450 research outputs found
Spontaneous sense inversion in helical mesophases
We investigate the pitch sensitivity of cholesteric phases of helicoidal
patchy cylinders as a generic model for chiral (bio-)polymers and helix-shaped
colloidal rods. The behaviour of the macroscopic cholesteric pitch is studied
from microscopic principles by invoking a simple density functional theory
generalised to accommodate weakly twisted director fields. Upon changing the
degree of alignment along the local helicoidal director we find that
cholesteric phases exhibit a sudden sense inversion whereby the cholesteric
phase changes from left- to right-handed and vice versa. Since the local
alignment is governed by thermodynamic variables such as density, temperature
or the amplitude of an external directional field such pitch sense inversions
can be expected in systems of helical mesogens of both thermotropic and
lyotropic origin. We show that the spontaneous change of helical symmetry is a
direct consequence of an antagonistic effective torque between helical
particles with a certain prescribed internal helicity. The results may help
opening up new routes towards precise control of the helical handedness of
chiral assemblies by a judicious choice of external control parameters.Comment: 6 pages, 4 figures, submitted. arXiv admin note: text overlap with
arXiv:1004.222
Effect of size polydispersity on the pitch of nanorod cholesterics
Many nanoparticle-based chiral liquid crystals are composed of polydisperse
rod-shaped particles with considerable spread in size or shape, affecting the
mesoscale chiral properties in, as yet, unknown ways. Using an algebraic
interpretation of Onsager-Straley theory for twisted nematics, we investigate
the role of length polydispersity on the pitch of nanorod-based cholesterics
with a continuous length polydispersity, and find that polydispersity enhances
the twist elastic modulus, , of the cholesteric material without
affecting the effective helical amplitude, . In addition, for the
infinitely large average aspect ratios considered here, the dependence of the
pitch on the overall rod concentration is completely unaffected by
polydispersity. For a given concentration, the increase in twist elastic
modulus (and reduction of the helical twist) may be up to 50% for strong size
polydispersity, irrespective of the shape of the unimodal length distribution.
We also demonstrate that the twist reduction is reinforced in bimodal
distributions, by doping a polydisperse cholesteric with very long rods.
Finally, we identify a subtle, non-monotonic change of the pitch across the
isotropic-cholesteric biphasic region.Comment: 8 pages, 4 figure
Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics
We present a generalized van der Waals theory for a lyotropic cholesteric
system of chiral spherocylinders based on the classical Onsager theory for hard
anisometric bodies. The rods consist of a hard spherocylindrical backbone
surrounded with a square-well potential to account for attractive (or soft
repulsive) interactions. Long-ranged chiral interactions are described by means
of a simple pseudo-scalar potential which is appropriate for weak chiral forces
of a predominant electrostatic origin. Based on the formalism proposed by
Straley [Phys. Rev. A {\bf 14}, 1835 (1976)] we derive explicit algebraic
expressions for the twist elastic modulus and the cholesteric pitch for rods as
a function of density and temperature. The pitch varies non-monotonically with
density, with a sharp decrease at low packing fractions and a marked increase
at higher packing fractions. A similar trend is found for the temperature
dependence. The unwinding of the helical pitch at high densities (or low
temperatures) originates from a marked increase in the local nematic order and
a steep increase of the twist elastic resistance associated with near-parallel
local rod configurations. This contrasts with the commonly held view that the
increase in pitch with decreasing temperature as often observed in cholesterics
is due to layer formation resulting from pre-smectic fluctuations. The increase
in pitch with increasing temperature is consistent with an entropic unwinding
as the chiral interaction becomes less and less significant than the thermal
energy. The variation of the pitch with density, temperature and contour length
is in qualitative agreement with recent experimental results on colloidal {\em
fd} rods.Comment: 17 pages, 6 figures, to appear in J. Chem. Phy
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