49 research outputs found
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
Parity Breaking in Nematic Tactoids
We theoretically investigate under what conditions the director field in a
spindle-shaped nematic droplet or tactoid obtains a twisted, parity-broken
structure. By minimizing the sum of the bulk elastic and surface energies, we
show that a twisted director field is stable if the twist and bend elastic
constants are small enough compared to the splay elastic constant, but only if
the droplet volume is larger than some minimum value. We furthermore show that
the transition from an untwisted to a twisted director-field structure is a
sharp function of the various control parameters. We predict that suspensions
of rigid, rod-like particles cannot support droplets with a parity broken
structure, whereas they could possibly occur in those of semi-flexible,
worm-like particles.Comment: 20 pages, 9 figures, submitted to Journal of Physics: Condensed
Matte
Liquid crystal director fluctuations and surface anchoring by molecular simulation
We propose a simple and reliable method to measure the liquid crystal surface
anchoring strength by molecular simulation. The method is based on the
measurement of the long-range fluctuation modes of the director in confined
geometry. As an example, molecular simulations of a liquid crystal in slab
geometry between parallel walls with homeotropic anchoring have been carried
out using the Monte Carlo technique. By studying different slab thicknesses, we
are able to calculate separately the position of the elastic boundary
condition, and the extrapolation length
Erratum: ``Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system'' [Condens. Matter Phys., 2023, 26, 33501: 1-12, DOI:10.5488/CMP.26.33501
Incorporation of the intensive and extensive entropy contributions in the disk intersection theory of a hard disk system
The one-body free volume, which determines the entropy of a hard disk system, has extensive (cavity) and intensive (cell) contributions. So far these contributions have not been unified and considered separately. The presented theory incorporates both contributions, and their sum is shown to determine the free volume and partition function. The approach is based on multiple intersections of the circles concentric with the disks but of twice larger radius. The result is exact formulae for the extensive and intensive entropy contributions in terms of the intersections of just two, three, four, and five circles. The method has an important advantage for applications in numerical simulations: the formulae enable one to convert the disk coordinates into the entropy contribution directly without any additional geometric construction. The theory can be straightforwardly applied to a system of hard spheres
Elastic multipoles in the field of the nematic director distortions
Theory of the interaction between all types of elastic dipoles and quadrupoles and distortions of the nematic director is presented. If a particle is small relative to the characteristic distortion length, the interaction is determined by the director derivatives at the particle location. We consider a spherical particle since, even under the standard assumptions of the multipole theory (weak deformations, one constant approximation), the problem can be solved analytically only in this case. Different dipoles interact with different distortion modes (e.g., isotropic dipole interacts with the splay, chiral dipole with the twist, and so on). In the main order, the interaction of a dipole is linear in the director derivatives, and the interaction of a quadrupole is linear in the second-order director derivatives. The theory goes beyond the main-order terms and predicts an effective distortion-induced dipolar component on a particle. This effect is described by the free energy term quadratic in the director derivatives and has contributions both of a bulk and surface origin. The bulk effect takes place even if the director at the particle surface is fixed, whereas the surface effect appears if the surface director is perturbed by the distortions due to a weak surface anchoring. The theory is illustrated by simple examples of the interaction of elastic dipoles with a disclination line, with cholesteric spiral, and with the director distortions in a hybrid cell
Elastic charge density representation of the interaction via the nematic director field
The interaction between particle-like sources of the
nematic director distortions (e.g., colloids, point
defects, macromolecules in nematic emulsions) allows for a useful
analogy with the electrostatic multipole interaction between
charged bodies. In this paper we develop this analogy to the level
corresponding to the charge density and consider the general
status of the pairwise approach to the nematic emulsions with
finite-size colloids. It is shown that the elastic analog of the
surface electric charge density is represented by the two
transverse director components on the surface imposing the
director distortions. The elastic multipoles of a particle are
expressed as integrals over the charge density distribution on
this surface. Because of the difference between the scalar
electrostatics and vector nematostatics, the number of elastic
multipoles of each order is doubled compared to that in the
electrostatics: there are two elastic charges, two vectors of
dipole moments, two quadrupolar tensors, and so on. The
two-component elastic charge is expressed via the vector of
external mechanical torque applied on the particle. As a result,
the elastic Coulomb-like coupling between two particles is found
to be proportional to the scalar product of the two external
torques and does not directly depend on the particles' form and
anchoring. The real-space Green function method is used to develop
the pairwise approach to nematic emulsions and determine its form
and restrictions. The pairwise potentials are obtained in the
familiar form, but, in contrast to the electrostatics, they
describe the interaction between pairs (dyads) of the elastic
multipole moments. The multipole moments are shown to be uniquely
determined by the single-particle director field, unperturbed by
other particles. The pairwise approximation is applicable only in
the leading order in the small ratio particle
size-to-interparticle distance as the next order contains
irreducible three-body terms