Strukture ograjenih modrih faz: modeliranje in simulacije

Structures of liquid crystalline blue phases (BPs) confined by patterned surfaces of different geometries are investigated using numerical simulation based on the Landau-de Gennes phenomenological approach. In the first part of the thesis, BPII sandwiched between a pair of parallel confining surfaces with specifically designed patterns is studied. Patterned confining surfaces are made by imposing different types of surface anchoring in different regions of the surfaces. Directed by the surface patterns, quasi-two-dimensional half-Skyrmion lattices are formed. Specifically, we observe the formation of square and triangular lattices of half-Skyrmions. These lattices of the swirling skyrmion textures are interspersed with singular -1/2 or -1 line defects which also constitute quasi-two-dimensional regular lattices. The demonstrated structures may have potential for photonic applications, including as waveplates and two-dimensional photonic crystals. In the second part of the thesis, edge and screw dislocation structures in confined BPI and BPII are extensively studied numerically. This work is inspired by the analogies between BPs and solid crystalstextemdash they both exhibit three-dimensional lattice structures. Dislocation structures are induced by confining BPs inside specifically designed boundaries, which are made by appropriately distorting the bulk BP unit cells or by patterning the molecular anchoring on the confining surfaces. Various dislocations with Burgers vector magnitude equaling one or two times the unit cell size are obtained. Networks of the defect lines and the double twist cylinders are analyzed. Unveiling these dislocation structures deepens the understanding of BP structures under confinement. Finally, our work is a contribution to designing and stabilizing complex birefringent layer profiles in BPs under various constraints.V doktorskem delu z uporabo numeričnih simulacij na osnovi Landau-de Gennes-ovega fenomenološkega pristopa preučujem strukture tekoče kristalnih modrih faz (BP), omejenih s površinami v različnih geometrijah in s specifično vzorčenim sidranjem tekoče kristalnih molekul. V prvem delu disertacije raziščem obnašanje plasti modre faze BPII, ujete med vzporedni površini s posebej načrtovanimi vzorci obdelave. Vzorce ustvarim z uporabo treh tipov površinskega sidranja tekoče kristalnih molekul (močno in šibko pravokotno sidranje ter močno usmerjeno planarno sidranje) na različnih območjih površin. Izbrani periodični površinski vzorci v materialu vsilijo nastanek dvodimenzionalnih kvadratnih in trikotnih mrež pol-skyrmionov. Mreže vrtinčastih skyrmionskih struktur spremljajo singularni -1/2 ali -1 linijski defekti, ki prav tako tvorijo pravilne kvazi-dvodimenzionalne mreže. Takšne strukture bi lahko bile uporabne v fotonskih aplikacijah kot so valovne ploščice in fotonski kristali. V drugem delu disertacije numerično raziščem vijačne in robne dislokacije v ograjenih fazah BPI in BPII ki jih karakterizirajo specifične trodimenzionalne periodične defektne strukture. Navdih za tovrstne raziskave so analogije med modrimi fazami in trdnimi kristali - oboji se namreč uredijo v tridimenzionalne mreže. Dislokacije vsilim z uporabo posebej načrtovane ograditve, bodisi preko popačenja osnovnih celic znotraj materiala, bodisi preko posebej vzorčenega molekularnega sidranja površin, ki ograjujejo modro fazo. Predstavim različne dislokacije z velikostjo Burgersovega vektorja od ene do več velikosti osnovnih celic BPI in BPII. Podrobno analiziram omrežja defektnih linij in cilindre z dvojnim zvojem. Razkritje tovrstnih dislokacij pripomore k globljemu razumevanju ograjenih modrih faz. Obe raziskavi sta tudi prispevek k razvoju in stabilizaciji kompleksno dvolomnih profilov v plasteh modrih faz s specifično ograditvijo