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Visualization and exploration of nematic liquid crystal (NLC) data is a challenging task due to the multidimensional and multivariate nature of the data. Simulation study of an NLC consists of multiple timesteps, where each timestep computes scalar, vector, and tensor parameters on a geometrical mesh. Scientists developing an understanding of liquid crystal interaction and physics require tools and techniques for effective exploration, visualization, and analysis of these data sets. Traditionally, scientists have used a combination of different tools and techniques like 2D plots, histograms, cut views, etc. for data visualization and analysis. However, such an environment does not provide the required insight into NLC datasets. This thesis addresses two areas of the study of NLC data---understanding of the tensor order field (the Q-tensor) and defect detection in this field. Tensor field understanding is enhanced by using a new glyph (NLCGlyph) based on a new design metric which is closely related to the underlying physical properties of an NLC, described using the Q-tensor. A new defect detection algorithm for 3D unstructured grids based on the orientation change of the director is developed. This method has been used successfully in detecting defects for both structured and unstructured models with varying grid complexity.

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Micrometer-sized liquid-crystal (LC) droplets embedded in a polymer matrix may enable optical switching in the composite film through the alignment of the LC director along an external electric field. When a ferroelectric material is used as host polymer, the electric field generated by the piezoelectric effect can orient the director of the LC under an applied mechanical stress, making these materials interesting candidates for piezo-optical devices. In this work, polymer-dispersed liquid crystals (PDLCs) are prepared from poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) and a nematic liquid crystal (LC). The anchoring effect is studied by means of dielectric relaxation spectroscopy. Two dispersion regions are observed in the dielectric spectra of the pure P(VDF-TrFE) film. They are related to the glass transition and to a charge-carrier relaxation, respectively. In PDLC films containing 10 and 60 wt% LC, an additional, bias-field-dependent relaxation peak is found that can be attributed to the motion of LC molecules. Due to the anchoring effect of the LC molecules, this relaxation process is slowed down considerably, when compared with the related process in the pure LC. The electro-optical and piezo-optical behavior of PDLC films containing 10 and 60 wt% LCs is investigated. In addition to the refractive-index mismatch between the polymer matrix and the LC molecules, the interaction between the polymer dipoles and the LC molecules at the droplet interface influences the light-scattering behavior of the PDLC films. For the first time, it was shown that the electric field generated by the application of a mechanical stress may lead to changes in the transmittance of a PDLC film. Such a piezo-optical PDLC material may be useful e.g. in sensing and visualization applications. Compared to a non-polar matrix polymer, the polar matrix polymer exhibits a strong interaction with the LC molecules at the polymer/LC interface which affects the electro-optical effect of the PDLC films and prevents a larger increase in optical transmission. / Mikrometer-große, in eine Polymermatrix eingebettete Flüssigkristall-Tröpfchen können als elektro-optische Lichtventile fungieren, da die Ausrichtung der Flüssigkristalle durch ein externes elektrisches Feld verändert werden kann. Wird nun ein ferroelektrisches Polymer als Matrix verwendet, so kann das durch den piezoelektrischen Effekt erzeugte und von der äußeren mechanischen Spannung abhängige elektrische Feld den Flüssigkristall ausrichten. Solche Materialien können daher als piezo-optische Lichtventile eingesetzt werden. Im Rahmen dieser Arbeit wurden PDLCs (polymer-dispersed liquid crystals) durch Einbettung von nematischen Flüssigkristallen in Poly(Vinylidenefluoride-Trifluorethylene) (P(VDF-TrFE)) erzeugt. Die Wechselwirkungen an der Grenzfläche zwischen Flüssigkristall und Polymer wurden mittels dielektrischer Spektroskopie untersucht. Im dielektrischen Spektrum des reinen P(VDF-TrFE) wurden zwei Dispersions-Regionen beobachtet, welche vom Glasübergang und einer Ladungsträgerrelaxation des Polymers herrühren. PDLC Folien mit unterschiedlichen Anteilen von Flüssigkristall-Tröpfchen (10 bzw. 60 Gewichtsprozente) zeigten beim Anlegen eines elektrischen Wechselfelds zusatzliche Relaxationseffekte, welche der Bewegung der eingebetteten Flüssigkristall-Moleküle zugeordnet werden konnten. Durch die Einlagerung der Flüssigkristall-Moleküle weist die Struktur eine Relaxation auf, die gegenüber vergleichbaren Prozessen im reinen Flüssigkristall deutlich verlangsamt ist. Des weiteren wurde das elektrooptische und piezo-optische Verhalten der mit 10 und 60 Gewichtsprozent Flüssigkristall geladenen Folien untersucht. Die Lichtstreuung hängt dabei ab von der Fehlanpassung der Brechungsindizes von Polymermatrix und Flüssigkristallen sowie von den Wechselwirkungen der Polymerdipole mit den Flüssigkristall-Molekülen an der Tröpfchenoberfläche. Es konnte erstmalig gezeigt werden, dass die Lichtdurchlässigkeit der PDLC-Folien durch eine externe mechanische Spannung gesteuert werden kann. Dieser Effekt macht das piezo-optische PDLC-Material für die Verwendung in Optik- und Sensoranwendungen interessant. Im Vergleich mit unpolaren Wirtspolymeren zeigen polare Wirtsmaterialien eine deutlich stärkere Wechselwirkung zwischen den Flüssigkristall-Molekülen an der Polymer/Flüssigkristall-Grenzfläche, welche den elektrooptischen Effekt beeinflusst und so die maximale transmissions änderung reduziert.

In this thesis we studied theoretically and numerically dynamics, order and fluctuations in two dimensional active matter with specific reference to the nematic phase in collections of self-driven particles.The aim is to study the ways in which a nonequilibrium steady state with nematic order differs from a thermal equilibrium system of the same spatial symmetry. The models we study are closely related to “flocking”[1], as well as to equations written down to describe the interaction of molecular motors and filaments in a living cell[2,3] and granular nematics [4]. We look at (i) orientational and density fluctuations in the ordered phase, (ii) the way in which density fluctuations evolve in a nematic background, and finally (iii) the coarsening of nematic order and the density field starting from a statistically homogeneous and isotropic initial state. Our work establishes several striking differences between active nematics and their thermal equilibrium counterparts. We studied two-dimensional nonequilibrium active nematics. Two-dimensional nonequilibrium nematic steady states, as found in agitated granular-rod monolayers or films of orientable amoeboid cells, were predicted [5] to have giant number fluctuations, with the standard deviation proportional to the mean. We studied this problem more closely, asking in particular whether the active nematic steady state is intrinsically phase-separated. Our work has close analogy to the work of Das and Barma[6] on particles sliding downhill on fluctuating surfaces, so we looked at a model in which particles were advected passively by the broken-symmetry modes of a nematic, via a rule proposed in [5]. We found that an initially homogeneous distribution of particles on a well-ordered nematic background clumped spontaneously, with domains growing as t1/2, and an apparently finite phase-separation order parameter in the limit of large system size. The density correlation function shows a cusp, indicating that Porod’s Law does not hold here and that the phase-separation is fluctuation-dominated[7]. Dynamics of active particles can be implemented either through microscopic rules as in[8,9]or in a long-wavelength phenomenological approach as in[5]It is important to understand how the two methods are related. The purely phenomenological approach introduces the simplest possible (and generally additive)noise consistent with conservation laws and symmetries. Deriving the long-wavelength equation by explicit coarse-graining of the microscopic rule will in general give additive and multiplicative noise terms, as seen in e.g., in [10]. We carry out such a derivation and obtain coupled fluctuating hydrodynamic equations for the orientational order parameter (polar as well as apolar) and density fields. The nonequilibrium “curvature-induced” current term postulated on symmetry grounds in[5]emerges naturally from this approach. In addition, we find a multiplicative contribution to the noise whose presence should be of importance during coarsening[11]. We studied nonequilibrium phenomena in detail by solving stochastic partial differential equations for apolar objects as obtained from microscopic rules in[8]. As a result of “curvature-induced” currents, the growth of nematic order from an initially isotropic, homogeneous state is shown to be accompanied by a remarkable clumping of the number density around topological defects. The consequent coarsening of both density and nematic order are characterised by cusps in the short-distance behaviour of the correlation functions, a breakdown of Porod’s Law. We identify the origins of this breakdown; in particular, the nature of the noise terms in the equations of motion is shown to play a key role[12]. Lastly we studied an active nematic steady-state, in two space dimensions, keeping track of only the orientational order parameter, and not the density. We apply the Dynamic Renormalization Group to the equations of motion of the order parameter. Our aim is to check whether certain characteristic nonlinearities entering these equations lead to singular renormalizations of the director stiffness coefficients, which would stabilize true long-range order in a two-dimensional active nematic, unlike in its thermal equilibrium counterpart. The nonlinearities are related to those in[13]but free of a constraint that applies at thermal equilibrium. We explore, in particular, the intriguing but ultimately deceptive similarity between a limiting case of our model and the fluctuating Burgers/KPZequation. By contrast with that case, we find that the nonlinearities are marginally irrelevant. This implies in particular that 2-dactive nematics too have only quasi-long-range order[14].