38 research outputs found
Static dielectric properties of an ensemble of restricted one-dimensional oscillators
Deviations from constancy of the Clausius-Mossotti
function, C[subscript M], with changes in density and temperature are
considered on the basis of a one-dimensional oscillator
model of the atom in which the valence electrons are assumed
restricted by infinite potentials, but interact with all
others in the medium through dipolar forces.
The density-dependence of C[subscript M] is qualitatively in
agreement with experiment, but the temperature-dependence
is negligible as the excited states of an oscillator do not
represent those of real atoms. In addition, the model does
not permit the existence of the ionized state of the atom.
The analysis here suggest a more promising, threedimensional
model which admits of realistic atomic potentials,
dipolar interaction based on continuous dielectric surroundings
and repulsive potentials which ensure the existence of
delocalized electronic states with consequent screening of
the dipolar forces
Clausius-Mossotti Function for Restricted One-dimensional Operators
Deviations from constancy of the C_M function, are considered on the basis of a one-dimensional oscillator model in which the valence electrons are assumed restricted by infinite potentials, but interact with all others through dipolar forces. A computer calculation shows that the density-dependence of C_M is qualitatively in agreement with experiment, but the temperature-dependence is negligible. An interesting feature is the occurrence of negative polarizabilities for the excited states at modest densities -indicating an insulator-to-metal transition. This result is in conflict with the basic precepts of the model which does not permit fully delocalized electronic states. However, this analysis suggests a more promising three-dimensional model which admits of realistic atomic potentials, dynamical dipolar interaction and repulsive potentials which ensure the existence of the ionized state of the atom
Molecular theory of elastic constants of liquid crystals. III. Application to smectic phases with tilted orientational order
Using the density functional formalism we derive expression for the
distortion free energy for systems with continuous broken symmetry and use it
to derive expression for the elastic constants of smectic phases in which
director is tilted with respect to the smectic layer normal. As in the previous
papers of the series (Phys. Rev. A {\bf 45}, 974 (1992), E {\bf 49}, 501,
(1994)) the expressions for the elastic constants are written in terms of order
and structural parameters. The structural parameters involve the generalised
spherical harmonic coefficients of the direct pair correlation function of an
effective isotropic liquid. The density of this effective isotropic liquid
depends on the nature and amount of ordering present in the system and is
evaluated self- consistently. We estimate the value of elastic constants using
reasonable guess for the order and structural- parameters.Comment: 31 pages; 1 Fig. in GIF format, To be appear in Phys. Rev.
Theory and simulation of the nematic zenithal anchoring coefficient
Combining molecular simulation, Onsager theory and the elastic description of
nematic liquid crystals, we study the dependence of the nematic liquid crystal
elastic constants and the zenithal surface anchoring coefficient on the value
of the bulk order parameter
Numerical study of surface-induced reorientation and smectic layering in a nematic liquid crystal
Surface-induced profiles of both nematic and smectic order parameters in a
nematic liquid crystal, ranging from an orienting substrate to "infinity", were
evaluated numerically on base of an extended Landau theory. In order to obtain
a smooth behavior of the solutions at "infinity" a boundary energy functional
was derived by linearizing the Landau energy around its equilibrium solutions.
We find that the intrinsic wave number of the smectic structure, which plays
the role of a coupling between nematic and smectic order, strongly influences
the director reorientation. Whereas the smectic order is rapidly decaying when
moving away from the surface, the uniaxial nematic order parameter shows an
oscillatory behavior close to the substrate, accompanied by a non-zero local
biaxiality.Comment: LaTeX, 17 pages, with 4 postscript figure
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
Elastic constants of hard and soft nematic liquid crystals
The Frank elastic constants for a nematic liquid crystal have been calculated by computer simulations for a fluid of hard
ellipsoids and by the Poniewierski-Stecki method for ellipsoids with and without an attractive square well. Required for
the Poniewierski-Stecki method is the direct correlation function c(1,2) and its dependence on the mutual molecular orientations.
This was addressed using several models: the Parsons model, a two-term virial expansion, and the PY and HNC theories
of Patey et al. In the Parsons model for c(1,2), the derived Frank elastic constants for hard ellipsoids were in agreement
with the Poniewierski-Holyst values for hard spherocylinders. However, the agreement with simulation values was less
satisfactory, as the simulation values exceeded the Parsons model values and the discrepancy grew with increasing particle
asymmetry. The Frank constants, derived using a hard-core potential with an exterior SW (convex peg in a round hole),
were in fair agreement with experimental data on prolate and oblate molecules, at the expense of employing overly large-order
parameters (characteristic of uniaxial hard particle models). Omitted long-range correlations in the c( 1,2), present even
in the hard-body models, is suspected to be the cause of the discrepancy of the simulation and experimental Frank constants
with those calculated on the basis of short-range models for c(1,2)