Packing of charged chains on toroidal geometries

Chiral nematic liquid crystals in torus-shaped and cylindrical cavities

We present a Monte Carlo simulation study of chiral nematic liquid crystals confined in torus-shaped and cylindrical cavities. For an achiral nematic with planar degenerate anchoring confined to a toroidal or cylindrical cavity, the ground state is defect free, with an untwisted director field. As chirality is introduced, the ground state remains defect free but the director field becomes twisted within the cavity. For homeotropic anchoring, the ground state for an achiral nematic within a toroidal cavity consists of two disclination rings, one large and one small, that follow the major circumference of the torus. As chirality is introduced and increased, this ground state becomes unstable with respect to twisted configurations. The closed nature of the toroidal cavity requires that only a half integer number of twists can be formed and this leads to the ground state being either a single disclination line that encircles the torus twice or a pair of intertwined disclination rings forming stable, knotted defect structures.

Excitonic channels from bio-inspired templated supramolecular assembly of J-aggregate nanowires

Supramolecular assemblies with controlled morphology are of paramount importance for energy transport in organic semiconductors. Despite considerable freedom in molecular design, the preparation of dyes that form one dimensional J-aggregates is challenging. Here, we demonstrate a simple and effective route to functionalize dendronized polymers (DPs) with J-aggregates to construct tubular DP/J-aggregate nanowires. When J-aggregates are adsorbed onto DPs anchored to glass substrates, they assemble into microcrystalline domains typical for J-aggregates adsorbed on functionalized surfaces. Differently, the complexation between the dendronized polymer and J-aggregates in solution leads to dense packing of J-aggregate strands on the periphery of the DPs. Using a layer-by-layer (LBL) technique, DPs loaded with J-aggregates can also be adsorbed onto a DP monolayer. In this case, the thin film absorption spectra are narrower and indicate higher ratios of J-aggregate to monomer and dimer absorption than bare J-aggregates deposited similarly. The demonstration of J-aggregate adsorption on filamentous polymeric templates is a promising step toward artificial 1D light harvesting antennas, with potential applications in opto-electronic devices.

Structure of curved crystals in the thermodynamic limit and the perfect screening condition

The dislocation and disclination density defining the structure of a crystal constrained on a general curved background is computed analytically in the thermodynamic limit, when the number of particles is arbitrarily large. It is shown that the minimum of the elastic energy, where strains are optimally close to zero, can be formulated in terms of a connection (a rule on how to parallel transport vectors), which allows to provide an explicit solution in the thermodynamic limit that consists of disclinations surrounded by scars (grain boundaries with variable spacing). The approach allows to compute the interaction potential. For a sphere, a full characterization of the scars is provided, and it is shown that the potential of interaction among disclinations "dressed" by scars is inversely proportional to the sinus of the geodesic distance and that the ground state consists of 12 dressed disclinations that display icosahedral symmetry. The case of a torus is also considered. More generally, the thermodynamic solution implements a "perfect screening" condition, where defects completely screen the Gaussian curvature. Implications for the problem of melting are discussed.

Saddle-splay screening and chiral symmetry breaking in toroidal nematics

We present a theoretical study of director fields in toroidal geometries with degenerate planar boundary conditions. We find spontaneous chirality: despite the achiral nature of nematics the director configuration shows a handedness if the toroid is thick enough. In the chiral state the director field displays a double twist, whereas in the achiral state there is only bend deformation. The critical thickness increases as the difference between the twist and saddle-splay moduli grows. A positive saddle-splay modulus prefers alignment along the meridian of the bounding torus, and hence promotes a chiral configuration. The chiral-achiral transition mimics the order-disorder transition of the mean-field Ising model. The role of the magnetisation in the Ising model is played by the degree of twist. The role of the temperature is played by the aspect ratio of the torus. Remarkably, an external field does not break the chiral symmetry explicitly, but shifts the transition. In the case of toroidal cholesterics, we do find a preference for one chirality over the other - the molecular chirality acts as a field in the Ising analogy.

Crystallization dynamics on curved surfaces

We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is rapidly relaxed through isolated defects. Further relaxation involves a mechanism of crystal growth and defect annihilation where regions with high curvature act as sinks for the diffusion of domain walls. The pinning of grain boundaries at regions of low curvature leads to the formation of a metastable structure of defects, characterized by asymptotically slow dynamics of ordering and activation energies dictated by the largest curvatures of the system. These glassylike ordering dynamics may completely inhibit the appearance of the ground-state structures.

Electrostatic repulsion-driven crystallization model arising from filament networks

The crystallization of bundles in filament networks interacting via long-range repulsions in confinement is described by a phenomenological model. The model demonstrates the formation of the hexagonal crystalline order via the interplay of the confinement potential and the filament-filament repulsion. Two distinct crystallization mechanisms in the short- and large- screening length regimes are discussed, and the phase diagram is obtained. Simulation of large bundles predicts the existence of topological defects within the bundled filaments. This electrostatic repulsion-driven crystallization model arising from studying filament networks can even find a more general context extending to charged colloidal systems.