674 research outputs found
Smectic Phases with Cubic Symmetry: The Splay Analog of the Blue Phase
We report on a construction for smectic blue phases, which have quasi-long
range smectic translational order as well as long range cubic or hexagonal
order. Our proposed structures fill space with a combination of minimal surface
patches and cylindrical tubes. We find that for the right range of material
parameters, the favorable saddle-splay energy of these structures can stabilize
them against uniform layered structures.Comment: 4 pages, 4 eps figures, RevTe
Chirality in Liquid Crystals: from Microscopic Origins to Macroscopic Structure
Molecular chirality leads to a wonderful variety of equilibrium structures,
from the simple cholesteric phase to the twist-grain-boundary phases, and it is
responsible for interesting and technologically important materials like
ferroelectric liquid crystals. This paper will review some recent advances in
our understanding of the connection between the chiral geometry of individual
molecules and the important phenomenological parameters that determine
macroscopic chiral structure. It will then consider chiral structure in
columnar systems and propose a new equilibrium phase consisting of a regular
lattice of twisted ropes.Comment: 20 pages with 6 epsf figure
Smectic blue phases: layered systems with high intrinsic curvature
We report on a construction for smectic blue phases, which have quasi-long
range smectic translational order as well as three dimensional crystalline
order. Our proposed structures fill space by adding layers on top of a minimal
surface, introducing either curvature or edge defects as necessary. We find
that for the right range of material parameters, the favorable saddle-splay
energy of these structures can stabilize them against uniform layered
structures. We also consider the nature of curvature frustration between mean
curvature and saddle-splay.Comment: 15 pages, 11 figure
Structure Function of Polymer Nematic Liquid Crystals: A Monte Carlo Simulation
We present a Monte Carlo simulation of a polymer nematic for varying volume
fractions, concentrating on the structure function of the sample. We achieve
nematic ordering with stiff polymers made of spherical monomers that would
otherwise not form a nematic state. Our results are in good qualitative
agreement with theoretical and experimental predictions, most notably the
bowtie pattern in the static structure function.Comment: 10 pages, plain TeX, macros included, 3 figures available from
archive. Published versio
Boundary Effects in Chiral Polymer Hexatics
Boundary effects in liquid-crystalline phases can be large due to long-ranged
orientational correlations. We show that the chiral hexatic phase can be locked
into an apparent three-dimensional N+6 phase via such effects. Simple numerical
estimates suggest that the recently discovered "polymer hexatic" may actually
be this locked phase.Comment: 4 pages, RevTex, 3 included eps figure
Order and Frustration in Chiral Liquid Crystals
This paper reviews the complex ordered structures induced by chirality in
liquid crystals. In general, chirality favors a twist in the orientation of
liquid-crystal molecules. In some cases, as in the cholesteric phase, this
favored twist can be achieved without any defects. More often, the favored
twist competes with applied electric or magnetic fields or with geometric
constraints, leading to frustration. In response to this frustration, the
system develops ordered structures with periodic arrays of defects. The
simplest example of such a structure is the lattice of domains and domain walls
in a cholesteric phase under a magnetic field. More complex examples include
defect structures formed in two-dimensional films of chiral liquid crystals.
The same considerations of chirality and defects apply to three-dimensional
structures, such as the twist-grain-boundary and moire phases.Comment: 39 pages, RevTeX, 14 included eps figure
Helical Tubes in Crowded Environments
When placed in a crowded environment, a semi-flexible tube is forced to fold
so as to make a more compact shape. One compact shape that often arises in
nature is the tight helix, especially when the tube thickness is of comparable
size to the tube length. In this paper we use an excluded volume effect to
model the effects of crowding. This gives us a measure of compactness for
configurations of the tube, which we use to look at structures of the
semi-flexible tube that minimize the excluded volume. We focus most of our
attention on the helix and which helical geometries are most compact. We found
that helices of specific pitch to radius ratio 2.512 to be optimally compact.
This is the same geometry that minimizes the global curvature of the curve
defining the tube. We further investigate the effects of adding a bending
energy or multiple tubes to begin to explore the more complete space of
possible geometries a tube could form.Comment: 10 page
Topological Constraints at the Theta Point: Closed Loops at Two Loops
We map the problem of self-avoiding random walks in a Theta solvent with a
chemical potential for writhe to the three-dimensional symmetric
U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of
topologically constrained polymers, with critical exponents that depend on the
chemical potential for writhe, which gives way to a fluctuation-induced
first-order transition.Comment: 5 pages, RevTeX, typo
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