Nematic liquid crystals (NLCs) under micron-range confinement exhibit a rich defect phenomenology that can be used to extract elastic (Frank moduli) material parameters of critical importance for next generation electro-optical devices. In this work we develop a model to predict defect-driven textural transformations that arise when a NLC is confined to a circular capillary. In the initial transformation stage an unstable disclination defect of strength +1 nucleates in the axis of the capillary and quickly branches into two stable +1/2 disclination defects. The model includes: (1) the Kirchhoff branch balance equation which predicts the splitting of a +1 into two +1/2 wedge disclinations; (2) the curvature of the +1/2 disclination lines as a function of elastic properties. This model shows that by increasing the ratio of tension strength to bending stiffness, the branch point angle increases, but the final defect distance decreases; and (3) the aperture branching angle of the +1/2 lines as a function of the elastic properties and the magnitude of the curvature at the branch point. These three predictions form the basis for the evaluation of the Frank elastic moduli on NLCs. The key advantage of the implemented methodology is to use time-dependent textural transformations under micron-range capillary confinement to extract elastic parametric data needed to further develop NLCs in functional and structural application.

The leaf petiole is an organ that connects the leaf blade to the stem of a plant. From a structural viewpoint, the petiole resembles a cantilever beam that withstands torsional loading due to wind action and bending deformation due to gravity acting on the leaf blade. During growth, the petiole develops defined structural features at multiple length scales, which synergistically determine its mechanical response to external stimuli. The focus of this study is on the hierarchical level (n=3) of the cellular tissue. The goal is to capture the elastic properties of the cellular tissues of the leaf petiole in Philodendron melinonii at that hierarchy. Since the microstructure of the plant tissues resembles a non-periodic cellular pattern, we resort to a 2-D Finite Edge Centroidal Voronoi tessellation (FECVT) to generate a realistic network of polygonal cells. An analysis based on finite element analysis (FEA) is performed to explore the relation between the effective stiffness of Voronoi model and the properties of the cellular tissue. The effective (homogenized) elastic properties of the cellular tissue can be used to calculate the overall flexural and torsional stiffness of the P. melinonii petiole. The FEA of the Voronoi microstructure depicts the anisotropic stiffness properties of the P. melinonii tissue and its dependence with the graded cellularity.

Thin films of GaNBi alloys with up to 12.5 at.% Bi were grown on sapphire using low-temperature molecular beam epitaxy. The low growth temperature and incorporation of Bi resulted in a morphology of nanocrystallites embedded in an amorphous matrix. The composition and optical absorption shift were found to depend strongly on the III:V ratio controlled by the Ga flux during growth. Increasing the incorporation of Bi resulted in an increase in conductivity of almost five orders of magnitude to 144 Ω-cm−1. Holes were determined to be the majority charge carriers indicating that the conductivity most likely results from a GaNBi-related phase. Soft x-ray emission and x-ray absorption spectroscopies were used to probe the modification of the nitrogen partial density of states due to Bi. The valence band edge was found to shift abruptly to the midgap position of GaN, whereas the conduction band edge shifted more gradually.

The wide majority of biological fibrous composites exhibit twisted plywood architectures (planar or cylindrical) for mechanical reasons [1–5]. These supramolecular organizations originate from the passage of the extracellular matrix (surrounding the chiral fibrous molecules) trough a lyotropic cholesteric liquid crystalline mesophase during the structure formation process [1–5]. In this work, we used the well-established Landau-de Gennes theory of liquid crystals in order to develop a fundamental understanding of the supramolecular self-assembly process leading to the planar monodomain (defect-free) twisted plywood architecture [6]. Simulations illustrate the importance of constraining surface in the formation of defect-free (mechanically effective) composites. These results provide a better understanding of tissue morphogenesis which is highly desirable for the development of new bio-inspired synthetic composites.

Shear–induced nucleation and annihilation of topological defects due to hydrodynamic instability in nematic liquid crystals is a phenomenon of both scientific interest and practical importance. We use a complete generalized non-linear second order tensor Landau-de Gennes model that takes into account short range order elasticity, long-range elasticity and viscous effects, to simulate the nucleation and annihilation of twist inversion walls in flow-aligning nematic polymers subjected to shear flow. Shearing a homogeneous nematic sample perpendicular to the director results in an linear instability that maybe symmetric at low shear rates, and antisymmetric at higher shear rates. At even higher shear rates the onset of nonlinearities results in the nucleation of a parallel array of twist inversion walls, such that asymmetry prevails. By increasing the shear rate the following director symmetry transition cascade is observed: symmetric → antisymmetric → asymmetric → symmetric. The nucleation of the parallel array of twist inversion walls in the asymmetric mode is due to the degeneracy in reorientation towards the shear plane. The annihilation of twist walls is mediated by twist waves along the velocity gradient direction. Twist walls annihilate by three mechanisms: wall-wall annihilations, wall-wall coalescence, and wall-bounding surface coalescence. The annihilation rate increases with increasing shear rate and at sufficiently high rates the layered structure is replaced by a homogeneously aligned system. The role of short range and long range elasticity on defect nucleation and annihilation is characterized in terms of the Deborah and Ericksen numbers. Close form solutions to approximated equations are used to explain the numerical results of the full Landau-de Gennes equations of nematodynamics.

Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of interfacial viscous shear forces due to flow in the viscous matrix. A representative axial nematic orientation texture is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wavenumber m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, including the orientation contribution to the surface elasticity and surface bending stresses. Surface gradients of bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic orientation and the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric, with finite or unbounded wavelengths. Thus, the classical fiber-to-droplet transformation is one of several possible instability pathways while others include surface fibrillation. The contribution of the viscosity ratio to the capillary instabilities of a thin nematic fiber in a viscous matrix is analyzed by two parameters, the fiber and matrix Ohnesorge numbers, which represent the ratio between viscous and surface forces in each phase. The capillary instabilities of a thin nematic fiber in a viscous matrix are suppressed by increasing either the fiber or matrix Ohnesorge number, but estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing matrix Ohnesorge number.

Flow modelling of mesophase pitches is performed using a previously formulated mesoscopic viscoelastic rheological theory [1] that takes into account flow-induced texture transformations. A complete extra stress tensor equation is developed from first principles for liquid crystal materials under non-homogeneous arbitrary flow. Predictions for a given simple shear flow, under non-homogeneous conditions, for the apparent shear viscosity and first normal stress differences are presented. The rheological functions are explained using macroscopic orientation effects, which predominate at low shear rates. The predicted normal stress differences and apparent shear viscosity are in agreement with experimental measurements.

Numerous studies [1-3] have shown that chiral biological structures share common properties with liquids crystals, in particular a tendency to assemble in three-dimensional lattices very similar to that of chiral nematics. Biological fibrous composites are usually found in planar (film) and cylindrical (fibber) twist geometries. In this work, the formation process of the planar twist architecture is numerically investigated using a mesoscopic model based on the Landau-de Gennes theory of chiral nematic liquid crystals. The simulations and visualizations of the computed textures provide new information on some of the principles that govern the formation of chiral biological structures. It is found that a defect-free planar twist architecture arises from a chiral front propagation process with a fully relaxed wake.

We propose a physical model of multiple domain nucleation and growth in order to perform the cross-scale simulation on envelope profiles of the domain and the internal structure. The model utilizes two coupled field: a nonconserved envelope vector field of the local macroscopic growth domains and a vector field of the local mesoscopic lamellae directors. The envelope evolution equation includes an envelope profile function, the domain growth and impingement kinetics, the relaxation of the envelope by a surface tension, a lowest-order nonlinear term, a noise term, and a surface diffusion term. The splay, twist and bend deformation and the interaction between lamellae and noise field are considered in the free energy density equation of the lamellar director field. Results of large-scale computer simulation are reported which are compared with experiments.

Image analysis and measurements on forimation and spatial statistics of spherulitic grain pattern in solidified films of a model polymer, isotactic polypropylene (iPP), have been carried out during in-situ observation experiments under isothermnl conditions. Topological correlations and geometrical distribution fuinctions of polymer grain sides and area are reported. Some topologically unstable configurations, such as multi-vertices, “T” type vertices and two sided grain (lens), have been found. Analysis by spatial tessellations shows that the tenWal evolution and spatial distributions of nuclei point patterns play a role in all of these microstructural properties.

Analysis of the nonlinear dynamical response of a rod-like nematic liquid crystalline polymer, between parallel untreate plates, in a magnetic field is presented. Numerical solutions to the torque balance equations showthat when a uniformly aligned polymer is acted by a magnetic field normal to the initial polymer orientation an array of inversion walls develops. Stability analysis shows that the inversion walls are unstable to localized perturbations. The nonlinear resolution ofthe instability leads to the nucleation of an array of disclination line pairs of strength ±1/2. A perturbation analysis is used to obtain the evolution of the polymer structure towards equilibrium

Four solutions to the Leslie-Ericksen equations for nematic liquid crystals are obtained for pressure-driven radial out-flow between concentric parallel disks and homeotropic director wall anchoring. At low pressure drops the in-plane mode is stable; the centerline director orientation is normal to the flow direction. For each radial distance from the entrance hole there is a critical pressure drop at which the elongational torque twist the director out-ofthe- plane of flow ; left and right rotations are possible. The transition results in the appearance of secondary flows in the azimuthal direction. The radius of the boundary between in-plane and out-of-the-plane modes increases with increasing pressure drops. At higher pressure drops a twist wall develops at the centerline. There is a second critical pressure drop at which the wall collapses with the nucleation and growth of a twist disclination loop. The resulting stable director field is in-plane and flow-aligned throughout the cell.