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Opis: We numerically studied localized elastic distortions in curved, effectively two-dimensional nematic shells. We used a mesoscopic Landau-de Gennes-type approach, in which the orientational order is theoretically considered by introducing the appropriate tensor nematic order parameter, while the three-dimensional shell shape is described by the curvature tensor. We limited our theoretical consideration to axially symmetric shapes of nematic shells. It was shown that in the surface regions of stomatocyte-class nematic shell shapes with large enough magnitudes of extrinsic (deviatoric) curvature, the direction of the in-plane orientational ordering can be mutually perpendicular above and below the narrow neck region. We demonstrate that such line-like nematic distortion configurations may run along the parallels (i.e., along the circular lines of constant latitude) located in the narrow neck regions of stomatocyte-like nematic shells. It was shown that nematic distortions are enabled by the order reconstruction mechanism. We propose that the regions of nematic shells that are strongly elastically deformed, i.e., topological defects and line-like distortions, may attract appropriately surface-decorated nanoparticles (NPs), which could potentially be useful for the controlled assembly of NPs.
Ključne besede: nematic shells, orientational order, topological defects, stomatocytes, order reconstruction mechanism
Objavljeno v DKUM: 28.03.2025; Ogledov: 0; Prenosov: 6
Celotno besedilo (4,60 MB)
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Opis: Of our interest are frustration-driven pattern generating mechanisms in systems which in bulk equilibrium display spatially homogeneous long-range orientational order in absence of perturbations. As testbed material, we select thermotropic nematic liquid crystals. In bulk, they exhibit weakly discontinuous order-disorder phase transformation on varying temperature where the ordered nematic phase features spatially uniform axial order along an arbitrary symmetry breaking direction. However, due to continuous symmetry breaking (CSB) the established order is extremely susceptible to various perturbations which are in real systems in general always present. We theoretically illustrate how diverse complex patterns could be excited. Particularly intriguing configurations could appear if topological defects are present that could be generated via CSB. Our analysis is based on a relatively simple Lebwohl-Lasher-type model in which we could get analytical insight into phenomena of our interest. Using it we illustrate history dependent early stage isotropic-nematic phase evolution and final patterns in presence of "impurities" (e.g., nanoparticles). We show how characteristic effective interaction characteristics predict qualitatively different emerging patterns. Our analysis is based on CSB which is ubiquitous in nature. Consequently, demonstrated mechanisms are expected to manifest also in other condensed matter systems whose ordered phase is formed via CSB. We illustrate how kinetics and impurities could impact key structural properties of the systems of our interest.
Ključne besede: continuous symmetry breaking, patterns, topological defects, nematic liquid crystals
Objavljeno v DKUM: 05.12.2024; Ogledov: 0; Prenosov: 7
Celotno besedilo (9,33 MB)
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Opis: We consider the theoretical and positional assembling of topological defects (TDs) in effectively two-dimensional nematic liquid crystal films. We use a phenomenological Helfrich–Landau–de Gennes-type mesoscopic model in which geometric shapes and nematic orientational order are expressed in terms of a curvature tensor field and a nematic tensor order parameter field. Extrinsic, intrinsic, and total curvature potentials are introduced using the parallel transport concept. These potentials reveal curvature seeded TD attractors. To test ground configurations, we used axially symmetric nematic films exhibiting spherical topology.
Ključne besede: topological defects, nematic liquid crystals, nematic shells, geometric potentials, curvature
Objavljeno v DKUM: 30.09.2024; Ogledov: 0; Prenosov: 10
Celotno besedilo (3,69 MB)
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Opis: We consider history-dependent behavior in domain-type configurations in orientational order that are formed in configurations reached via continuous symmetry-breaking phase transitions. In equilibrium, these systems exhibit in absence of impurities a spatially homogeneous order. We focus on cases where domains are formed via (i) Kibble-Zurek mechanism in fast enough quenches or by (ii) Kibble mechanism in strongly supercooled phases. In both cases, domains could be arrested due to pinned topological defects that are formed at domain walls. In systems exhibiting polar or quadrupolar order, point and line defects (disclinations) dominate, respectively. In particular, the disclinations could form complex entangled structures and are more efficient in stabilizing domains. Domain patterns formed by fast quenches could be arrested by impurities imposing a strong enough random-field type disorder, as suggested by the Imry-Ma theorem. On the other hand, domains formed in supercooled systems could be also formed if large enough energy barriers arresting domains are established due to large enough systems’ stiffness. The resulting effective interactions in established domain-type patterns could be described by random matrices. The resulting eigenvectors reveal expected structural excitations formed in such structures. The most important role is commonly played by the random matrix largest eigenvector. Qualitatively different behavior is expected if this eigenvector exhibits a localized or extended character. In the former case, one expects a gradual, non-critical-type transition into a glass-type structure. However, in the latter case, a critical-like phase behavior could be observed.
Ključne besede: topological defects, domains, disorder
Objavljeno v DKUM: 01.07.2024; Ogledov: 140; Prenosov: 7
Celotno besedilo (2,07 MB)
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Opis: We considered general mechanisms enabling the stabilization of localized assemblies of topological defects (TDs). There is growing evidence that physical fields represent fundamental natural entities, and therefore these features are of interest to all branches of physics. In general, cores of TDs are energetically costly, and consequently, assemblies of TDs are unfavorable. Owing to the richness of universalities in the physics of TDs, it is of interest to identify systems where they are easily experimentally accessible, enabling detailed and well-controlled analysis of their universal behavior, and cross-fertilizing knowledge in different areas of physics. In this respect, thermotropic nematic liquid crystals (NLCs) represent an ideal experiment testbed for such studies. In addition, TDs in NLCs could be exploited in several applications. We present examples that emphasize the importance of curvature imposed on the phase component of the relevant order parameter field. In NLCs, it is represented by the nematic tensor order parameter. Using a simple Landau-type approach, we show how the coupling between chirality and saddle splay elasticity, which can be expressed as a Gaussian curvature contribution, can stabilize Meron TDs. The latter have numerous analogs in other branches of physics. TDs in 2D curved manifolds reveal that the Gaussian curvature dominantly impacts the assembling and stabilization of TDs. Furthermore, a strong enough curvature that serves as an attractor for TDs is a respective field that could be imposed in a fast enough phase transition. Assemblies of created TDs created in such a disordered environment could be stabilized by appropriate impurities.
Ključne besede: topological defects, nematic liquid crystals, Gaussian curvature, topological charge
Objavljeno v DKUM: 17.07.2023; Ogledov: 421; Prenosov: 28
Celotno besedilo (6,14 MB)
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