Anisotropic molecules confined on a spherical or other curved surface can display coupled positional and orientational orderings, which make possible applications in physics, chemistry, biology, and material science. Therefore, controlling the order of such system has attracted much attention recently. Several distinct conformations of rod-like or chain-like molecules confined on a spherical surface have been predicted, including states such as tennis-ball, rectangle, and cut-and-rotate splay. These conformations have four +1/2 defects and are suggested to dominate over the splay conformation that has two +1 defects. For the purpose of investigating the conformations of 2-fold anisotropic molecules confined on the spherical surface, the author of this thesis utilizes the Onsager model to study the system of rigid rods and conducts Monte Carlo simulations on the bead-bond model to research the system of semiflexible polymer chains. At low surface coverage density, no particular pattern of the molecules would form. However, coupled positional and orientational ordering begins to emerge beyond a transition density. On the basis of the numerical solutions of the Onsager model of rigid rods, the splay conformation is shown to be the only stable state. On the other hand, Monte Carlo simulations on a polymer system indicate that the ordered state always accompanies the tennis-ball symmetry. With comparison to the continuous isotropic-nematic transition of a fluid of hard rods embedded in a flat two-dimensional space, the disorder-order transition for both the system of rigid rods and the system of polymer chains confined on the spherical surface has first-order phase-transition characteristics.

A liquid crystal (LC) at its boundary surface adopts a preferential alignment, which is referred to as anchoring. The direction of this alignment (i.e., anchoring direction) may be perpendicular, parallel or tilted with respect to the surface. Transitions from one anchoring condition to another may occur when the parameters (e.g., temperature) charactering the surface change, as referred to as anchoring transitions. In the LC-polymer composite systems under our study, the anchoring and temperature- driven anchoring transitions of nematic fluids is very sensitive to the structure of the side chain of poly (alkyl acrylate) matrixes that encapsulate the LC. We have shown that the anchoring transition temperature of these systems can be tuned far below the nematic-to-isotropic transition temperature, by varying either the length, branching structure of the side chains of homopolymers, or the composition of copolymer of two dissimilar monomers. Both sharp and broad anchoring transitions with respect to the temperature range over which a transition occurs were observed. It is postulated that microscopic interactions between the polymer side chains and LC molecules play an important role in determining the anchoring. In particular, the conformation of the polymer side chain is proposed to have important control over the anchoring. Anchoring strength and tilt angle as a function of temperature during the anchoring transitions were also experimentally investigated, which contribute to understanding of the microscopic mechanism for such transitions. Based on the LC-polymer composites with controlled anchoring, a LC display with reverse switching mode and a novel electrically switchable diffraction grating have been demonstrated. The advantages of these devices are ease of manufacturing, low operation voltage, and mechanical stability offered by polymer matrix. Moreover, a detailed study of the director configuration of wall defects found in these composite films was carried out using fluorescence confocal polarized microscopy.

The laser-induced holographic gratings in the Azo dye-doped PMMA thin films with liquid crystal were investigated by changing the temperature of the sample, the angle of two writing beams and the rubbing. The high power Q-switch pulse laser has been used as the writing beams and the He-Ne cw laser has been used as a real-time probe beam to detect the first order diffraction singals. The grating are the results of photo-isomerization of azo dye and diffusions of liquid crystal. The model has been established to analyze the first order diffraction signals in order to understand the mechanism of grating and the effect of temperature and angle.

The process of forcibly dewetting a solid substrate from a bulk liquid so as to leave a thin residual layer on the surface is referred to as forced dewetting. This novel experimental approach helps to investigate interfacial species by minimizing the interference of the bulk liquid when coupled with spectroscopy. In this work, the scope of liquids investigating using this approach has been expanded from simple fluids to one type of complex fluid, a nematic liquid crystal, 4-n-pentyl-4'-cyanobiphenyl (5CB).In order to better understand the interfacial behavior of the simple fluids, water, chloroform, and n-pentane vapors were adsorbed onto omega-terminated SAM-modifed Ag (11-mercaptoundecanoic acid, 11-mercaptoundenanol, and undecanethiol) surfaces under vapor-saturated conditions. The kinetics of solvent adsorption on each of these surfaces were investigated and the thicknesses of the adsorbed layer were compared to predictions from Lifshitz theory of long-range van der Waals interactions. Although the predicted thicknesses do not match the experimental values for adsorbed films, the predicted thicknesses do match those observed experimentally using forced dewetting. The correlation between these predicted and observed thicknesses implies that residual film formation under the conditions of forced dewetting used in this laboratory is dictated by interfacial forces alone.The surface adsorption behavior of 5CB was investigated using surface-enhanced Raman spectroscopy with the aid of localized surface plasmon resonances-surface plasmon polaritron coupling. The results clearly indicate that 5CB is adsorbed to smooth Ag surface in a facial orientation with pi-d orbital interaction suggested.Finally, forced dewetting studies of bare, -NH2-temintaed SAM, and -CH3-temintaed SAM modified-SiO2 substrates from 5CB were undertaken. Residual layer thicknesses were monitored as a function of substrate velocity. The transition from the regime in which interfacial forces dictate residual layer thickness to the regime in which fluid dynamic forces dictate thickness was observed for the first time and was evaluated in terms of the average 5CB director orientation. Unlike simple fluids, 5CB has strong interfacial interactions from surface anchoring depending on the chemical nature of the substrate, which makes the residual layer thicknesses at least 100 times larger than observed in simple fluids.

Liquid crystals (LCs) are an interesting class of materials that are attracting significant attention due to their ever-growing applications in a wide variety of fields such as liquid crystal display (LCD) technology, materials science and bioscience. In recent years, along with the developments of materials at the nanoscale, doping LCs with nanoparticles (NPs) has emerged as a very promising approach for improving LC properties. Nanoparticle additives can introduce novel effects on optical and electro-optical properties of nematic liquid crystals (N-LCs), such as altered molecular alignment, faster response time and increased efficiency. This thesis studies the impacts that the inclusion of metallic NPs made of gold or semiconductor CdSe quantum dots (QDs), have on optical and electro-optical properties of N-LCs. Using polarized optical microscopy and detailed capacitance and transmittance measurements of nematic mixtures in electro-optic test cells, characteristics such as optical texture, phase transition temperatures, switching voltages and dielectric anisotropy are investigated in pure as well as doped samples. Surface ligands in NPs and their chemical functionalization play an important role in the LC-NP interactions, largely by determining the dispersibility of NPs and stability of the nanocomposites. One important objective of this thesis is to investigate and prepare a series of gold nanoparticles (Au NPs) with specially formulated robust coatings that maximizes solubility and stability in LC medium. Silanization of NPs is developed as a method to overcome the stability challenge. The functionalization of silanized NPs with aliphatic ligands or liquid crystalline molecules, provides chemically and thermally stable NPs with hydrophobic and structurally compatible surfaces required for dispersion in N-LCs. After complete characterization the synthesized particles are used to make the new nematic nanocomposites. By analysis of the structure-property relationships governing LC-nanomaterial composites and by comparison of new results and data from previous studies on other types of NPs, this thesis will further reveal the mechanism of the interrelations between host LC molecules and NP, considering the role of variables such as core composition, size and surface chemistry of NPs (e.g. siloxane shell, aliphatic ligand vs. liquid crystalline ligand) in achieving stable LC composites with desired optical and electro-optical properties.

The goal of this thesis is to study the ground or metastable state structure of nematic liquid crystal systems confined inside handled shapes such as a torus or double torus. We begin our work by introducing a new method to generate a toroidal droplet from a Newtonian liquid inside another, immiscible, Newtonian liquid. In this situation, a toroidal droplet is unstable and follows one of two routes in transforming into a spherical droplet: (i) its tube breaks in a way reminiscent to the breakup of a cylindrical jet, or (ii) its tube grows until it finally coalesces onto itself. However, to be able to probe the nematic structure, we need to address the issue of instabilities. This is done by replacing the outer liquid with a yield stress material, which ultimately leads to the stabilization of the toroidal droplet. Through the experimental investigation, we are able to establish the stabilization conditions. Finally, we generate and stabilize toroidal droplets with a nematic liquid crystal as the inner liquid and a yield stress material as the outer medium. Here we observe that in the ground state, the nematic liquid crystal exhibits an intriguing twisted structure irrespective of the aspect ratio of the torus. While there are no defects observed in a toroidal droplet case, two defects with -1 topological charge each emerge each time we increase the number of handles.

Anisotropic molecules confined on a spherical or other curved surface can display coupled positional and orientational orderings, which make possible applications in physics, chemistry, biology, and material science. Therefore, controlling the order of such system has attracted much attention recently. Several distinct conformations of rod-like or chain-like molecules confined on a spherical surface have been predicted, including states such as tennis-ball, rectangle, and cut-and-rotate splay. These conformations have four +1/2 defects and are suggested to dominate over the splay conformation that has two +1 defects. For the purpose of investigating the conformations of 2-fold anisotropic molecules confined on the spherical surface, the author of this thesis utilizes the Onsager model to study the system of rigid rods and conducts Monte Carlo simulations on the bead-bond model to research the system of semiflexible polymer chains. At low surface coverage density, no particular pattern of the molecules would form. However, coupled positional and orientational ordering begins to emerge beyond a transition density. On the basis of the numerical solutions of the Onsager model of rigid rods, the splay conformation is shown to be the only stable state. On the other hand, Monte Carlo simulations on a polymer system indicate that the ordered state always accompanies the tennis-ball symmetry. With comparison to the continuous isotropic-nematic transition of a fluid of hard rods embedded in a flat two-dimensional space, the disorder-order transition for both the system of rigid rods and the system of polymer chains confined on the spherical surface has first-order phase-transition characteristics.

Polymer nanocomposites (PNCs) are hybrid materials incorporating organic or inorganic nanoparticles (NPs) with at least one dimension in the submicron scale. Over the last two decades, these materials have drawn a remarkable attention due to their central role in industrial formulations and technological applications, extending from food packaging to smart coatings. Incorporating nanoparticles (NPs) to a polymer matrix can significantly alter the conformation and the mobility of the polymer chains in their proximity. Moreover, understanding the delicate balance between the enthalpic and entropic interactions is crucial to control and predict the ability of NPs to diffuse and disperse in the polymer matrix. The impact of these interactions on the structure and the dynamics of polymer chains and NPs is fully revealed in how a number of macroscopic properties changes, justifying the high interest on these materials for industrial applications. In this thesis, the impact on the structure, dynamics, viscosity and thermal conductivity of a number of microscopic properties is investigated by performing Molecular Dynamics (MD) simulations. Specifically, the PNC is represented by a coarse-grained model of a melt of linear homopolymer chains containing spherical NPs. Throughout this work, a number of parameters are modified in order to unveil possible patterns in the PNC’s performance. To this end, this work focuses on the consequences of modifying the NP size dispersity, NP-polymer chain relative size, and chains’ degree of stiffness. Four theoretical models describing the diffusivity of NPs, three of which include nano-scale corrections, have been averaged to study the dependence of dilute NPs’ diffusivity on the NP polydispersity index. By comparing these models to the simulation results at different degrees of polydispersity, it is possible to obtain a more complete picture of their validity as compared to the monodisperse case. Regarding the diffusion of polymer chains, simulation results were in good agreement with the experimental results previously obtained by Composto and coworkers (Soft Matter 2012, 8, 6512), which relate the chains’ diffusivity to the average interparticle distance. As far as the transport properties are concerned, they show a weaker dependence on the polydispersity index. By contrast, results on viscosity and thermal conducitivity show that they are conditioned by the polymer-NP specific interfacial area and the inverse average mass, respectively. These results are in good agreement with previous experimental results. A deeper examination of this intriguing deviation from viscosity predictions in traditional composites, reveals a non-trivial combination of thickening and thinning effects contributing to the final viscosity of the PNC. This thesis also address the influence of the chains’ stiffness on the dynamical and viscous behaviour. An isotropic-to-nematic phase transition is observed, regardless of the NP-monomer interactions, below which a monotonic increase of both properties is observed, whereas orientationally ordered systems dramatically modify them, resulting into a steep increase or a smooth decrease depending on the direction in which they are measured.

Thermal and viscous forces compete for dominance at the microscopic length-scales which govern the behaviour of many soft or biological systems. We study three systems of increasing complexity with the central goal of understanding the statistical or hydrodynamic nature of their mechanics. First we study experiments that have been conducted on ferromagnetic colloidal rods. At equilibrium, the magnetically pinned rod is observed to randomly flip between two orientational states, which our theoretical analysis shows is due to a competition between entropic and Hamiltonian forces. We show analytically how entropic forces can arise by considering the coupling between observed and unobserved variables of a system. Experiments in which a rod is driven out of equilibrium by a rotating field display three phases of steady-state behaviour as a function of driving frequency. Using Brownian dynamics simulations we match the lower critical frequency to the experimentally obtained values, showing that thermal fluctuations play an important role in this regime and propose a simple argument to demonstrate that hydrodynamic interactions between the substrate and rod affect the upper critical frequency. We then turn to the biophysical topic of cell locomotion in viscoelastic media. In order to study how bacterial flagella interact with similarly-sized polymers in their environment, we construct a Stokesian dynamics model of a helical filament and bead--spring polymer. Simulating their interaction first for a pinned--rotating helix, then for a swimming helix, we demonstrate that large polymers become hydrodynamically entrained by the flagellum and coil around it, causing both pinned and swimming flagella to expend more work. For the swimming helix, this results in a reduction of swimming speed on average. Finally, we consider an active nematic fluid confined to a channel and show that the inclusion of a passive colloid induces a global state of coherent flow maintained by the intrinsic activity of the system. This flow is persistent, and transports the colloid with it along the channel. By this mechanism, a passive colloid is able to spontaneously induce its own transport through an otherwise quiescent fluid.

The theory and computation of line defects are discussed in the context of both solids and liquid crystals. This dissertation includes four parts. The Generalized Disclination theory is discussed and applied to numerous interfacial and bulk line defect problems. An augmented Oseen-Frank energy as well as a novel 2D-model is proposed and demonstrated for disclination dynamics in liquid crystal. A model based on kinematics and thermodynamics is devised to predict tactoid dynamics during the process of the isotropic-nematic phase transition in LCLC. In the first part of the thesis, the utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects. The Burgers vector of a disclination dipole in linear elasticity is derived, clearly demonstrating the equivalence of its stress field to that of an edge dislocation. An explicit formula for the displacement jump of a single localized composite defect line in terms of given g.disclination and dislocation strengths is deduced based on the Weingarten theorem for g.disclination theory at finite deformation. The Burgers vector of a g.disclination dipole at finite deformation is also derived. In the second part, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of various line defects and grain/phase boundary problems are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclinationdipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics (plus kinetics) in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. In the third part, nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. A novel 2D-model of disclination dynamics in nematics is proposed, which is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. In the fourth part, the isotropic-nematic phase transition in chromonic liquid crystals is studied. We simulate such tactoid equilibria and dynamics with a model using degree of order, a variable length director as state descriptors, and an interfacial descriptor. We introduce an augmented Oseen-Frank energy, with non-convexity in both interfacial energy and the dependence of the energy on the degree of order. A strategy is devised based on continuum kinematics and thermodynamics. The model is used to predict tactoid dynamics during the process of phase transition. We reproduce observed behaviors in experiments and perform an experimentally testable parametric study of the effect of bulk elastic and tactoid interfacial energy constants on the interaction of interfacial and bulk fields in the tactoids.