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Abstract

The dissertation considers singular topological defects (TDs) and also dynamic solition-like excitations in nematic liquid crystals (NLCs). TDs are an inevitable consequence of continuous symmetry breaking phase transitions, which are ubiquitous in nature. Due to topological origin TDs display several universalities and therefore bridge diverse fields of physics. Furthermore, fields might represent fundamental entities of nature and possible candidates for “fundamental particles” could be TDs. Consequently, it is of interest to identify systems in which TDs are relatively easy created, manipulated and experimentally observed. For this purpose, NLC configurations represent ideal testing grounds due to their unique combination of softness, liquid character, optical anisotropy&transparency and a large diversity of TDs that they display. In fact, NLCs are even named after TDs.
Our investigations were directed towards an understanding of general mechanisms to generate, stabilize and manipulate singular and nonsingular topological excitations. In particular, we consider configurations to which we enforce relatively large topological charges, we demonstrate new electrostatic analogies, we analyze the impact of extrinsic curvature on number and position of TDs, we study interactions between appropriate nanoparticles (NPs) and TDs, and we analyze dynamically generated topological excitations in plane-parallel cells. The work consists of theoretical modeling and numerical simulations. Defect structures are described either by the nematic tensor order parameter or the nematic director field. In the former case, the Landau-de Gennes phenomenological approach was used. In the latter case, we used the Lebwohl-Lasher lattice type modeling.
In quasi-two-dimensional (2D) planar systems, we demonstrate that confinement-enforced total topological charge 𝑚≫1 decays into elementary TDs bearing charge 𝑚=1/2. These assemble close to the bounding substrate to enable essentially bulk-like uniform nematic ordering in the central part of a system. This effect is reminiscent of the Faraday cavity phenomenon in electrostatics. In addition, we showed that the total topological charge within a 2D region enclosed by a boundary possessing sharp edges is not uniquely defined due to the head-to-tail invariance of nematic ordering. In this study, a nematic LC was confined within a square, where the strong tangential anchoring condition was enforced at the boundaries. We demonstrated that using an external electric field one could switch between different topological configurations without melting NLC. In addition, we demonstrated that "domain"-type reorientations could be enabled by creation or/and annihilation of pairs {defect,antidefect}. Finally, we analysed topologically enforced structures consisting of several TDs where the total topological charge of the system was zero. We investigated possible mechanism which would trigger annihilation of TDs into a defect-free state. Our analysis revealed different annihilation channels which are in general relatively strongly sensitive to various perturbations. We also observed that in certain confinement geometries varying the order parameter correlation length size could trigger global rotation of an assembly of TDs. Finally, we showed in three-dimensional (3D) that an external electric field could be used to drag the boojum fingertip towards a confinement cell interior. This proof-of-concept reveals that assemblies of TDs could be exploited as movable traps for appropriate nanoparticles, opening several opportunities for development of functional nanodevices.
In curved geometries, we analyzed the impact of intrinsic and extrinsic curvature on the distribution of TDs in 2D patches exhibiting negative Gaussian curvature. As model geometries, we choose catenoids and pseudospheres. Such geometries are often locally present in biological membranes. For example, catenoids roughly mimic neck-like shapes which appear in membrane fission, fusion or budding processes. On the other hand, pseudospheres roughly mimic structures realized in inter-membrane cellular cargo exchange. We demonstrated that defects robustly assemble in regions exhibiting strong enough localized distortions in the substrate curvature field. In particular, we investigated the impact of extrinsic curvature on TDs, which has been in most studies so far neglected. Our analysis revealed that the extrinsic curvature contributions are in general always present and are of comparable strength with respect to the intrinsic curvature contributions. Furthermore, we showed that the extrinsic curvature strongly affects the position of TDs in geometries exhibiting the negative Gaussian curvature. We also demonstrated that local assembling tendency of TDs can be well predicted by the Effective Topological Charge Cancellation mechanism.
Finally, we studied NLC confined in a plane-parallel cell which enforces the so-called double easy axis at the confining plates. In addition, a rotating external field was present. The resulting frustrations yielded complex patterns and dynamics if the external field was strong enough to enable synchronized global nematic order dynamics. Of particular interest were conditions suggesting the presence of the edge of chaos. On approaching this regime, we obtain diverse and complex nematic patterns on varying the external field frequency.