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V delu obravnavamo kompleksne strukture linijskih defektov v enoosni nematski fazi, ograjeni v planparalelno geometrijo, in različne načine njihovega prevezovanja. Nematske strukture opisujemo na mezoskopski skali s tenzorskim nematskim ureditvenim parametrom. Ravnovesna stanja določimo z numerično minimizacijo pripadajoče proste energije sistema. Različne defektne strukture vsiljujemo topološko z robnimi pogoji na ograjujočih ploščah. Preko slednjih vsiljujemo dvodimenzionalne (2D) površinske defekte, karakterizirane z ovojnim številom m. Te robne pogoje lahko eksperimentalno realiziramo, npr. z vtisno metodo z uporabo mikroskopa na atomsko silo. Pozornost posvečamo predvsem t. i. topološko "nenabitim" disklinacijam z |m| = 1/2, katerih 3D topološki naboj je enak 0. Najprej preučimo strukturno raznovrstnost, ki jo omogoča površinsko vsiljen topološki defekt z m = 1. V odvisnosti od razmerja debeline celice glede na dvoosno korelacijsko dolžino in začetnih pogojev se v celici realizira bodisi linijski defekt z m = 1, razcepljeni defekt, ki ga sestavljata dve medsebojno odbijajoči liniji z m = 1/2, ali pa brezdefektna pobegla struktura. Stabilnosti ravnovesnih nematskih struktur in preklapljanje med njimi z uporabo zunanjega električnega polja preverimo tudi eksperimentalno. Pretežno antiparalelne "nenabite" linije v dovolj debelih celicah, ki so lokalizirane ob ograjujočih površinah, stabiliziramo s kvadratno mrežo 2 × 2 alternirajočih m = ±1/2 površinskih defektov. Pokažemo, da se takšni antiparalelni disklinaciji obnašata kot defekt in antidefekt s težnjo medsebojne anihilacije. Demonstriramo možno prevezavo med različnimi defektnimi nematskimi strukturami z uporabo zunanjega električnega polja. Z vsiljevanjem 4 × 4 vzorca alternirajočih defektov z m = ±1 na komandni površini v dovolj debelih celicah ustvarimo multistabilen sistem z 18 kvantitativno in 7 kvalitativno različnimi (meta)stabilnimi konfiguracijami. Na izbranih konfiguracijah demonstriramo, da jih lahko reverzibilno prevezujemo z zunanjim električnim poljem, kar kvalitativno tudi eksperimentalno reproduciramo. Pokažemo, da lahko "nenabite" disklinacije stabiliziramo tudi preko koloidov toroidne topologije. Topološko "nenabite" disklinacije izkazujejo lastnosti, podobne Majoranovim delcem. Rezultati so zanimivi zaradi fundamentalnih in aplikativnih razlogov. Različne konfiguracije defektov, ki jih vsilimo preko regularnih vzorcev 2D vtisnjenih defektov, potencialno tvorijo zanke periodičnih 3D struktur, ki so lahko uporabne za različne fotonske ali elektro-optične aplikacije. The thesis covers complex line defect structures in a uniaxial nematic phase, bound by a planparallel geometry, and the different methods of reconfiguring them. We describe the nematic structures on a mesoscopic scale with a tensor nematic order parameter. Equilibrium states are determined through numerical minization of the corresponding free energy. We enforce different defect structures topologically using boundary conditions on enclosing surfaces, through which we enforce two-dimensional (2D) surface defects, characterized with a winding number m. The boundary conditions are experimentally reproducible with methods such as AFM scribing. We pay special attention to the so-called topologically "chargeless" |m| = 1/2 disclinations, whose 3D topological charge is equal to 0. First we study the structural diversity enabled by an m = 1 defect enforced by the surface. Depending on the ratio between the cell thickness and biaxial correlation length or the starting conditions, either an m = 1 line defect, a split defect, comprised of two mutually repulsive m = 1/2 lines, or a defect-less escaped structure is realized. We investigate the stability of equilibrium nematic structures and switching between them using an external electric field, which we verify experimentally. We stabilize the mostly antiparallel "chargeless" lines using a 2×2 pattern of alternating m = ±1/2 surface defects in thick enough cells. We show that such antiparallel disclinations behave like a defect and antidefect with a tendency to mutually annihilate. We demonstrate the possibility of rewiring between different defect structures using an external electric field. By enforcing a 4 × 4 pattern of m = ±1 alternating defects on the master surface, creating a multistable system with 18 quantitatively and 7 qualitatively (meta)stable configurations in thick enough cells. We demonstrate the ability to reversibly switch in select cases using an external electric field, which we qualitatively reproduce experimentally. We show the possibility of stabilizing "chargeless" disclinations using colloids with toroidal topology. Topologically "chargeless" disclinations exhibit properties, similar to Majorana particles. The results are interesting for fundamental and applicative reasons. The different defect configurations that we enforce using the regular patterns of 2D imprinted defects can potentially form loops of periodic 3D structures, which can be useful for various photonic or electro-optic applications.

Samopodobni fotonski kristali so fotonski kristali, katerih deli osnovne celice so podobni celotni osnovni celici. Fotonski kristali so materiali, ki imajo periodični lomni količnik in posledično imajo v pasovni strukturi energijske reže, pri čemer je širina in lega rež odvisna od mikroskopske strukture fotonskega kristala. V tem magistrskem delu predstavimo pet različnih tipov samopodobnih fotonskih kristalov. Začnemo z enodimenzionalnimi fotonskimi kristali z dvema strukturnima parametroma, za katere pokažemo, da imajo v pasovni strukturi zgoščine energijskih rež, katerih lega je linearno odvisna od enega strukturnega parametra. Z drugim strukturnim parametrom kontroliramo širino energijskih rež in zgoščin. Nadaljujemo z dvodimenzionalnimi samopodobnimi fotonskimi kristali, za katere ugotovimo, da lahko z obema strukturnima parametroma fino spreminjamo lego in širino specifične energijske reže. Zaključimo s strukturami koncentričnih obročev, kvadratnih stolpcev in trikotnih stolpcev, kjer pokažemo, da z enim strukturnim parametrom lahko močno vplivamo na pozicije energijskih rež. Splošneje je delo prispevek k razvoju mehke fotonike in prilagodljivih fotonskih kristalov. Self-similar photonic crystals are photnic crystals, for which smaller regions of their unit cells are partially or fully similar to the unit cell itself. Photonic crystals are materials, which have a periodic refractive index, and as a consequence their band structure exhibits photonic bandgaps. In this master's thesis we present five families of self-similar photonic crystals. First we examine a family of one-dimensional self-similar photonic crystals, with two structural parameters. In the band structure of this photonic crystals there are groups of bandgaps, position of which changes linearly with the value of one structural parameter, whereas the other structural parameter has a direct effect on their width. We continue with a two-dimensional family of self-similar photonic crystals, where we are able to fine tune the width and the postion of a specific band gap with both structural parameters. We conclude with the results on three self-similar two-dimenisonal photonic crystal families, which are composed of concetric rings, and square and triangular coloumns. For all three families we show that the postions of the bandgaps can be stongly changed via a single structural parameter. This master's thesis is a contribution to the research of soft photonics and tuneable photonic crystals.

V magistrskem delu je kot razširitev osnovne metode diferenčne dinamične mikroskopije za namen opazovanja hitre dinamike v mehki snovi predstavljena metoda križne diferenčne dinamične mikroskopije. V običajni metodi poteka zajemanje videoposnetka fluktuacij intenzitete sipane svetlobe v vzorcu pri konstantni frekvenci zajemanja slik, zato je najmanjši časovni zamik med dvema slikama obratno sorazmeren s frekvenco. V novi metodi z uporabo dveh poravnanih kamer pridobimo dva nabora slik istega dela vzorca, s Fourierovo analizo pa izračunamo križno slikovno strukturno funkcijo kot funkcijo valovnega vektorja in časovnega zamika. Naključna shema proženja kamer poskrbi, da lahko najmanjši časovni zamik med dvema slikama poljubno skrajšamo ter tako efektivno povečamo frekvenco zajemanja, zato lahko dinamiko v mehki snovi opazujemo tudi v primeru hitrih procesov. Z meritvijo dinamike nematičnega tekočega kristala ter s simulacijami Brownovega gibanja sferičnih delcev smo preučili razlike med obema metodama, z namernim izmikanjem obeh kamer iz poravnane lege pa preverili robustnost križne diferenčne dinamične mikroskopije. In this master's thesis Cross-Differential Dynamic Microscopy is introduced as an extension to the established method of Differential Dynamic Microscopy, for the purpose of observing the fast dynamics in soft matter. With the standard method, a video of the fluctuating intensity of light, scattered by the observed sample, is taken at a constant frame rate. The smallest time delay between two consecutive frames is therefore inversely proportional to the frame rate. With the new method we obtain two sets of data, taken with two aligned cameras observing the same area in the sample, and we calculate the cross-image structure function as a function of the wave vector and the time delay. Random triggering of the cameras can greatly decrease the minimum time delay between the two frames, which results in a faster effective frame rate. This way we can observe the dynamics of fast processes in soft matter. In the experiment we compared both the standard and the new method by measuring the dynamics of a nematic liquid crystal and by analyzing simulated videos of Brownian motion of spherical particles. Lastly, robustness of the proposed method was tested against various camera misalignments.

Doktorska disertacija zajema teoretično študijo treh primerov zloma simetrije v aplikativne namene. Osredotočimo se na možne aplikacije v sistemu tekočih kristalov, ki združujejo unikatno kombinacijo optične anizotropije, delnega značaja tekočine in »mehkobe«. Slednja opisuje možnost relativno močnega makroskopskega odziva na sorazmerno majhne motnje. Kot prvo obravnavamo uporabo fazno spremenljivih materialov v gradbenih kompozitih. Z numeričnimi simulacijami pokažemo, da s fazno spremenljivimi materiali lahko zagotovimo manjša temperaturna nihanja v prostoru in tako izboljšamo toplotno stabilnost prostora, pri čemer ima ključni pomen ustrezno izbrana temperatura faznega prehoda. Nadalje predstavimo dve možni izboljšavi. Prva izboljšava je kombinacija dveh fazno spremenljivih materialov, ki preideta fazni prehod pri različnih temperaturah, kar podaljša časovno konstantno toplotne stabilizacije. Pri drugi izboljšavi manipuliramo temperaturo faznega prehoda z zunanjimi perturbacijami. Na sistemu tekočih kristalov ograjenih v celico analitično prikažemo odvisnost temperature faznega prehoda od karakteristične razdalje celice, na katero lahko vplivamo z zunanjimi perturbacijami kot je na primer zunanje električno polje. S predlaganima izboljšavama razširimo območje optimalnega delovanja kompozita s fazno spremenljivimi materiali. Druga aplikacija zloma simetrije je elektrokalorični pojav, ki ga podrobneje preučimo na sistemu tekočih kristalov v bližini faznih prehodov in v bližini kritične točke z dodajanjem nanodelcev. Za teoretično obravnavo elektrokaloričnega pojava uporabimo Landau-de Gennes – Ginzburgov model na mezoskopski skali. Rezultati numeričnih simulacij razkrivajo, da se s približevanjem temperaturi faznega prehoda iz izotropne v nematsko fazo elektrokalorični odziv sistema veča kot posledica večje spremembe v orientacijski entropiji sistema. Analitično in numerično dokažemo, da lahko elektrokalorični odziv povečamo z direktnim faznim prehodom med izotropno in smektično A fazo. V slednji smektična urejenost efektivno deluje kot zunanje električno polje, kar posledično lahko vodi v ojačenje elektrokaloričnega odziva. Jakost odziva je močno odvisna od jakosti nezveznega prehoda med tekmujočima fazama. Fazno obnašanje v preučevanih sistemih kontroliramo z jakostjo sklopitve med orientacijskim in translacijskim redom. Za vrednosti nad kritično dosežemo direktni fazni prehod 1. reda iz izotropne v smektično A fazo, ki rezultira v povečanju elektrokaloričnega odziva sistema. Predstavimo tudi hladilni sistem in aktivni regenerator, ki delujeta na principu elektrokaloričnega pojava v tekočih kristalih, s čimer dosežemo večje razmerje med hladilno močjo in maso hladilnega sistema. Pri analizi elektrokaloričnega pojava v bližini kritične točke v sistem tekočih kristalov naključno porazdelimo različno koncentracijo nanodelcev. Sistem obravnavamo na semi- mikroskopski skali z Lebwohl Lasherjevim mrežnim modelom. Ugotovimo, da prisotnost nanodelcev ne prispeva k povečanju elektrokaloričnega odziva. Razlog je zmanjševanje možne električno povzročene spremembe orientacijske entropije, kar prevlada nad mehanizmom večjega odziva v bližini kritične točke. Kot tretjo aplikacijo zloma simetrije obravnavamo možnost detekcije nanodelcev. Prisotnost nanodelcev v celici tekočega kristala v nematski fazi povzroči frustracijo, ki se odraža v lokalno dvoosni urejenosti sistema. Posledično s spreminjanjem zunanjih pogojev kot so zunanje električno polje, temperatura in pozicija nanodelca, dobimo kvalitativno različne konfiguracije, kar lahko uporabimo za detekcijo nanodelcev. Rezultati doktorske disertacije prispevajo k boljšemu razumevanju obnašanja sistema tekočih kristalov v bližini faznih prehodov pod vplivom zunanjih dejavnikov. The doctoral thesis covers a theoretical study of three cases of symmetry breaking phenomenon for applicative purposes. We focus on possible applications in liquid crystals, which combine a unique combination of optical anisotropy, the partial character of the liquid and the "softness". The latter describes the possibility of a relatively strong macroscopic response to relatively small external perturbations. First, we consider the use of phase change materials in construction composites. With numerical simulations, we show that phase change materials can decrease room temperature fluctuations and thereby improve the thermal stability of the room. In the latter, the phase transition temperature has a key role. Furthermore, we present two possible improvements. The first improvement is a combination of two different phase change materials that undergo phase transitions at different temperatures, which prolongs the time constant of the heat stabilization. The second improvement is the manipulation of the phase transition temperature with external perturbations. For liquid crystals enclosed in a cell, we show that the phase transition temperature depends on the characteristic length of the cell. The following can be manipulated by external perturbations, for example, the external electric field. With proposed improvements, we expand the optimal operation interval of innovative composites with phase change materials. The second symmetry breaking application is an electrocaloric effect. In the doctoral thesis, we study electrocaloric effect in liquid crystals near the phase transitions and near the critical point by the addition of nanoparticles. For a theoretical study, we use the Landau-de Gennes – Ginzburg model at the mesoscopic scale. Numerical results reveal that by approaching the phase transition temperature from an isotropic to a nematic phase, the electrocaloric response of the system increases because of the increase in the orientational entropy change. We prove that the electrocaloric response increases for a direct phase transition between the isotropic and the smectic A phase both analytically and numerically. In the latter, the smectic ordering effectively acts as an external electric field. Consequently, it can enhance the electrocaloric response, which strongly depends on the intensity of discontinuous transitions between the competing phases. The phase behaviour is controlled by the coupling strength between the orientational and the translational order. In addition, we present an electrocaloric based cooling system and an active regenerator, which can increase performance and cooling power yield per mass. We analyse the electrocaloric effect near a critical point by randomly distributing different concentrations of nanoparticles in the liquid crystal system. Numerical simulations are based on Lebwohl Lasher model at a semi- microscopic scale. We reveal that the presence of nanoparticles does not contribute to an increase in electrocaloric response. The reasoning behind this is a decrease in the electrically induced change in orientational entropy, which prevails over the possible increase due to the critical point. The third symmetry breaking application is the detection of nanoparticles. The presence of nanoparticles in a nematic liquid crystal cell causes frustration, which results in a local biaxiality. At varying external conditions such as the external electric field, temperature, and position of the nanoparticle, we obtain qualitatively different configurations, which can be used to detect nanoparticles. The results of the doctoral thesis contribute to a better understanding of the behaviour of the liquid crystal system in the vicinity of phase transitions under the influence of external factors.

V doktorski disertaciji sem raziskal optične in temperaturne vplive zunanjih polj na direktorsko polje nematskega tekočega kristala v različnih tokovnih režimih znotraj mikrofluidičnih kanalčkov z močnim homeotropnim sidranjem. Uporabljal sem polarizacijski optični mikroskop, opremljen z lasersko pinceto, ki pri večjih močeh laserske svetlobe zaradi absorpcije v prevodnem substratu mikrokanalčka povzroči lokalno segrevanje nematika v izotropno fazo in ob hipnem ugašanju posledično sproži hiter fazni prehod v nematsko fazo. Na ta način sem pokazal, da je z laserskim snopom optične pincete v toku nematika mogoče nukleirati in stabilizirati topološko ograjene, orientacijske domenske strukture. Raziskal sem dinamiko teh struktur pri različnih hitrostih toka in skonstruiral fazni diagram prehodov med podkritičnim in nadkritičnim območjem parametrov, ki kvantitativno ločijo krčenje in širjenje domen v dani geometriji. Osredotočil sem se na frekvenčne modulacije tokovnih režimov in relaksacijske procese ob zaustavitvi tokov, ki povzročijo reorientacijo v domeno ujetega direktorskega polja in nastanek točkastih defektov s solitoni. Pokazal sem, da je orientacijske domenske strukture, razen v nematiku 5CB, mogoče tvoriti in stabilizirati tudi v tekočem kristalu CCN z negativno dielektrično anizotropijo in majhno optično dvolomnostjo. Izkazalo se je, da temperaturne spremembe v mikrofluidičnem kanalčku znatno vplivajo na stabilnost z laserjem segretih nematskih plasti, tvorjenje domenskih struktur in na tokovne režime, zato sem te pojave podrobneje raziskal pri višji temperaturi. Pri faznem prehodu toka tekočega kristala iz izotropne v nematsko fazo sem zasledil soobstoj nematskih in izotropnih domen. Nato sem z različnimi geometrijami mikrokanalčkov kontrolirano vplival na obliko, velikost in življenjski čas domen, saj ima takšna manipulacija anizotropne tekočine potencial za uporabo v kompleksnejših mikrofluidičnih vezjih, senzorjih tlaka in nastavljivih optičnih filtrih. S tokom potujoče domene lahko tudi razcepimo, združujemo in sortiramo. V sodelovanju s teoretičnimi fiziki sem kot prvi pokazal obstoj novega kiralnega stanja v toku homeotropnega nematika, ki je doslej, zaradi premalo natančne regulacije tokov, ostalo neopaženo. Nazadnje sem preučil vpliv električnega polja na tokovne režime in domenske strukture. Zaradi dielektrične anizotropije in polarizabilnosti tekočekristalnih molekul lahko z električnim poljem spreminjamo obliko domenskih struktur, jih pri tem razpolavljamo, usmerjamo ali pa jih z močnejšim preklapljanjem električnega polja celo tvorimo. Precizna frekvenčna modulacija električnega polja je nenazadnje uporabna za tvorbo kiralnih domenskih stanj brez uporabe laserske pincete. In the thesis I examine optical and thermal effects on the nematic director field configurations in various flow regimes confined to microfluidic channels with homeotropic surface alignment. Polarizing optical microscopy in combination with laser tweezers is applied to locally heat the nematic flow into the isotropic phase and quench it back to the nematic phase. Thereby, realigned phase domains with encircled defect loops are nucleated, stabilized and transported in a flowing nematic phase. I study the dynamic evolution of orientational phase domains in stationary nematic microflows to construct a phase diagram of shrinking and growing loops for a wide range of flow velocities. Further, I focus on careful tuning and active control of the flow to reveal reorientational dynamics of the flow-aligned director field in oscillatory flows, followed by a nucleation of solitons and point defects as it seeks relaxation to equilibrium. I demonstrate the phenomena in single component liquid crystal 5CB, as well as in a mixture of two CCN liquid crystals with negative dielectric anisotropy and very low birefringence. The laser light interaction with the confined nematic flow is further explored at higher temperatures that approach the nematic to the isotropic phase transition. The study shows impacts of heating on the stability of applied optical traps, nucleation and coexistence of oriented nematic and isotropic domains, and evolution of flow regimes after cooling back to the nematic phase. Next, I demonstrate the dynamic control over the growth and shape of nematic domains by varying only the shape of the channels. This way, splitting and coalescence of the domains can be achieved without use of the laser tweezers. The complete control over domain size manipulation and their birefringent colors may find applications in highly sensitive microfluidic pressure sensors or tunable optofluidic filters. In collaboration with theoretical physicists, I present a hidden pre-transitional state with broken chiral symmetry which can occur before the homeotropic to flow-aligned transition, and characterize the underlying mechanisms of its formation. Lastly, I study effect of external electric field on different flow regimes and domain structure formation. Due to the dielectric anisotropy and the polarizability of liquid-crystalline molecules, applied electric field can reorient, split or nucleate the before-studied flow-aligned domains. Finally, precise frequency modulation of an alternating electric field can produce a sequence of chiral domains in a steady nematic flow.

Liotropni tekoči kristali z lamelarno strukturo so zaradi svoje termodinamske stabilnosti, enostavne izdelave, velike solubilizacijske kapacitete in hkrati strukturne podobnosti z roženo plastjo kože ter ugodnih učinkov na njeno hidratacijo vedno bolj proučevani kot dermalni nosilni sistemi ter zagotovo premalo zastopani na trgu, kjer prevladujejo klasične emulzije, geli itd.. Da lahko v polni meri izkoristimo učinke kozmetično aktivnih sestavin, jih moramo namreč vgraditi v ustrezno podlago, da zagotovimo optimalno stabilnost in dermalno absorpcijo ter tako dosežemo željen učinek. Pri načrtovanju nosilnega sistema na osnovi tekočih kristalov moramo zagotoviti, da vgrajene kozmetično aktivne sestavine ne spremenijo ali podrejo mikrostrukture, slednja je namreč ključna za njihove prednosti pri nanosu na kožo. Na podlagi tega nas je v okviru diplomske naloge zanimalo, kako vgradnja izbranih kozmetično aktivnih sestavin vpliva na mikrostrukturo tekočih kristalov. Slednjo smo ovrednotili z metodo elektronske paramagnetne resonance. V izbran sistem tekočih kristalov z lamelarno strukturo smo želeli vgraditi tri različne kozmetično aktivne sestavine, ki se med seboj razlikujejo v topnosti, ter v različnih deležih (m/m %). V sistem smo uspeli vgraditi dekspantenol, ki je analog pantotenske kisline (vitamina B5) ter tokoferil acetat, ki deluje kot antioksidant. Dekspantenol smo vgradili v različnih deležih, in sicer 0%, 1%, 2%, 5%, 7,5%, 10%, 15% ali 30%, tokoferil acetat pa v 5% deležu. Alantoina pa nismo uspeli vgraditi, ker se ni raztapljal v izbranem sistemu. Nadalje smo jih označili z izbranimi spinskimi označevalci, kar je ključen korak pri meritvah z elektronsko paramagnetno resonanco, saj preko spinskih označevalcev dobimo informacije o mikrostrukturi tekočih kristalov. Ugotovili smo, da različni deleži dekspantenola ne spremenijo značilno mikrostrukture tekočih kristalov. Razlika je bila očitna le pri višjih koncentracijah, saj je imel maksimalni hiperfini razcep večjo vrednost, kar nakazuje na bolj urejeno strukturo. Čeprav bi bilo optimalno vgraditi različne deleže tokoferil acetata v tekoče kristale, so rezultati pri 5% deležu spodbudni, saj večjega odstopanja v primerjavi s kontrolnim vzorcem nismo zaznali. Dekspantenol in tokoferil acetat torej na strukturo tekočih kristalov ne delujeta destruktivno, prav tako pa ne izzoveta faznih prehodov pri spremembi temperature, kar je za razvoj kozmetičnega izdelka ugodno. Liotropic liquid crystals with lamellar structure have been, due to their thermodynamic stability, ease of manufacture, high solubilization capacity as well as structural similarity to the corneal skin layer and their beneficial effects on hydration, increasingly studied as dermal carrier systems and certainly underrepresented in the market, dominated by classic emulsions, gels, etc. In order to take full advantage of the effects of cosmetically active ingredients, they must be incorporated into a suitable vehicle to ensure optimal stability and dermal absorption, and thus achieve the desired effect. When designing a carrier system based on liquid crystals, we have to ensure that the incorporated cosmetically active ingredient(s) do not alter or disrupt their microstructure, the latter being crucial for their advantages in applying it to the skin. On this basis within this diploma thesis, we were interested in how the incorporation of the selected cosmetically active ingredients affects the microstructure of liquid crystals. The latter was evaluated by the electron paramagnetic resonance method. Three different cosmetically active ingredients with different solubility and in different ratios (w/w %) were incorporated into the selected system of liquid crystals with lamellar structure. Into the system, we also managed to incorporate dexpanthenol, which is an analogue of pantothenic acid (vitamin B5) and tocopherol acetate, which acts as an antioxidant. The dexpanthenol was then incorporated in shares of 0 %, 1 %, 2 %, 5 %, 7.5 %, 10 %, 15 % or 30 %, and tocopherol in share of 5 %. However, we could not incorporate allantoin because it did not dissolve in the selected system. We further labelled them with selected spin labels, which is a key step in electron paramagnetic resonance measurements, as the information on the microstructure of liquid crystals is obtained through spin labels. Different ratios of dexpanthenol did not significantly alter the microstructure of the liquid crystals. The structural differences were only observed at higher ratios due to the observed higher value of maximum hyperfine splitting, suggesting a more orderly structure. Although it would be optimal to incorporate different proportions of tocopherol acetate in liquid crystals, the results are encouraging, at 5 %, since no significant deviation from the sample without cosmetically active ingredient was detected. Dexpanthenol and tocopherol acetate, therefore, do not have a destructive effect on the liquid crystal structure nor do they cause phase transitions, which is advantageous for the development of cosmetic products.

Tekoči kristali so snovi, ki imajo tudi anizotropno tekočinsko fazo. Zgrajeni so iz velikih organskih molekul anizotropnih oblik. V magistrskem delu obravnavamo tekoče kristale iz molekul z ukrivljeno sredico. Zaradi svoje oblike imajo takšne molekule permanentni električni dipol, kadar pa se zlagajo v plasti, so plasti praviloma polarizirane. Molekule z ukrivljeno sredico se učinkovito zlagajo tudi v stolpiče, ki jih tvorijo fragmenti smektičnih plasti. Med stolpičaste tekočekristalne faze iz molekul z ukrivljeno sredico uvrščamo faze B_1, nagnjeno B_1, B_1rev in nagnjeno B_1rev. Razlikujejo se po različni povprečni smeri dolgih in kratkih osi molekul. Za ločevanje med strukturami se uporablja več optičnih, električnih, termičnih in drugih metod, mi pa se omejimo na klasično in resonančno elastično rentgensko spektroskopijo. S klasično rentgensko spektroskopijo merimo razlike v porazdelitvi elektronske gostote, kar nam da sliko prostorske ureditve molekul. Klasično dopolnjuje resonančna rentgenska spektroskopija, ki je občutljiva tudi na orientiranost dolgih in kratkih osi molekul. Oblikovni faktor molekule z ukrivljeno sredico je anizotropna količina, zato ga opišemo s tenzorjem, ki je premo sorazmeren z anizotropnim delom tenzorja dielektričnosti. Izračunamo tenzorske oblikovne faktorje za pet možnih ureditev ukrivljenih molekul v nagnjeni B_1rev fazi. Iz tenzorskega oblikovnega faktorja napovemo intenziteto in polarizacijo interferenčnih vrhov v odvisnosti od polarizacije vpadnega valovanja. S primerjavo lege vrhov, ki so dovoljeni pri klasični rentgenski spektroskopiji, in lege interferenčnih vrhov pri resonančni rentgenski spektroskopiji napovemo, kateri vrhi so čisto resonančni, torej klasično prepovedani. Vrhi, ki jih napovemo pri klasični in resonančni rentgenski spektroskopiji, so lahko resonančno ojačani. S teoretičnim modelom napovemo, da je smer polarizacije linearno polariziranega valovanja, ki se resonančno sipa na vzorcu tekočega kristala iz molekul z ukrivljeno sredico, zmeraj pravokotna na smer polarizacije vpadnega valovanja. Ugotovimo, da lahko med strukturami z različnimi orientacijami molekul najdemo razlike v interferenčnih spektrih pri resonančni rentgenski spektroskopiji, zato je ta metoda ustrezna za razlikovanje med strukturami. Liquid crystals are materials that possess at least one anisotropic liquid phase. Their building blocks are long organic molecules of anisotropic shapes. In the master thesis, we focus on liquid crystals consisting of bent-core molecules. Because of their bent shape, such molecules have a permanent electric dipole, so layered structures are usually polarized. Bent-core molecules are also effectively distributed into columns, which are made up of smectic layer fragments. B_1, tilted B_1, B_1rev and tilted B_1rev are examples of the columnar liquid crystal phases made of bent-core molecules. These phases differ in the average direction of the long and short molecular axes in smectic layer fragments. To differentiate between the phases, several optic, electric, thermic and other methods can be employed. In this work, we limit ourselves to the hard and soft resonant elastic x-ray spectroscopy. With the hard x-ray spectroscopy, we measure the differences in the distribution of the electron density, which in turn gives us information on the spatial distribution of molecules. The hard x-ray spectroscopy is complimented by the soft resonant x-ray spectroscopy, which is sensitive to the orientation of the long and short molecular axes. The form factor of a bent-core molecule is an anisotropic quantity that is described by a tensor, which is proportional to the anisotropic part of the dielectric tensor. We calculate tensorial form factors for five possible packings of bent-core molecules in the tilted B_1rev phase. Then we use the tensorial form factor to predict the intensity and polarization of the interference peaks as a function of the polarization of the incident wave. By comparing the position of the peaks allowed in the hard x-ray spectroscopy with the position of peaks found with the soft resonant x-ray spectroscopy, we predict, which peaks are purely resonant, therefore forbidden in the hard x-ray spectroscopy. Peaks, which are predicted by both the hard and soft resonant x-ray scattering, can be resonantly enhanced. The theoretical model predicts that the direction of the polarization of the scattered wave is perpendicular to the direction of the polarization of the incident wave for all the studied structures of the tilted B_1rev phase. The soft resonant x-ray scattering pattern differs significantly for the studied structures, so we conclude that the method can be used to determine the structure of the tilted B_1rev phase.

Nanodelci dispergirani v nematičnih tekočih kristalih v splošnem deformirajo nematično strukturo. V številnih primerih dispergirani nanodelci vplivajo na tekočekristalno ureditev podobno kot naključno polje. Slednje vsiljuje molekulam tekočih kristalov relativno naključno orientacijsko urejenost, katere verjetnostna porazdelitev je odvisna predvsem od geometrije nanodelcev in jakosti ter vrste sklopitve med nanodelci in obdajajočo tekoče kristalno matriko. Nedavne eksperimentalne meritve nakazujejo, da pri povečevanju koncentracije nanodelcev preide klasična nematična ureditev v fazo, ki spominja na paranematično ureditev. Prehod je postopen in se izvede v relativno ozkem oknu koncentracij nanodelcev pri relativno nizki koncentraciji (okoli 0,1%). Pri nadaljnjem povečevanju se stopnja nematične urejenosti relativno malo spreminja do koncentracij 1%. Slednje obnašanje še ni bilo teoretično obravnavano. V magistrskem delu izdelamo minimalni matematični model, ki kvantitativno in kvalitativno opiše spremembo orientacijskega ureditvenega parametra v prisotnosti nanodelcev, ki vsiljujejo naključno urejenost. Izpeljemo dvodimenzionalni mrežni model v odvisnosti od ureditvenega parametra pri temperaturi absolutne ničle. V približku povprečnega polja numerično rešimo izpeljane enačbe. Rezultati simulacij v dobrem približku reproducirajo modelirane eksperimentalne meritve. Nanoparticles dispersed in nematic liquid crystals generally deform the nematic structure. In numerous examples dispersed nanoparticles affect liquid crystal ordering in a similar way as a random field. The latter enforces a random orientational order on the liquid crystal molecules, whose probability distribution depends mainly on the geometry of the nanoparticles and on the strength and type of coupling between the nanoparticles and the surrounding liquid crystal matrix. Recent experimental measurements indicate, that upon increasing the concentration of nanoparticles, the classical nematic order transitions into a paranematic order like phase. The transition is gradual and appears at a relatively low concetration (around 0,1%) within a relatively narrow range of nanoparticle concentration. Further increasing the concentration of nanoparticles up to 1% has relatively little effect on the degree of nematic ordering. This behaviour has yet to be theoretically studied. In this master thesis we construct a minimal mathematical model, which qualitatively and quantitatively descibes the change of the orientational order parameter due to the presence of nanoparticles, which enforce a random order. We derive a two-dimensional lattice model in terms of the order parameter at absolute zero kelvin. In the mean field approximation we numerically solve the equations of the derived model. The simulation results in a good approximation reproduce the modeled experimantal results.

V delu obravnavamo fizikalne lastnosti holesteričnih tekočih kristalov in njihovo uporabo v kapljični geometriji za realizacijo 3D mikrolaserjev. Holesterični tekoči kristali so fotonski material, v katerih obstaja prepovedan pas fotonov v disperzijski enačbi. Tako je za določene valovne dolžine propagacija prepovedana hkrati pa se na robovih prepovedanega fotonskega pasu poveča fotonska gostota stanj, zaradi česar je v takih resonatorjih možno lasersko delovanje pri nizkih pragih. Pri črpanju z ekscitacijskim pulznim laserjem povzročimo obrnjeno zasedenost aktivnega medija, emisija katerega se optično ojača zaradi optičnih lastnosti holesteričnega tekočega kristala. Resonatorji holesteričnih tekočih kristalov so občutljivi na zunanje motnje zaradi katerih se valovna dolžina laserske črte spremeni. Valovna dolžina laserske emisije se spremeni zvezno v območju fluorescence aktivnega medija kot odziv na spreminjanje strukture resonatorja. To omogoča njihovo uporabo za zaznavanje fizikalnih in kemijskih količin v opazovanem sistemu. Z eksperimentom smo realizirali merjenje temperature z opazovanjem premika laserske črte, pri čemer smo mikrolaserje vzbujali in merili odziv na daljavo. Ta metoda omogoča merjenje temperature v majhnem volumnu, ki ni vezan le na površino opazovanega sistema, na razdaljah več deset metrov, v realnem času in z natančnostjo pod stopinjo celzija v nekaj sekundah. V prvem delu predstavimo osnovne pojme in enačbe s področja fizike laserjev in fizike tekočih kristalov. Pri obravnavanju svetlobnih interakcij s tekočimi kristali se poglobimo v mehanizem ojačanja svetlobe v holesteričnih tekočih kristalih ter zajemanje svetlobnega signala z eksperimentalno napravo. Zaradi geometrije kapljic opazimo več načinov laserskega delovanja. Te načine opišem in analiziram njihove spektre, ter proučim kako jih lahko izkoristimo v različnih sistemih. V osrednjem delu opišem optične sisteme, ki sem jih uporabil pri eksperimentalnih meritvah in izdelavo holesteričnih tekoče-kristalnih kapljic. Pokažem rezultate in analiziram eksperimentalne meritve ter ovrednotim možnost uporabe izdelanega optičnega sistema v kombinaciji s 3D mikrolaserskimi senzorji v industriji, medicini in raziskovanju. In this thesis we present physical properties of cholesteric liquid crystals and their usability in spherical geometry as 3D microlasers. Cholesteric liquid crystals are photonic materials in which a band gap in dispersion relation of propagating wave exist. Therefore the propagation for specific wavelengths of light are forbidden inside the structure at the same time as a result of the bandgap, there is an increase of density of states at the edges of the forbbiden band, making low-threshold lasing possible at the edges of the bandgap. The excitation of dye molecules by an external pump laser source creates population inversion in these systems, which results in stimulated laser emission. Since the cholesteric liquid crystal structure acts as a resonator cavity and is sensitive to external stimuli, the lasing wavelength changes in response. Lasing wavelength changes continuously in the region of fluorescent emission of the gain medium for sustained/ever-present stimuli. This enables their use as sensors for measuring physical and chemical properties of the observed system. We demonstrate their sensisivity and usability for remote temperature measurements. This method enables temperature measurements in a very small volume, which is not constrained to the surface of the measured system, at distances up to tens of meters, in real time and with the accuracy below a one degree Celsius in less than a secound. In the first part we present basic concepts and equations from the area of laser physics and physics of liquid crystals. We discuss in depth the interaction of light with cholesteric liquid crystals, which enables laser operation in these stuctures. We also discuss the collection of light with the constructed optics system. The spherical geometry of the cholesteric liquid crystal droplets enables multiple modes of lasing. We describe these modes and analyze their spectra in the experiment. In the main part we describe the optical systems, that were used during the experimentation, the preparation of the samples and show the experimental results. We also discuss the possibility of impoving the optical system as well as the sensors and mention why that could be used in industry, medicine or research.

V nalogi preučujemo sklopitev med nanodelci in termotropnimi nematičnimi tekočimi kristali (NTK). Slednje obravnavamo kot cilindrično simetrične objekte, ki jih v literaturi pogosto imenujejo kot rotorji. V prvem delu naloge preučujemo vpliv NTK na urejanje dispergiranih ogljikovih nanocevk (ON). Uporabili smo mezoskopski model, v katerem smo NTK opisali z Landau-de Gennesovo teorijo z enoosnim ureditvenim parametrom. Prisotnost ON smo upošteval z Doi-ovo prosto energiji, s katero smo modelirali liotropni značaj ON. Slednja interakcija upošteva t. i. sklopitev izključitvenega volumna. Obravnavali smo primer bi-disperzne porazdelitve ON v limiti šibke sklopitve NTK-ON. V tej limiti na sklopitev dominantno vpliva anizotropija površinske napetosti, medtem ko je interakcija z nematično orientacijsko urejenostjo relativno zanemarljiva. Glede na jakost ON-NTK interakcije smo zasledil dva kvalitativno različna režima obnašanja. V prvem režimu dispergirane ON posedujejo nezvezni prehod iz izotropne v orientacijsko urejeno fazo. V drugem nadkritičnem režimu pa je prehod med fazama postopen. NTK močno vsiljujejo ON stopnjo urejenosti, medtem ko je povratni urejevalni vpliv zanemarljiv. Tako je nematični ureditveni parameter NTK odvisen predvsem od temperature in le šibko od koncentracije ON. V nematični fazi urejenosti daljše ON izkazujejo močnejšo orientacijsko urejenost. V drugem delu naloge smo preučeval histerezno obnašanje NTK pri cikličnem spreminjanju zunanjega urejevalnega polja. Pri tem smo predpostavili, da relativno homogeno dispergirani nanodelci v NTK delujejo kot orientacijsko naključno polje. Takšne primere npr. zasledimo v mešanicah NTK in aerosilnih nanodelcev. Osredotočili smo se na določitev režimov s kvalitativno različnim histereznim odzivom. Pri tem smo spreminjali jakost nematične sklopitve in jakost naključnega polja. Večino raziskav smo izvedli v dveh prostorskih dimenzijah. V teoretični analizi smo uporabili dva različna pristopa. Sistem smo najprej analizirali v približku povprečnega molekularnega polja. V prvem koraku smo analogno s klasično izpeljavo v magnetizmu vpeljali efektivno polje, ki deluje na lokalno nematično urejenost. Slednjo smo opisali s tenzorskim ureditvenim parametrom. V efektivnem polju smo upoštevali prisotnost »povprečnih« sosedov. Predpostavili smo, da sta lastna okvirja tenzorskega efektivnega polja in nematične urejenosti vzporedna in na ta način dobili samo-usklajevalno enačbo. V slednji smo vpeljali povprečenje po orientacijski neurejenosti nanodelcev. V drugem pristopu smo numerično preučevali nematično urejenost za dane vrednosti interakcij v sistemu in nato iz dobljene konfiguracije izračunali povprečni globalni nematični ureditveni parameter. V obeh pristopih smo enačbe reševali numerično pri temperaturi nič. Pri spreminjanju jakosti značilnih interakcij sistema smo dobili kvalitativno različne histerezne zanke in določili področja stabilnosti kvalitativno različnih zank. V obeh pristopih smo dobili kvalitativno podobno obnašanje in pojavile so se samo razlike v kvantitativnem obnašanju. Torej približek molekularnega polja predstavlja v tem primeru relativno zanesljivo in preprosto orodje. Rezultati naloge so potencialno zanimivi za številne aplikacije v nanotehnologiji, ki so osnovane na interakcijah med nematičnimi tekočimi kristali in različnimi nanodelci. V primeru ON bi NTK komponento lahko izkoristili za kontrolirano orientacijsko manipulacijo dispergiranih ON. Tako bi lahko npr. kreirali različne prilagodljive in odzivne vzorce ON s specifičnim makroskopskim obnašanjem. Pri tem bi izkoriščali »mehkobo« NTK komponente in njeno odzivnost na zunanja urejevalna polja in na ograjevalno geometrijo. Po drugi strani bi lahko specifično histerezno obnašanje NTK v cikličnih urejevalnih poljih v prisotnosti nanodelčno generiranega nereda uporabili za različne »mehke« spominske elemente. In the thesis we have examined the coupling of nanoparticles and thermotropic nematic liquid crystals (NLC). The latter are regarded as cylindrically symmetrical objects, often referred to in scientific literature as rotors. In the first part of the thesis we examined the effect of NLC on the ordering of dispersed carbon nanotubes (CN). A mesoscopic model was used, in which NLC were described with the Landau-de Gennes theory with a uniaxial order parameter. Presence of CN was considered with Dois free energy, with which the lyotropic character of CN was modelled. The latter interaction considers the so-called coupling of excluded volume. A case of bi-dispersed distribution of CN was addressed in the weak anchoring limit of NLC-CN. In this limit the anisotropy of surface tension has a dominant effect on the coupling, whereas the interaction with nematic orientation ordering is relatively negligible. Depending on the strength of the NCL-CN interaction two qualitatively different behavioural regimes were detected. In the first regime, the dispersed CN have a discontinuous transition from isotropic to the orientationally ordered phase. In the second supercritical regime, the transition from one phase to the other is gradual. NCL strongly force the degree of ordering to CN, whereas the reverse ordering effect is negligible. It follows that the nematic order parameter of NCL is mostly dependant on temperature and only slightly on the concentration of CN. In the nematic ordering phase the longer CN exhibit a stronger orientation ordering. In the second part of the thesis we examined the hysteretic behaviour of NCL when cyclically changing the external ordering field. We assumed that the relatively homogeneously dispersed nanoparticles in NCL work as an orientationally random field. Such cases can be found for instance in the mixtures of NCL and aerosil nanoparticles. We focused on the determination of regimes with the qualitatively different hysteretic response. This was achieved with the changing of the strength of the nematic coupling and the strength of the random field. Most of the research was conducted in two spatial dimensions. In the theoretic analysis two different approaches were used. In the beginning the system was analysed in the mean field approximation. In the first step, we analogically introduced with a classical derivation in magnetism an effective field, which affects the local nematic ordering. We described the latter with a tension order parameter. In the effective field the "mean" neighbour presence was considered. We assumed that the inherent frames of the tension effective field and nematic ordering are parallel, which produced a self-adapting equation. In the latter, the averaging was introduced on the orientational disorder of nanoparticles. In the second approach, we numerically researched the nematic ordering from the given value of interactions in the system and then calculated the mean global nematic order parameter from the obtained configuration. In both approaches the equations were numerically solved at zero temperature. With the changing of the strength of characteristic interactions of the system we obtained qualitatively different hysteresis loops and determined the areas of stability of qualitatively different loops. In both approaches we obtained qualitatively similar behaviour, differences were evident only in the quantitative behaviour. Thus, the mean field approximation represents, in this case, a relatively reliable and simple tool. Results of the thesis are potentially interesting for numerous applications in nanotechnology, which are based on interactions between nematic liquid crystals and various nanoparticles. In the case of CN, the NCL component could be used for a controlled orientational manipulation of dispersed CN. Thusly different adaptable and responsive patterns of CN could be created with specific macroscopic behaviour.

V magistrskem delu so predstavljene meritve močenja in kapilarnega dviga vode, glicerola, silikonskega olja in tekočega kristala na obdelanih steklenih površinah z namenom določitve površinske napetosti. Delo je sestavljeno iz teoretičnega opisa kapilarnih pojavov s poudarkom na računanju oblike meniskusa in višine kapilarnega dviga, predstavitve fizikalnih lastnosti uporabljenih materialov in eksperimentalnih metod ter rezultatov. Razvil sem postopek merjenja kontaktnih kotov kapljevin na ravnih podlagah s prilagojenim optičnim mikroskopom s horizontalno postavitvijo objektivov, ki je bil uporaben tudi za določanje oblike meniskusov in meritve višin kapilarnih dvigov v cilindričnih kapilarah. Ugotovil sem, da ima obdelava steklenih površin s silanom različen vpliv na močenje polarnih in nepolarnih kapljevin, kar se pozna tudi pri spreminjanju višine kapilarnih dvigov. Pokazal sem tudi, da se anizotropne lastnosti nematskega tekočega kristala izrazijo v anizotropiji površinske napetosti, ki je odvisna od robnih pogojev na površini stekla. Metoda kapilarnega dviga v ozkih cilindričnih kapilarah se je izkazala kot enostaven, učinkovit, ponovljiv in dovolj natančen način določanja površinske napetosti različnih vrst kapljevin, ki je uporabna tudi za raziskovanje vpliva kemijske funkcionalizacije površin na lastnosti močenja. The master’s thesis presents measurements of wetting and capillary rise of water, glycerol, silicone oil and nematic liquid crystal on chemically treated glass surfaces with intention of determining the surface tension. The work consists of a theoretical description of the capillary phenomena, presentation of the physical properties of the materials, applied experimental methods and final results. I demonstrated the technique of measuring the contact angles of liquids on flat surfaces with an adjusted optical microscope which was also applied to measure the shape of liquid meniscus and the height of capillary rise in cylindrical capillaries. I have shown that the functionalization of glass surfaces with a silane strongly influences wetting of polar and non-polar liquids, which is also reflected in changing the height of the capillary rise. Further, I demonstrated that the anisotropic properties of a nematic liquid crystal are reflected in anisotropy of the surface tension since it strongly depends on the glass surface boundary conditions. I found that the method of capillary rise provides simple, accurate, comparable and reproducible way of determining the surface tension of various types of liquids. Lastly, it can be also used to investigate wetting properties on chemically functionalized surfaces.

V magistrskem delu je predstavljen razvoj novega koncepta delovanja aktivnega tekočekristalnega optičnega filtra oz. »aktivni LCD-filter« za zaščito oči pred močnimi svetlobnimi bliski, kot nastajajo med elektroobločnim varjenjem. Tehnološke rešitve, ki se uporabljajo za prikaz velikega števila informacij v ploščatih prikazovalnikih z veliko gostoto slikovnih elementov (TV-zasloni, računalniški zasloni,…), ne predstavljajo najugodnejših rešitev za področja, ki so osnovana na uporabi tekočekristalnih optičnih preklopnikov z zelo specifičnimi lastnostmi. Za lažje razumevanje delovanja in predstavitev aktivne tekočekristalne optične celice smo razvili preprosto modelsko nazornejšo celico, ki pojasni različna optična stanja v celici. Zaščitni aktivni LCD-optični filter za svoje delovanje izkorišča anizotropne optične lastnosti tekočih kristalov. Povečanje intenzitete svetlobnega toka (npr. pri varjenju) povzroči spremembo napetosti na optičnem preklopniku, kar privede do spremembe strukture tekočega kristala v celici in sicer iz superzasukane v homeotropno urejeno strukturo. V procesu optimizacije strukture aktivnega LCD filtra je bil razvit superzasukani tekočekristalni optični preklopnik (STN LCD). Dva takšna preklopnika, postavljena v »tandem«, z najugodnejšo postavitvijo medsebojno pravokotno orientiranih polarizatorjev in polimernih optično negativno dvolomnih filmov (retarderjev), aktivno vplivata na optično prepustnost celotnega sendviča plasti in omogočata visoko absorpcijo prepuščene svetlobe oz. zatemnitev zaščitnega optičnega filtra. Sestavljeni aktivni LCD-filtri povsem ustrezajo najvišjim zahtevam za optično kvaliteto po mednarodno priznanih standardih DIN Plus in EN 379. Navedene raziskave so omogočile vpeljavo znanja o delovanju super zasukane tekočekristalne celice v poučevanje. Razvit je bil model celice, ki je sestavljen iz devetih plasti cvetličarske folije in dveh plošč polarizatorja. Z različnimi postavitvami modela celice nazorno demonstriramo delovanje aktivne tekočekristalne celice, optično odprto in optično zaprto stanje celice v varilskih očalih oz. tudi drugih optičnih prikazovalnikih z veliko gostoto slikovnih elementov. UDK: 532.783:535-84(043.2), 37.091.3:53(043.2) Gesla: tekoči kristali, super zasukana struktura tekočega kristala STN LCD, dvolomnost, zatemnitev, model celice, poučevanje In this Master thesis we present our invention of a new concept of an active liquid-crystal optic filter, “an active LCD filter”, used for the eye protection from the strong light flashes during the electroslag welding process. Technological solutions, used to present a large quantity of information’s on the flat screens with high density of visual elements (TV, screens, computer monitors,…) are not suitable solutions for optical filters, where very specific properties are required. For an easier understanding and explicit presentation of the active liquid-crystalline cell, a simple cell model was developed, which is used to explain various optical mechanisms inside the cell. Protective active LCD optic filters are based on the anisotropic optical properties of liquid crystals. An increase in the light intensity (for example at welding) causes a change in the electric voltage in the optical switcher, which leads to a modification of the structure of liquid crystals from the super-twisted nematic to the homeotropic structure. During the active LCD filter optimisation process a super twisted liquid crystal optical switcher (STN LCD) was developed. Two of the STN LCD switchers, placed in a tandem, with the most effective position of perpendicularly oriented polarizers and optically negative polymer birefringent films (retarders), actively effect the optical transmission of a sandwich of layers, which enables a high absorption of transmitted light or attenuation of the protective filter. The compound active LCD filters comply the highest optical quality demands according to the valid International standards (DIN Plus and EN 379). Results of the research can be implemented into the teaching process. A cell model, made of nine layers of a florist foil and two layers of polarizers was developed. With various compositions of the cell model we can demonstrate how the active liquid-crystal cell works. We can demonstrate the optically open and optically closed state of the cell in the welding protective filters as well as in other optical screens with a high density of pixels. UDK: 532.783:535-84(043.2), 37.091.3:53(043.2) Key words: liquid crystals, birefringence, liquid-crystal super twisted structure STN-LCD, attenuation, cell model, education

Superprevodne kovine lahko delimo na dva tipa, ki jih karakteriziramo s tipičnimi razdaljami sistema. V analogiji lahko tudi za smektične tekoče kristale uvedemo podobno delitev. Smektike tipa I in tipa II ločimo s t. i. Ginzburgovim parametrom. V magistrski nalogi bomo preučevali odziv obeh tipov smektikov na vsiljeno upogibno deformacijo. Ta je v sistemu povzročena s t. i. strukturo ribje kosti na površini. Z naklonom brazd strukture vsiljujemo lokalne napetosti v sistemu, kar posledično vpliva na urejanje molekul tekočega kristala znotraj posamezne smektične plasti. V teoretični obravnavi problema zapišemo prosto energijo sistema s pomočjo Landau – de Gennesovega fenomenološkega pristopa. Prosto energijo bomo enodimenzionalno parametrizirali za primer strukture ribje kosti in zapisali Euler – Lagrangeovi enačbi, ki ju rešujemo numerično. Raziskali bomo odziv smektikov tipa I in tipa II na vsiljeno upogibno deformacijo znotraj strukture ribje kosti. Superconducting metals can be divided into two types which are characterized by typical distances of the system. In analogy one can also introduce similar division in smectic liquid crystals. The division of smectics type I and type II is characterized by the Ginzburg smectic parameter. In this master thesis we will examine the response of both types of smectics on a forced bend deformation which will be applied to the system with a so – called herringbone structure. The slope of the latter structure imposes local stresses in the system which consequently affects the ordering of liquid crystal molecules within an individual smectic layer. In this theoretical research of the problem the free energy of the system is written according to the Landau – de Gennes phenomenological approach. We parametrize the free energy in one dimension for the herringbone structure and derive Euler – Lagrange equations which we solve numerically. We will investigate the response of the type I and type II smectics on forced bend deformation in the herringbone structure.

Tekoči kristali omogočajo številne vizualizacije geometrijskih zakonitosti. V magistrski nalogi bomo s pomočjo dvodimenzionalnega Landau-de Gennes tenzorskega formalizma proučevali topološke defekte v nematičnih lupinah. Slednje predstavljajo tanko plast nematičnih tekočih kristalov, nanesenih na površino koloidnih delcev. Zapisali bomo funkcional proste energije in za poseben primer osno-simetričnih lupin izpeljali Euler-Lagrangeovi enačbi, ki jih bomo reševali numerično. Raziskali bomo, kako različni seti elastičnih konstant vplivajo na konfiguracije topoloških defektov pri različnih elipsoidih. Poudarek bo na vplivu tako imenovanega Napolijevega polja. Liquid crystals offer several visual representations of the underlining geometric rules. In thesis, we study topological defects in nematic shells, within a two-dimensional Landau-de Gennes tensorial formalism. Nematic shells are colloidal particles, coated with a thin sheet of nematic liquid crystal. For a special case of axis-symmetric shells, we derive the Euler-Lagrange equations for the free-energy functional. We solve Euler-Lagrange equation numerically. We present, how different combinations of elastic constants, influences on topological defect configurations for different ellipsoids. Our main focus is the influence of the term proposed by Napoli.

V doktorski disertaciji smo preučevali vpliv naključnega nereda na strukturne lastnosti nematskih tekočih kristalov (NTK). Slednje na semi-mikroskopski skali predstavljamo kot delce anizotropnih oblik cilindrične simetrije. Takšen sistem je primeren za preučevanje temeljnih lastnosti vpliva nereda, doseženega z zlomom zvezne simetrije. Sorodne primere predstavljajo naključni magneti, nečisti superprevodniki oz. superfluidi, mešanice različnih ogljikovih nano-cevk ter številni drugi sistemi kondenzirane materije. Sistemi, ki jih direktno obravnavamo, so najbližji naključno motenim magnetnim spinom. V slednji primerjavi je na semi-mikroskopski skali ena bistvena razlika. Za nematsko ureditveno polje je značilna t.i. »head-to-tail« invariance (neobčutljivost na 180° obrat). Nasprotno so magnetni sistemi občutljivi na spremembo predznaka magnetizacije. Omenjena razlika pomembno vpliva na možno strukturo topoloških defektov v strukturnem polju. Toda makroskopska domenska struktura, ki ji bomo posvetili največ pozornosti, je od tega le šibko odvisna. Omejili smo se na primere, v katerih so izviri naključnega polja »nečistoče« koncentracije ter so anizotropnih oblik. Pri preučevanju smo uporabili Lebwohl-Lasherjev mrežni model, v katerem je kubična mreža zapolnjena z NTK in »nečistočami«. Interakcije v modelu so kratkega dosega (čutijo jih le najbližji sosednji spini). Iskali smo mezoskopske statične rešitve sistema pri temperaturi nič, kar v realnosti pomeni sisteme globoko v nematski fazi. Vektorska polja, ki opisujejo orientacijsko porazdelitev NTK in »nečistoč«, so ponazorjeni s t.i. nematskimi spini oz. spini »nečistoč«. »Head-to-tail invariance« je upoštevana le pri nematskih spinih. Preučevali smo vrsto kvalitativno različnih modelov. Najprej smo preučili t.i. klasični RAF (random anisotropic field) model, v katerem so izviri naključnega polja »nečistoče«, kjer smo slednje delce poimenovali dis-orientacijski centri (DOC). V tem modelu je lahko posamezno mesto v mreži hkrati zasedeno tako z NTK kot DOC. V nadaljevanju smo preučili model, v katerem smo onemogočili hkratno zasedanje posameznega mesta v mreži s prej omenjenimi delci. Ta model smo poimenovali razširjeni RAF model. V obeh modelih so DOC orientacijsko »zamrznjeni« (statični), kjer je njihova orientacijska porazdelitev izotropna. V tretjem primeru smo preučevali model, v katerem obe vrsti spinov (nematski spini ter spini DOC) opišemo z variacijskimi polji. Poudarimo, da v slednjem modelu sistem ni frustriran na lokalnem ali globalnem nivoju. Pri tem smo vsiljevali medsebojno pravokotno postavitev NTK in DOC. V simulacijah smo izhajali iz homogene ali naključne začetne konfiguracije sistema, kar smo poimenovali zgodovina vzorca. Iz izračunane mezoskopsko-stacionarne konfiguracije sistema smo izračunali orientacijsko korelacijsko funkcijo nematskega spinskega polja. Iz korelacijske funkcije lahko sklepamo na vrsto ureditve sistema ter na različne druge makroskopske strukturne lastnosti posameznega sistema. Sistem lahko zavzame ureditev kratkega (SRO), kvazi red dolgega dosega (QLRO) ali red dolgega dosega (LRO). Za razlikovanje med slednjima dvema ureditvama je potrebna analiza končne velikosti. Iz poteka korelacijske funkcije lahko poleg dosega ureditve sistema razberemo še povprečno domensko dolžino, sistema ter razpršenost okrog njene vrednosti preko domenskega disperzijskega parametra. Ključni rezultati naloge so naslednji. Z uporabo klasičnega RAF modela smo pokazali, da je veljavnost Imry-Ma teorema, ki pomeni pomemben temelj statistične mehanike nereda, odvisna od zgodovine vzorca. Dobljeni rezultati namreč kažejo na to, da neskončno majhna naključna motnja uniči LRO in ga nadomesti s SRO le v sistemih z naključno začetno konfiguracijo. Za takšne sisteme smo dokazali, da ustrezajo skalni napovedi Imry-Ma teorema. V sistemih s homogeno začetno konfiguracijo omenjeni teorem ne velja. S temi rezultati lahko razložimo, zakaj različni eksperimenti na navidezno en We studied the impact of random field-type disorder on structural properties of nematic liquid crystals (LCs). The latter are on the semi-microscopic scale represented by rod-like objects exhibiting cylindrical symmetry. Such configurations are adequate for studying fundamental properties of influence of disorder on systems exhibiting continuous symmetry breaking. Examples of such systems are random magnets, impure superconductors or superfluids, mixtures of different carbon tubes and numerous other condensed matter materials. The closest condensed matter analogs to our study are randomly perturbed magnetic spins. However, on the semi-microscopic scale these configurations exhibit one crucial difference. Namely, nematic orientational field exhibits head-to-tail symmetry while magnetization can be described with an ordinary vector field. This detail strongly influences topological defect gauge field structure however macroscopic domain-type behavior is weakly affected. We focused on cases where random anisotropic field (RAF) perturbations were imposed by rod-like impurities of different concentration. We used Lebwohl-Lasher type lattice model where LC molecules and impurities occupied lattice cites of a cubic lattice. Interactions within the model are short ranged. We searched static solutions at temperature zero, which represent in reality systems well below the isotropic-nematic phase transition. Vector fields describing orientational distribution of LC molecules and impurities are presented by nematic and impurity spins. In the case of nematic spins head-to-tail invariance is taken into account. We studied several qualitatively different models. In the first case we considered classical RAF-type model, in which impurities act as a local field. At a given site both nematic and impurity spins could be defined, if RAF is present at a site. In the second case we consider cases where sites are occupied either by LC or impurity field. In both cases impurities are orientationally quenched and their orientational distribution is isotropic. Note that in the latter study we do not have any true frustrations at local or global level. In the third case we studied examples where both fields are variational fields. In this case we assumed that LC and impurity fields tend to be perpendicular to each other. In simulations we used two different histories of samples. We either started from random or homogenously aligned initial states. From calculated static configurations we calculated orientational correlation function of the nematic spin field. From it we could infer range of order and its characteristics. In studied cases orientational ordering could be either short ranged (SRO), quasi long ranged (QLRO) or long ranged (LRO). The latter two could be distinguished by finite-size analysis. In the case of SRO we extracted from the correlation function characteristic average domain size and dispersion of domain sizes with distribution parameter. The key results of the thesis are as follows. Using the classical random-field type model we have demonstrated that the Imry-Ma theorem, one of the pivotal stone of statistical mechanics of disorder, is obeyed only for certain histories of samples. Namely, our simulations suggest that infinitesimally weak degree of disorder destroys LRO and replaces it with SRO, if a system is quenched from the isotropic phase. Furthermore, the predicted scaling within Imry-Ma teorem is obeyed. If a system is quenched from a homogeneous initial configuration Imry-Ma scaling is not obeyed. Our results explain why different experiments on seemingly identical samples yield substantially different results. Furthermore, our simulations reveal that in systems of our interest qualitatively different configurations exist which are trapped in potential energy valleys with relatively deep minima. In the case of model, where sites are occupied either with LC or impurity we obtain qualitatively similar results in the regime below percolation threshold. The main quantitative difference is due to the effective change in

Tekoči kristali so tema, ki je tesno povezana z izkušnjami dijakov in trenutno zelo aktualna tema v raziskovalnih krogih, zato je dober primer sodobne fizikalne teme, ki jo skušamo vnesti v pouk. Na podlagi naših izkušenj in znanj o tekočih kristalih in na podlagi predstav študentov prvega letnika univerzitetnega študija o tekočih kristalih smo oblikovali učno gradivo o tekočih kristalih. Učno gradivo, ki je podrobno predstavljeno v tej disertaciji, skuša študente voditi do usvojitve konceptov, ki so pomembni za razumevanje delovanja tekočekristalnega prikazalnika. Gradivo je sestavljeno iz treh delov, in sicer iz predavanja in laboratorijskih vaj pri kemiji in fiziki. Eksperimenti, ki so predstavljeni v okviru fizikalnega dela vaj, se nanašajo na fazni prehod, značilen za tekoče kristale, polarizacijo svetlobe, dvojni lom in barve. Učno gradivo je bilo testirano pri študentih 1. letnika na študijskem programu Razredni pouk na Pedagoški fakulteti Univerze v Ljubljani. Rezultati kažejo, da je gradivo dejansko možno uporabiti v praksi in tudi napredek v znanju v povezavi s tekočimi kristali je znaten, od uspeha 24 % na predtestu, do 68 % na testu takoj po končanem učnem posegu z učnim gradivom in 64 % na testu, ki se je izvajal ob izpitu mesec dni kasneje. Predhodna raziskava je pokazala, da je znanje o tekočih kristalih, ki so ga študenti prvih letnikov različnih študijskih smeri pridobili pred študijem, zanemarljivo. Ker študente razrednega pouka naravoslovje povečini ne zanima, lahko sklepamo, da bodo študenti naravoslovnih študijskih smeri z učnim gradivom usvojili vsaj toliko znanja kot študenti razrednega pouka. Zato smo testirali fizikalni del učnega gradiva tudi pri študentih 1. letnika študijskega programa fizika z vezavami na Pedagoški fakulteti Univerze v Ljubljani. Rezultati kažejo, da so študenti dvopredmetne fizike na večino testiranih vprašanj odgovorili bolje kot študenti razrednega pouka. Za študente fizike smo učno gradivo dopolnili z zahtevnejšim eksperimentom, s katerim izmerimo kotno odvisnost izrednega lomnega količnika. Z eksperimentom neposredno in nazorno pokažemo dvojni lom v tekočih kristalih. V ta namen sta bili izdelani homeotropna in planarna klinasta tekočekristalna celica, ki omogočata kvalitativne in kvantitativne meritve izrednega lomnega količnika v odvisnosti od smeri. V disertaciji predstavimo fizikalne osnove razširjanja svetlobe skozi anizotropno snov, postavitev eksperimenta, meritve in rezultate. Fizikalni del učnega gradiva smo preoblikovali za namene poučevanja v srednji šoli, saj želimo, da so dijaki po zaključenem srednješolskem izobraževanju naravoslovno pismeni. Gradivo je bilo testirano v dveh srednjih šolah v dveh oddelkih 3. letnika gimnazijskega programa. Rezultati testiranja in mnenja učiteljev kažejo, da gradivo lahko uporabimo za predstavitev teme tekoči kristali v srednješolskem izobraževanju, saj so dijaki usvojili ključne koncepte, ki so potrebni za razumevanje delovanja tekočekristalnih prikazalnikov. V disertaciji predstavimo podrobno evalvacija gradiva in smernice za nadaljnje delo. Liquid crystals are linked to everyday students’ experiences and are also a topic of a current scientific research, so they are a good candidate of a modern topic to be introduced into education. Taking into account our experience with liquid crystals and students' preconceptions we designed a teaching module about liquid crystals, which is presented in the dissertation. The teaching module consists of a lecture and experimental work in a chemistry and physics lab. In the chemistry lab students synthesise liquid crystal MBBA and in the physics lab they study its physical properties. Within the experimental work they study phase transitions, polarization of light, double refraction and colours. The evaluation of the module was performed among the first year pre-service primary school teachers who have no special preferences for natural sciences. The evaluation shows that the module is very efficient in transferring knowledge and feasible in practice since the students achieved 24 % on the pre-test, 68 % on the test performed after the physics lab and 64 % on the test that was performed one month later as a part of an exam. A prior study showed that the informally obtained pre-knowledge on liquid crystals of the first year students on several different study fields is negligible. Since the social science students are the ones that are the least interested in natural sciences it can be expected that students in any study programme will on average achieve at least as good conceptual understanding of phenomena related to liquid crystals as the group involved in the pilot study. The physics part of the module was evaluated among the first year pre-service physics teachers from the Faculty of Education at University of Ljubljana. At most of the tested questions the achievements of the pre-service physics teachers were better than the achievements of the pre-service primary school teachers. The teaching module for future physics teachers was upgraded with a more elaborate experiment that directly and illustratively demonstrates double refraction. For this purpose, two, homeotropic and planar, liquid crystalline wedge cells were designed, which enable qualitative and quantitative measurements of the extraordinary refractive index direction dependency in a uniaxial nematic liquid crystal. The basic physics of the propagation of light in anisotropic materials, the experimental setup, measurements and results are described in detail in the dissertation. Because we want the high school students to be scientifically literate at the end of the high school studies, the physics part of the module was adapted, in line with the nature of work in high schools. The teaching module was evaluated in two high schools in two third-year classes in each school (on average students were 17.8 years old). The results of the evaluation and teachers’ opinions show that the module is efficient in transferring knowledge also in the high school and feasible in practice. Students assimilated crucial physical concepts that are necessary for the understanding of how liquid crystal displays work. The thesis presents a detailed evaluation of the high school module and gives guidelines for future work.

V diplomski nalogi smo opisali smo strukturo znanstvenih teorij in spoznali metode, ki opisujejo delovanje znanosti ter uporabo različnih oblik sklepanja v okviru znanosti. Sečišče med fiziko in filozofijo, v okviru znanosti, predstavlja področje filozofije znanosti, ki se med drugim ukvarja z znanstvenimi metodami, kriteriji za določitev in preverjanje posameznih znanstvenih teorij, razlago zgodovine znanosti in poskusom nastanka in sprejetja posameznih znanstvenih teorij. Spoznali smo problem demarkacije, ki se ukvarja z ločevanjem znanosti in neznanosti ter preverili teorijo strun s pomočjo različnih kriterijev za ločevanje med znanostjo in psevdoznanostjo. Podrobneje smo so ogledali značilnosti teorije strun, ki v tem trenutku predstavlja obetavno kandidatko za končno teorijo vsega. Dotaknili smo se problemov, s katerimi se spopada, in orisali njen nadaljnji razvoj. Kot njeno rivalsko teorijo smo opisali standardni model, ki ima več uspeha, a ne vključuje vseh znanih sil narave. Ker je teorija strun za zdaj nezmožna proizvajanja empirično preverljivih napovedi, smo želeli preveriti, ali jo lahko označimo za znanstveno ali filozofsko teorijo. S pomočjo analogije smo povezali topološke defekte (kozmološke strune) in defekte v nematičnih tekočih kristalih ter vzpostavili laboratorij, ki nam omogoča vpogled v svet strun. Na koncu smo s pomočjo teorij štirih različnih filozofskih teorij, ki se ukvarjajo s problemom razmejitve med znanostjo in psevdoznanostjo in razvojem znanosti, in kritik dveh fizikov, preverili domet teorije strun. In this graduation thesis, we have learnt about the problem of demarcation, which, among other things, deals with demarcation between science and non-science and to verify string theory using a variety of criteria to distinguish science from pseudo-science. The common ground between physics and philosophy represents a field called philosophy of science, which deals with scientific methods, finding criteria to determine and verify individual scientific theories, interpretation of history of science and attempts to define various scientific theories and their origin. We tried to explain the structure of scientific theories, learn about the methods describing how science works and finally the use of various forms of inference in the scientific context. More specifically, we have explained the most important features of string theory, which currently represents the most promising candidate for a final theory of everything. We described the problems that the theory is facing and its future development. As a rival theory we have also described the standard model. Since, for the time being, the string theory was incapable of producing empirically verifiable predictions, we wanted to test whether it can be considered as a legitimate physical (scientific) theory, or only as a philosophical theory. With analogy between topological defects (especially cosmic strings) and defects in liquid crystals we formed a laboratory to get a confirmation and to have an insight into the world of strings. We have used four different philosophical theories, that try to explain the problem of demarcation between science and pseudoscience, and criticism of two physics experts, to determine whether string theory is scientific or not.