Dimension reduction for the Landau-de Gennes model on curved nematic thin films

We use the method of $\Gamma$-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach that we used previously to study a similar problem for a planar surface. Since the anchoring energy dominates when the thickness of the film is small, it is essential to understand its influence on the structure of the minimizers of the limiting energy. In particular, the anchoring energy dictates the class of admissible competitors and the structure of the limiting problem. We assume general weak anchoring conditions on the top and the bottom surfaces of the film and strong Dirichlet boundary conditions on the lateral boundary of the film when the surface is not closed. We establish a general convergence result to an energy defined on the surface that involves a somewhat surprising remnant of the normal component of the tensor gradient. Then we exhibit one effect of curvature through an analysis of the behavior of minimizers to the limiting problem when the substrate is a frustrum

Non-isothermal model for the direct isotropic/smectic-A liquid crystalline transition

An extension to a high-order model for the direct isotropic/smectic-A liquid crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase-ordering. Multi-scale multi-transport simulations of the non-isothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth, under shallow quench/undercooling conditions. Non-isothermal simulations, where meta-stable nematic pre-ordering precedes smectic-A growth, were also conducted and novel non-monotonic phase-transformation kinetics observed.Comment: First revision: 20 pages, 7 figure

Properties of surface Landau-de Gennes Q-tensor models

Uniaxial nematic liquid crystals whose molecular orientation is subjected to a tangential anchoring on a curved surface offer a non trivial interplay between the geometry and the topology of the surface and the orientational degree of freedom. We consider a general thin film limit of a Landau-de Gennes Q-tensor model which retains the characteristics of the 3D model. From this, previously proposed surface models follow as special cases. We compare fundamental properties, such as alignment of the orientational degrees of freedom with principle curvature lines, order parameter symmetry and phase transition type for these models, and suggest experiments to identify proper model assumptions

Surface, size and topological effects for some nematic equilibria on rectangular domains

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, ϵ, which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the ϵ→ 0 limit relevant for macroscopic domains and the ϵ→∞ limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the ϵ→∞ limit, whereas we observe fractional point defects in the ϵ→ 0 limit. The analytical studies are complemented by some bifurcation diagrams for these reduced equilibria as a function of ϵ and the rectangular aspect ratio. We also introduce the concept of ‘non-trivial’ topologies and study the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics

Liquid Crystal Anchoring Control and its Applications in Responsive Materials

Liquid crystals (LCs), owing to their anisotropy in molecular ordering, are of interests not only in the display industry, but also in the soft matter community, e.g., to direct colloidal assembly and phase separation of surfactants, and to actuate two-dimensional (2D) sheets into three-dimension (3D). The functionality and performance of LC materials extensively rely on the molecular ordering and alignment of LCs, which are dictated by LC anchoring at various boundaries. Therefore, this thesis focuses on the study of LC anchoring from both small molecule LCs and liquid crystal monomers (LCMs), which in turn guides my design of surface topography and surface chemistry to control formation of uniform LC defect structures over cm2 samples under complex boundary conditions. The ability to precisely embed defect structures in a LC material also allows me to exploit the responsiveness of LCs to create actuators and scaffolds to (dis)assemble nano- and micro-objects. Specifically, by exploiting the bulk disclinations formed in the nematic phase of 4-octyl-4’-cyanobiphenyl (8CB) surrounding the micropillar arrays, we demonstrate (dis)assembly of gold nano-rods (AuNRs) for dynamic tuning of surface plasmon resonance (SPR). Due to the highly temperature-sensitive elastic anisotropy of 8CB, the bulk disclinations and consequently the AuNR assemblies and SPR properties can be altered reversibly by heating and cooling the LC system. Then we design and synthesize a new type of nematic LCMs with a very large nematic window. Therefore, they can be faithfully aligned at various boundary conditions, analogous to that of small molecule LCs. After crosslinking LCMs into liquid crystal polymers (LCPs), we are able to study the LC assembly, director field, and topological defects using scanning electronic microscopy (SEM) at the 100 nm resolution. We then turn our attention to direct LCM alignment through controlling of surface chemistry and topography. We demonstrate the essential role of surface chemistry in the fabrication of liquid crystal elastomer (LCE) micropillar arrays during soft lithography. A monodomain LCM alignment is achieved in a poly(2-hydroxyethyl methacrylate) coated polydimethylsiloxane (PDMS) mold. After crosslinking, the resultant LCE micropillars display a large radial strain (~30%) when heated across the nematic-isotropic phase transition temperature (TNI). The understanding of surface alignment in LCMs is then transferred to LCEs with embedded topological defects. On micron-sized one-dimensional channels with planar surface chemistry, LCMs can be faithfully oriented along the local channel direction. After crosslinking, the 2D LCE sheets show pre-programmed shape transformation to complex 3D structures through bending and stretching of local directors when heated above TNI. Last, we control LC alignment and defect formation on a flat surface simply by using chemical patterns. Planar anchored SU8 is photopatterned on homoetropically anchored dimethyloctadecyl[3-(trimethoxysilyl)propyl] ammonium chloride (DMOAP) coated glass. By exploiting the pattern geometry, thus, boundary conditions, in combination with anisotropy of LC elasticity, we show that LC orientation can be precisely controlled over a large area and various types of topological defects are generated. Such defect structures can be further used to trap micro- and nanoparticles

Fabrication and Actuation of Hierarchically-Patterned Polymer Substrates for Dynamic Surface and Optical Properties

Switchable optical materials, which possess reversible color and transparency change in response to external stimuli, are of wide interest for potential applications such as windows and skylights in architectural and vehicular settings or optical sensors for environmental monitoring. This thesis considers the tuning of optical properties by tailoring and actuating responsive materials. Specifically, we demonstrate the design and fabrication of tilted pillar arrays on wrinkled elastomeric polydimethylsiloxane (PDMS) as a reversibly switchable optical window. While the original PDMS film exhibits angle-dependent colorful reflection due to Bragg diffraction of light from the periodic pillar array, the tilted pillar film appears opaque due to random scattering. Upon re-stretching the film to the original pre-strain, the grating color is restored due to the straightened pillars and transmittance is recovered. Then, we develop a composite film, consisting of a thin layer of quasi-amorphous array of silica nanoparticles (NPs) embedded in bulk elastomeric PDMS, with initial high transparency and angle-independent coloring upon mechanical stretching. The color can be tuned by the silica NP size. The switch between transparency and colored states could be reversibly cycled at least 1000 times without losing the film’s structural and optical integrity. We then consider the micropatterning of nematic liquid crystal elastomers (NLCEs) as micro-actuator materials. Planar surface anchoring of liquid crystal (LC) monomers is achieved with a poly(2-hydroxyethyl methacrylate)-coated PDMS mold, leading to monodomains of vertically aligned LC monomers within the mold. After cross-linking, the resulting NLCE micropillars show a relatively large radial strain when heated above nematic to isotropic transition temperature, which can be recovered upon cooling. Finally, the understanding of liquid crystal surface anchoring under confined boundary conditions is applied to the self-assembly of gold nanorods (AuNRs) driven by LC defect structures and to dynamically tune the surface plasmon resonance (SPR) properties. By exploiting the confinement of the smectic liquid crystal, 4-octyl-4’-cyanobiphenyl (8CB), to patterned pillars treated with homeotropic surface anchoring, topological defects are formed at precise locations around each pillar and can be tuned by varying the aspect ratio of the pillars and the temperature of the system. As a result, the AuNR assemblies and SPR properties can be altered reversibly by heating and cooling between smectic, nematic and isotropic phases