43 research outputs found
Long-range order in quadrupolar systems on spherical surfaces
Understanding the interplay between topology and ordering in systems on
curved manifolds, governed by anisotropic interactions, takes a central role in
many fields of physics. In this paper, we investigate the effects of lattice
symmetry and local positional order on orientational ordering in systems of
long-range interacting point quadrupoles on a sphere in the zero temperature
limit. Locally triangular spherical lattices show long-range ordered
quadrupolar configurations only for specific symmetric lattices as strong
geometric frustration prevents general global ordering. Conversely, the ground
states on Caspar-Klug lattices are more diverse, with many different symmetries
depending on the position of quadrupoles within the fundamental domain. We also
show that by constraining the quadrupole tilts with respect to the surface
normal, which models interactions with the substrate, and by considering
general quadrupole tensors, we can manipulate the ground state configuration
symmetry.Comment: 16 pages, 8 figures, Supplemental materia
Symmetry breaking of dipole orientations on Caspar-Klug lattices
Anisotropic dipole-dipole interaction often plays a key role in biological,
soft, and complex matter. For it to induce non-trivial order in the system,
there must be additional repulsive interactions or external potentials involved
that partially or completely fix the positions of the dipoles. These positions
can often be represented as an underlying lattice on which dipole interaction
induces orientational ordering of the particles. On lattices in the Euclidean
plane, dipoles have been found to assume different ground state configurations
depending on the lattice type, with a global ordering in the form of a
macrovortex being observed in many cases. A similar macrovortex configuration
of dipoles has recently been shown to be the sole ground state for dipoles
positioned on spherical lattices based on solutions of the Thomson problem. At
the same time, no symmetric configurations have been observed, even though the
positional order of Thomson lattices exhibits a high degree of symmetry. Here,
we show that a different choice of spherical lattices based on Caspar-Klug
construction leads to ground states of dipoles with various degrees of
symmetry, including the icosahedral symmetry of the underlying lattice. We
analyze the stability of the highly symmetric metastable states, their symmetry
breaking into subsymmetries of the icosahedral symmetry group, and present a
phase diagram of symmetries with respect to lattice parameters. The observed
relationship between positional order and dipole-induced symmetry breaking
hints at ways of fine-tuning the structure of spherical assemblies and their
design.Comment: 9 pages, 7 figure
Singular Values, Nematic Disclinations, and Emergent Biaxiality
Both uniaxial and biaxial nematic liquid crystals are defined by
orientational ordering of their building blocks. While uniaxial nematics only
orient the long molecular axis, biaxial order implies local order along three
axes. As the natural degree of biaxiality and the associated frame, that can be
extracted from the tensorial description of the nematic order, vanishes in the
uniaxial phase, we extend the nematic director to a full biaxial frame by
making use of a singular value decomposition of the gradient of the director
field instead. New defects and degrees of freedom are unveiled and the
similarities and differences between the uniaxial and biaxial phase are
analyzed by applying the algebraic rules of the quaternion group to the
uniaxial phase.Comment: 5 pages, 1 figure, submitted to PR
Reconfigurable knots and links in chiral nematic colloids
Tying knots and linking microscopic loops of polymers, macromolecules, or
defect lines in complex materials is a challenging task for material
scientists. We demonstrate the knotting of microscopic topological defect lines
in chiral nematic liquid crystal colloids into knots and links of arbitrary
complexity by using laser tweezers as a micromanipulation tool. All knots and
links with up to six crossings, including the Hopf link, the Star of David and
the Borromean rings are demonstrated, stabilizing colloidal particles into an
unusual soft matter. The knots in chiral nematic colloids are classified by the
quantized self-linking number, a direct measure of the geometric, or Berry's,
phase. Forming arbitrary microscopic knots and links in chiral nematic colloids
is a demonstration of how relevant the topology can be for the material
engineering of soft matter.Comment: 6 pages, 3 figure
Three-dimensional active defect loops
We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modeling, that they are governed by the local profile of the orientational order surrounding the defects. Analyzing a continuous span of defect loop profiles, ranging from radial and tangential twist to wedge
±
1
/
2
profiles, we show that the distinct geometries can drive material flow perpendicular or along the local defect loop segment, whose variation around a closed loop can lead to net loop motion, elongation, or compression of shape, or buckling of the loops. We demonstrate a correlation between local curvature and the local orientational profile of the defect loop, indicating dynamic coupling between geometry and topology. To address the general formation of defect loops in three dimensions, we show their creation via bend instability from different initial elastic distortions