit{isotropic attraction} is predicted for large distances
; maps of attraction and repulsion zones are crucially changed
for all interactions near the planar wall and in the planar cell; one dipole
particle in the homeotropic nematic cell was found to be shifted by the
distance from the center of the cell \textit{independent} of the
thickness of the cell. The proposed theory fits very well with experimental
data for the confinement effect of elastic interaction between spheres in the
homeotropic cell taken from [M.Vilfan et al. Phys.Rev.Lett. {\bf 101}, 237801,
(2008)] in the range .Comment: 18 pages, 23 figure
Ordered droplet structures at the liquid crystal surface and elastic-capillary colloidal interactions
We demonstrate a variety of ordered patterns, including hexagonal structures
and chains, formed by colloidal particles (droplets) at the free surface of a
nematic liquid crystal (LC). The surface placement introduces a new type of
particle interaction as compared to particles entirely in the LC bulk. Namely,
director deformations caused by the particle lead to distortions of the
interface and thus to capillary attraction. The elastic-capillary coupling is
strong enough to remain relevant even at the micron scale when its
buoyancy-capillary counterpart becomes irrelevant.Comment: 10 pages, 3 figures, to be published in Physical Review Letter
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