Diffraction gratings formed by bent-core liquid crystals in the twist-bend nematic phase

doctoral dissertation

Muhammad Ali (Author), Nataša Vaupotič (Mentor), Damian Pociecha (Co-mentor)

Abstract

In this thesis, we study the structure and optical transmission properties of the twist-bend nematic liquid crystalline phase, made of bent dimers, confined in thin planar cells. Confinement leads to the formation of a periodic modulated structure, the formation of which is explained as follows. The twist-bend nematic phase is characterized by a heliconical modulation of the molecular long axes. Due to a short pitch of modulation (approximately 10 nm), the twist-bend nematic phase behaves as a pseudo-layered medium. At temperatures below the nematic - twist-bend nematic phase transition, the heliconical pitch and thus the thickness of the pseudo-layers reduces, which leads to a two-dimensional undulation of pseudo-layers in the direction perpendicular to the cell surfaces and along the surfaces. The undulated structure is responsible for a stripe texture observed under a polarizing microscope and acts as a diffraction grating. We constructed theoretical models to predict the pseudo-layer structure of a confined twist-bend nematic phase and to describe the properties of light diffracted on such cells. The free energy of the two-dimensional pseudo-layer structure of the twist-bend nematic phase is expressed in terms of the nematic director field, by which we describe the direction of the heliconical axis, and a complex smectic order parameter, the gradient of which gives the direction of the layer normal. At first, we assume that pseudo-layers are perpendicular to the surfaces (bookshelf geometry) and find a stable structure by assuming an ansatz for the pseudo-layer displacement from the bookshelf geometry and then minimizing the free energy at a very strong and very weak surface anchoring. In this way a threshold condition for the onset of the modulated structure is obtained, as well as the amplitude and period of modulation. Next, we assume that, at the onset of the twist-bend nematic phase, pseudo-layers are formed at some angle (pre-tilt) with respect to the surface. We find that in both cases, the bookshelf and pre-tilted one, the calculated period of modulation far from the phase transition is always approximately twice the cell thickness, which agrees with experimental observations. The properties of light diffracted by the spontaneously formed grating were studied both experimentally and theoretically. We measured the intensity and polarization properties of the first two orders of the diffracted light and the temperature dependence of the polarization of the second order diffraction peaks. To predict the observed properties of the diffracted light and to simplify the description of such gratings, we consider different preliminary models of a one-dimensional spatial variation of the optic axis, the direction of which is given by two angles. A transfer matrix method is used and a good agreement between the experimental and theoretical results is obtained. In a more comprehensive approach, we determine the spatial variation of the optic axis direction from the modeled structure. The electric field in the diffracted light is obtained by using the transfer matrix method and beam propagation method. In the case of a pre-tilt of the pseudo-layers and very strong surface anchoring both methods give good qualitative agreement with experimental results, only in the case of the temperature dependence of the second order diffraction peaks, a more complex beam propagation method is superior to the transfer matrix method. The thesis is divided into three parts. In the first part, we focus on the physical properties of the twist-bend nematic phase and its structure in thin planar cells. In the second part, a continuum model is proposed and finally, the properties of diffracted light are discussed and theoretically predicted by using the beam propagation method and transfer matrix method.

Keywords

bent-dimer liquid crystals;twist-bend nematic phase;undulation of pseudo-layers;polarization;diffraction grating;beam peopagation method;transfer matrix method;dissertations;

Data

Language:	English
Year of publishing:	2021
Typology:	2.08 - Doctoral Dissertation
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	M. Ali]
UDC:	535.428:544.25(043.3)
COBISS:	81794051
Views:	357
Downloads:	36
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	UKLONSKE MREŽICE V ZVOJNO – UPOGIBNI NEMATIČNI FAZI TEKOČIH KRISTALOV Z UKRIVLJENO SREDICO
Secondary abstract:	V doktorski disertaciji obravnavamo zvojno-upogibno ne matično tekočekristalno fazo, v kateri so osnovni gradniki upognjeni dimeri. Tekoči kristal omejimo v tanke planarne celice. Zaradi omejenosti se v zvojno-upogibni fazi tvori periodično modulirana struktura, katere nastanek razložimo na sledeč način. Za zvojno-upogibno ne matično fazo je značilna vijačna ureditev molekul. Ker je vijačnica kratka (okoli 10 nm), se zvojno-upogibna faza obnaša kot plastna struktura. Pri temperaturah nižjih od temperature prehoda iz ne matične v zvojno-upogibno ne matično fazo se perioda vijačnice krajša, s tem pa tudi debelina plasti. Ker so plasti na površini zasidrane, tekoči kristal zmanjšanje debeline plasti v notranjosti doseže z nagubanjem plasti v smeri vzdolž površin in pravokotno na njih. Zaradi periodične modulacije plasti pod polarizacijskim mikroskopom opazimo značilno črtasto strukturo, ki deluje kot uklonska mrežica. Izdelali smo teoretične modele, s katerimi lahko napovemo ureditev plasti v omejeni zvojno-upogibni ne matični fazi in lastnosti svetlobe po prehodu skozi takšno celico. Prosto energijo sistema izrazimo z ne matskim direktorjem, ki opiše smer vijačne osi, in s kompleksnim smektičnim ureditvenim parametrom, katerega gradient podaja smer pravokotnice na plast. Najprej privzamemo, da so se plasti ob nastanku tvorile v smeri pravokotno na površino. Izberemo nastavek za odmik plasti od te pravokotne ureditve in poiščemo pogoje, pri katerih je prosta energija sistema najnižja ob upoštevanju zelo močnega in zelo šibkega sidranja plasti na površini. Na tak način dobimo pogoje, pri katerih modulirana struktura postane stabilna, dobimo pa tudi amplitudo in periodo modulacije. Nato privzamemo, da so se plasti tvorile pod nekim kotom glede na površino in ponovimo postopek. V obeh primerih dobimo, da je perioda modulacije pri temperaturah daleč od temperature prehoda v ne matično fazo enaka približno dvojni debelini celice, kar se ujema z eksperimentalnimi opažanji. Lastnosti prepuščene svetlobe smo raziskovali tako eksperimentalno kot teoretično. Merili smo intenziteto prepuščene svetlobe in določili njeno polarizacijo. Za uklonske snope drugega reda smo merili tudi temperaturno odvisnost intenzitete in polarizacije. Najprej skonstruiramo preprost teoretični model, ki predpostavi enodimenzionalno modulacijo optične osi, katere smer opišemo z dvema kotoma. Lastnosti prepuščene svetlobe izračunamo z metodo prenosne matrike in dobimo dobro ujemanje med eksperimentalnimi rezultati in teoretičnimi napovedmi. Nato uporabimo bolj kompleksen pristop in lokalno smer optične osi povežemo z lokalno smerjo pravokotnice na plast. Električno polje v prepuščeni svetlobi izračunamo z metodo prenosne matrike in z metodo razširjanja snopa. Dobro ujemanje z eksperimentalnimi meritvami dobimo v primeru nagnjenih plasti in zelo močnega sidranja na površini. Obe metodi podata primerljive rezultate, le v primeru temperaturne odvisnosti uklonskih vrhov drugega reda da metoda razširjanja snopa boljše ujemanje z meritvami. Disertacija je razdeljena v tri dele. V prvem delu obravnavamo strukturo in fizikalne lastnosti zvojno-upogibne ne matične faze v tankih planarnih celicah. V drugem delu predlagamo kontinuumski model za izračun strukture, v tretjem delu pa predstavimo eksperimentalne meritve lastnosti uklonjene svetlobe ter jih teoretično napovemo z metodo prenosne matrike in metodo razširjanja snopa.
Secondary keywords:	tekoči kristali iz ukrivljenih dimerov;zvojno-upogibna nematična faza;nagubanje plasti;polarizacija;uklonska mrežica;metoda razširjanja snopa;metoda prenosne matrike;disertacije;Tekoči kristali;Univerzitetna in visokošolska dela;
Type (COBISS):	Doctoral dissertation
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za fiziko
Pages:	VI, 105 f.
ID:	12744315