Colloidal dipolar interactions in 2D smectic-C films

We use a two-dimensional (2D) elastic free energy to calculate the effective interaction between two circular disks immersed in smectic-C films. For strong homeotropic anchoring, the distortion of the director field caused by the disks generates topological defects that induce an effective interaction between the disks. We use finite elements, with adaptive meshing, to minimize the 2D elastic free energy. The method is shown to be accurate and efficient for inhomogeneities on the length scales set by the disks and the defects, that differ by up to 3 orders of magnitude. We compute the effective interaction between two disk-defect pairs in a simple (linear) configuration. For large disk separations, D, the elastic free energy scales as similar to D-2, confirming the dipolar character of the long-range effective interaction. For small D the energy exhibits a pronounced minimum. The lowest energy corresponds to a symmetrical configuration of the disk-defect pairs, with the inner defect at the mid-point between the disks. The disks are separated by a distance that, is twice the distance of the outer defect from the nearest disk. The latter is identical to the equilibrium distance of a defect nucleated by an isolated disk.

Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nernatic is investigated i) analytically using the tenser order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nernatic director changes from oblique to perpendicular.

Liquid crystal beads constrained on thin cellulosic fibers: Electric field induced microrotors and N-I transition

We directly visualize the response of nematic liquid crystal drops of toroidal topology threaded in cellulosic fibers, suspended in air, to an AC electric field and at different temperatures over the N-I transition. This new liquid crystal system can exhibit non-trivial point defects, which can be energetically unstable against expanding into ring defects depending on the fiber constraining geometries. The director anchoring tangentially near the fiber surface and homeotropically at the air interface makes a hybrid shell distribution that in turn causes a ring disclination line around the main axis of the fiber at the center of the droplet. Upon application of an electric field, E, the disclination ring first expands and moves along the fiber main axis, followed by the appearance of a stable "spherical particle" object orbiting around the fiber at the center of the liquid crystal drop. The rotation speed of this particle was found to vary linearly with the applied voltage. This constrained liquid crystal geometry seems to meet the essential requirements in which soliton-like deformations can develop and exhibit stable orbiting in three dimensions upon application of an external electric field. On changing the temperature the system remains stable and allows the study of the defect evolution near the nematic-isotropic transition, showing qualitatively different behaviour on cooling and heating processes. The necklaces of such liquid crystal drops constitute excellent systems for the study of topological defects and their evolution and open new perspectives for application in microelectronics and photonics.

Simulation of defects in bubble clusters

Topological defects in foam, either isolated (disclinations and dislocations) or in pairs, affect the energy and stress, and play an important role in foam deformation. Surface Evolver simulations were performed on large finite clusters of bubbles. These allow us to evaluate the effect of the topology of the defects, and the distance between defects, on the energy and pressure of foam clusters of different sizes. The energy of such defects follows trends similar to known analytical results for a continuous medium.

Liquid crystal necklaces: cholesteric drops threaded by thin cellulose fibres

Liquid crystals in confined geometries exhibit numerous complex structures often including topological defects that are controlled by the nematic elasticity, chirality and surface anchoring. In this work, we study the structures of cholesteric droplets pierced by cellulose fibres with planar anchoring at droplet and fibre surfaces. By varying the temperature we demonstrate the role of twisting power and droplet diameter on the equilibrium structures. The observed structures are complemented by detailed numerical simulations of possible director fields decorated by defects. Three distinct structures, a bipolar and two ring configurations, are identified experimentally and numerically. Designing cholesteric liquid crystal microdroplets on thin long threads opens new routes to produce fibre waveguides decorated with complex microresonators.

Three-dimensial patchy lattice model: Ring formation and phase separation

We investigate the structural and thermodynamic properties of a model of particles with 2 patches of type A and 10 patches of type B. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self- assembly of chains, rings, and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension ofWertheim's theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio r epsilon(AB)/epsilon(AA) of the interaction between patches A and B, epsilon(AB), and between A patches, epsilon(AA) (epsilon(BB) is set to theta) as well as the relative position of the A patches, i.e., the angle. between the (lattice) directions of the A patches. We found that both r and theta (60 degrees, 90 degrees, or 120 degrees) have a profound effect on the phase diagram. In the empty fluid regime (r < 1/2) the phase diagram is reentrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for theta = 120 degrees but deteriorates as. decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings. (C) 2014 AIP Publishing LLC.

Invariant integrals applied to nematic liquid crystals with small Ericksen number and topological defects

Invariant integrals are derived for nematic liquid crystals and applied to materials with small Ericksen number and topological defects. The nematic material is confined between two infinite plates located at y = -h and y = h (h is an element of R+) with a semi-infinite plate at y = 0 and x < 0. Planar and homeotropic strong anchoring boundary conditions to the director field are assumed at these two infinite and semi-infinite plates, respectively. Thus, a line disclination appears in the system which coincides with the z-axis. Analytical solutions to the director field in the neighbourhood of the singularity are obtained. However, these solutions depend on an arbitrary parameter. The nematic elastic force is thus evaluated from an invariant integral of the energy-momentum tensor around a closed surface which does not contain the singularity. This allows one to determine this parameter which is a function of the nematic cell thickness and the strength of the disclination. Analytical solutions are also deduced for the director field in the whole region using the conformal mapping method. (C) 2013 Elsevier Ltd. All rights reserved.

Redox-active cytotoxic diorganotin(IV) cycloalkylhydroxamate complexes with different ring sizes: Reduction behaviour and theoretical interpretation

Two series of new diorganotin(IV) cycloalkylhydroxamate complexes with different ring sizes (cyclopropyl, cyclobutyl, cyclopentyl and cyclohexyl), formulated as the mononuclear [R2Sn(HL)(2)] (1:2) (a, R=Bu-n and Ph) and the polymeric [R2SnL](n) (1:1) (b, R=Bu-n) compounds, were prepared and fully characterized. Single crystal X-ray diffraction for [(Bu2Sn)-Bu-n{C5H9C(O)NHO}(2)] (3a) discloses the cis geometry and strong intermolecular NH center dot center dot center dot O interactions. The in vitro cytotoxic activities of the complexes were evaluated against HL-60, Bel-7402, BGC-823 and KB human tumour cell lines, the greater activity concerning [(Bu2Sn)-Bu-n(HL)(2)] [HL=C3H5C(O)NHO (1a), C6H11C(O)NHO (4a)] towards BGC-823. The complexes undergo, by cyclic voltammetry and controlled-potential electrolysis, one irreversible overall two-electron cathodic process at a reduction potential that does not appear to correlate with the antitumour activity. The electrochemical behaviour of [R2Sn(C5H9C(O)NHO)(2)] [R=Bu-n (3a), Ph (7a)] was also investigated using density functional theory (DFT) methods, showing that the ultimate complex structure and the mechanism of its formation are R dependent: for the aromatic (R = Ph) complex, the initial reduction step is centred on the phenyl ligands and at the metal, being followed by a second reduction with Sn-O and Sn-C ruptures, whereas for the alkyl (R=Bu-n) complex the first reduction step is centred on one of the hydroxamate ligands and is followed by a second reduction with Sn-O bond cleavages and preservation of the alkyl ligands. In both cases, the final complexes are highly coordinative unsaturated Sn-II species with the cis geometry, features that can be of biological significance.

The semigroup ring of a restriction semigroup with an inverse skeleton

In this paper we investigate some classes of semigroup rings with respect to (semi)primeness and (semi)primitivity. We do so by extending the techniques developed by Munn in (Proc R Soc Edinbur Sect A 107:175-196, 1987) and (Proc R Soc Edinbur Sect A 115:109-117, 1990) for the study of semigroup rings of inverse semigroups. Restriction, weakly ample and ample semigroups are considered.