Dissertationen zum Thema „Nematic and Smectic phases“

This thesis presents the investigation of the liquid crystal (LC) - particle suspensions. Particles from nano- to micro-size, spherical to two-dimensional shapes, with different functionality are dispersed into nematic and smectic phases. The aim is to create ordered nanoparticle (NP) assemblies and thereby modify the common properties of the liquid crystal, such as dielectric anisotropy and electro-optical, revealing any interaction between particles and LC properties. It is found that for concentrations (>0.5vol%), the ferroelectric NPs have increased the sensitivity of the nematic liquid crystal to the electric field through electro-optical responses, which is seen by an enhancement in the dielectric anisotropy. This could be induced by the coupling of the electrical dipole moments in the spherical NPs with the LC director field. The electro-optical properties of the chiral smectic (SmC*) phase (tilt angle Θ, switching time τ_s and spontaneous polarisation P_s) are found to be independent of the concentration and sizes of the doped NPs. The relaxation frequency f_R of the Goldstone mode is faster in the ferroelectric NPs suspensions of 2.0vol% compared to the paraelectric NPs. In the graphene oxide (GO) - nematic LC (5CB) suspensions, the small GO sizes of mean size 560 nm are more easily dispersible than larger flakes of 2.8 micro metre mean size. As the GO concentration is increased, each of the threshold voltage and splay elastic constant dramatically increases, reaching saturation at ≈1.0wt%. The field driven switching-on time is practically not affected, while the purely elastically driven switching-off time is strongly sped-up. Interestingly, thermotropic and lyotropic LC phases are exhibited in the GO-5CB suspensions when heating the thermotropic liquid crystal into its isotropic phase. The isotropic phase of 5CB acts as a solvent for the GO particles, forming a lyotropic nematic phase with largely reduced birefringence. It is found that the nematic to isotropic phase transition is shifted toward higher temperature for the GO-5CB system compared to the BaTiO3-5CB system. Dispersions of different sizes of GO flakes are prepared in isotropic and nematic fluid media. The dielectric relaxation behaviour of GO-dispersions was examined for a wide temperature range (25-60 ℃) and frequency range (100 Hz-2 MHz). The mixtures containing GO flakes were found to exhibit varying dielectric relaxation processes, depending on the size of the flakes and the elastic properties of the dispersant fluid. The relaxation frequencies in the isotropic media were lower compared to the nematic medium. Relaxation frequencies (~10 kHz) are observed in the GO-isotropic media, which are reduced as the size of the GO flakes are decreased, are anticipated to be inherited from GO flakes. However, the fast relaxations (~100 kHz) that are observed in the nematic suspensions could imply strongly slowed down molecular relaxation modes of the nematogenic molecules. Finally, the phase diagram of lyotropic LC as a function of the lateral dimensions of the GO flakes, their concentration, geometrical confinement configuration and solvent polarity was investigated. Polarising optical microscopy was used to determine isotropic-biphasic-nematic phase evolution. The confinement volume and geometry of the sample relative to the GO size are shown to be vital to the observation of the lyotropic phase. GO LCs have the potential for a range of applications from display technologies to conductive fibres. The confinement related LC phase transition is critical toward their applications. It is also found that the stability of the LC phase is higher for the solvent of higher dielectric constant.

Liquid crystals (LCs) are anisotropic fluids that exhibit numerous thermodynamically stable phases in between an isotropic liquid and a three-dimensionally ordered solid. In their simplest ordered phase, the nematic, LCs show orientational order due to molecular self assembly and at the same time maintaining fluid flow properties. In the smectic phase, they show both orientational and partial translational order characterized by a 1-d density wave. Liquid crystalline substances have been extensively studied due to their applications and as important physical models of self-assembly. The effect of the disorder and impurities on LC systems is an important and challenging problem to the fundamental understanding of phases ordering or self-assembly and continually attracts the attention of researchers. The disordered systems often display complex and rich phenomena, being the generalization of the pure (ideal) systems. Disorder can dramatically alter the physical properties of multi-component, composite systems. In particular, the effect of disorder on phase transitions is important as the disorder typically couples to the order parameter, which can be usefully described as a random local field that is conjugate to the order parameter. This is usually realized in systems with random inclusions in a phase ordering media, e.g., a colloidal dispersion of solids in a complex fluid. Another form of disorder is presented by dilution effects, which imposes instead the random breaking or weakening of intermolecular bonds or interactions responsible for the phase ordering. Exploring a good physical system representing random dilution effects in a controlled manner offers a physical probe to unresolved problems in the understanding of mesophasic order. This Dissertation presents a series of studies of dilution and different form of disorder effect on liquid crystal phase transitions. We have used high-resolution AC-calorimetry, dielectric spectroscopy as well as polarizing microscopy to characterize the effects of solvent such as hexane, acetone, decane, and nanomaterials such as multiwall carbon nanotubes and ferroelectric nanoparticles on the phase transitions of several liquid crystals. The liquid crystals of interest are: pentylcyanobiphenyl (5CB), octylcyanobiphenyl (8CB), and decylcyanobiphenyl (10CB). Studies have been carried out as a function of solvent, nanotube, and nanoparticles concentration and temperature spanning the isotropic to nematic (I-N), nematic to smectic-A (N-SmA), and isotropic to smectic-A (I-SmA) phase transitions.

Dissertation (Ph.D.) -- Worcester Polytechnic Institute.
Keywords: smectic-A to smectic-C; nematic to smectic-A; isotropic-nematic; phase transition; quenched random disorder; liquid crystal; gel structure; turbidity; gel dynamics; x-ray intensity fluctuation spectroscopy ( XIFS ); ac-calorimetry; x-ray diffraction Includes bibliographical references (p. 210-218).

Dissertation (Ph.D.) -- Worcester Polytechnic Institute.
Keywords: random-field interactions; radio frequency field heating; modulation calorimetry technique; heat capacity; aerosil; nematic; isotropic; phase transitions Includes bibliographical references.

The investigation of the possible uniaxial phases of a fluid of biaxial particles undertaken by Bergersen, Palffy-Muhoray and Dunmur forms the starting point for further research into the full range of possible phases of such a fluid. A generalization of their interaction model, free from constraints having to do with interaction details, retaining only the biaxial symmetry, is used in the mean-field approximation to explore the range of possible orientationally-ordered phases for such a system. This model is an equilibrium model which does not include dynamic effects. The basic inter-particle interaction is abstract, having the correct symmetry for biaxial particles, and is the most general biaxial interaction constructable from lowest-order scalar invariants. The self-consistent equations resulting from this formulation are obtained in the mean-field approximation and therefore retain both the symmetry and the generality at the cost of exact numerical correctness. Four order parameters are identified, corresponding (within a numerical factor) to those found by Straley and Freiser, as well as those of Bergersen et al. The phase diagram of a fluid of biaxial particles, then, is mapped out in terms of the behavior of these order parameters, as indicated by the self-consistent equations, as a function of three anisotropy parameters and the temperature. The primary method of analysis is iteration of the self-consistent equations obtained from differentiating the free energy. Numerical results are obtained for the location of the phase boundaries, and the temperature dependence of the order parameters in various phases.
Science, Faculty of
Physics and Astronomy, Department of
Graduate

This thesis presents an investigation into the effects of an external electric field on the three- and four-layer intermediate smectic phases. Experiments were performed using electro-optic techniques; thresholds between phases were measured by studying changes in the effective optical tilt. A quantitative measure of the interlayer interaction constant was obtained from the analysis of field-temperature phase diagrams in several materials, which exhibited the intermediate smectic phases in various degrees of stability. Excellent agreement with theory was observed in the field-temperature phase diagrams of these materials. The effect of adding a chiral dopant to liquid crystal compounds was studied and it was found that the interlayer interaction strength is significantly lower in mixtures with a chiral dopant. These measurements provided quantitative information on the importance of the interlayer interaction, which is only indicated qualitatively by other measurements. Deviations from theory were reported in mixtures with increasing concentrations of chiral dopant, in particular in the nature of the transition from the four-layer phase to the three-layer phase. Interesting behaviour in the thresholds between phases was observed in several liquid crystal mixtures in temperature regions close to the triple point on the field- temperature phase diagrams. Measurements of the thresholds between the intermediate phases revealed an unexpected threshold. Further evidence of this unexpected threshold was presented in the form of results of the temperature dependence of effective optical tilt of the various phases; electric field dependence of the response time; and the transient current that flows upon the reversal of an electric field. These measurements revealed that the unexpected threshold was to a field-induced ferrielectric phase with a larger effective tilt than the three-layer phases. Finally, preliminary results are presented from an investigation into defects that form in the thin films in the antiferroelectric smectic phases, with the aim of studying how the elastic constants may affect the stability of the intermediate phases.

The recent interest in bent core liquid crystal has shown many unique physical properties, such the anomalous behaviour of the elastic constants (SplayK1, Twist K2, and BendK3). In bent core liquid crystals it is observed that K3K1). Such behaviour is analogous to calamitic liquid crystals but is in contrast to all other bent-core nematic materials reported to date. Such a result questions some of the current explanations for the elastic behaviour of bent-core materials. Using molecular field theory and atomistic modelling the different elastic behaviour predicted is again in excellent agreement with experimental results. The bend angle is again shown to be an important part in determining the physical properties of bent-core nematic liquid crystals. In a mixture from an oxadiazole dopant and calamitic host liquid crystal, it was found that a filament structure appears in the nematic phase. The filaments appear to interfere with the measurements for elastic constants. In order to understand the filament structure many methods were used including SAXS, dielectric permittivity, and DSC. It was found that the mixture had formed a gel - like phase. The gel is composed of a liquid crystal network and a liquid crystal background, not seen before in any gel system. Due to the liquid crystalline properties both the network and the background can be aligned and manipulated. The new gel phase can possess many new unique properties which warrant further studies understand further into how fundamentally the phase is forming.

The orientational order of the methylene segments adjacent to the head group in the lamellar liquid crystalline phase of potassium palmitate/D₂0 was investigated using multinuclear magnetic resonance. Previous studies had shown that the orientational order near the soap--water interface decreased with decreasing temperature, contrary to intuition. To investigate this phenomenon, three isotopically substituted species of palmitic acid were synthesized: palmitic acid-d₃₁, 1-¹³C-2,2-H₂- palmitic acid-d₂₉, and 2,2,3,3-H₄- palmitic acid-d₂₇. These compounds were treated in two complementary fashions: the acids were dissolved in the liquid crystal 4 - (octyloxy) - benzoic acid (p - OOBA) and the corresponding potassium salts were dispersed in D₂0 at a constant water concentration. Dipolar and quadrupolar couplings were obtained from the ¹H, ¹³C, and ²H nmr spectra of these molecules, in nematic and lamellar liquid crystalline phases, as a function of temperature. In a parallel study, nmr spectra of acetic, propionic, and butyric-2,2 - d₂ acids dissolved in p - OOBA were recorded. In order to observe ¹H - ¹H dipolar couplings, a two dimensional spin echo (π/2 - t₁/2 - π - t₁/2 - echo) was necessary to remove heteronuclear dipolar couplings to the chain deuterons. A refocussing pulse applied simultaneously to the spins allowed observation of the heteronuclear ¹H - ¹³C dipolar couplings in the carbon 13 labelled compound. The complete orientational order matrix of the alpha methylene segment of potassium paImitate/D₂0 and of palmitic acid/p - OOBA was determined from the dipolar and quadrupolar couplings. As the temperature is decreased from 110°C to a temperature just above the gel-liquid crystalline phase transition (45°C), the orientation of the methylene segment of potassium palmitate is rotated by 3° towards a configuration in which the first C - C bond is parallel to the bilayer normal. This is in direct agreement with a previous model, the Abdollal model of lipid - water interaction, in which the decrease in orientational order was postulated to be a strictly geometric effect arising from electrostatic interactions of the lipid with the water. A mean field equilibrium statistical mechanical model, based on the Samulski Inertial Frame Model, was developed to simulate the experimental dipolar and quadrupolar nmr couplings. In potassium palmitate, electrostatic interactions, approximately constant at higher temperatures, increase dramatically as the phase transition is approached. In contrast mean field steric repulsive forces remain constant over the entire temperature range studied. This evidence also supports the Abdollal model of lipid - water interaction. The electrostatic interaction was shown to be of greater importance in the orientational ordering of the solutes in the liquid crystal than in potassium palmitate and this was attributed to intermolecular H - bonding between solute and p - OOBA. The ordering of the head group of carboxylic acids dissolved in p - OOBA was demonstrated to be remarkably similar regardless of the chain length of the solute.
Science, Faculty of
Chemistry, Department of
Graduate

Active nematics are a class of nonequilibrium systems which have received much attention in the form of continuum models in recent years. For the dense, highly ordered case which is of particular interest, these models focus almost exclusively on suspensions of active particles in which the flow of the medium plays a key role in the dynamical equations. Many active nematics, however, reside at an interface or on a surface where friction excludes the effects of long-range flow. In the following pages we shall construct a general model which describes these systems with overdamped dynamical equations. Through numerical and analytical investigation we detail how many of the striking nonequilibrium behaviors of active nematics arise in such systems.

We shall first discuss how the activity in these systems gives rise to an instability in the nematic ordered state. This instability leads to phase-separation in which bands of ordered active nematic are interspersed with bands of the disordered phase. We expose the factors which control the density contrast and the stability of these bands through numerical investigation.

We then turn to the highly ordered phase of active nematic materials, in which striking nonequilibrium behaviors such as the spontaneous formation, self-propulsion, and ordering of charge-half defects occurs. We extend the overdamped model of an active nematic to describe these behaviors by including the advection of the director by the active forces in the dynamical equations. We find a new instability in the ordered state which gives rise to defect formation, as well as an analog of the instability which is seen in models of active nematic suspensions. Through numerical investigations we expose a rich phenomenology in the neighborhood of this new instability. The phenomenology includes a state in which the orientations of motile, transient defects form long-range order. This is the first continuum model to contain such a state, and we compare the behavior seen here with similar states seen in the experiments and simulations of Stephen DeCamp and Gabriel Redner et. al. [1]

Finally, we propose the measurement of defect shape as a mechanism for the comparison between continuum theories of active nematics and the experimental and simulated realiza- tions of these systems. We present a method for making these measurements which allows for averaging and statistical analysis, and use this method to determine how the shapes of defects depend on the parameters of our continuum theory. We then compare these with the shapes of defects which we measure in the experiments and simulations mentioned above in order to place these systems in the parameter space of our model. It is our hope that this mechanism for comparison between models and realizations of active nematics will provide a key to pairing the two more closely.

L’objectif de ce travail est d’étudier les transitions de phases sol-gel et isotrope-nématique dans des suspensions de smectites dioctaédriques en fonction de la morphologie et de la nature minéralogique des argiles. Bien que tous les systèmes étudiés présentent une transition sol-gel à de faibles fraction volumique, la transition cristal-liquide isotrope-nématique n’a pu être identifiée que dans le cas de suspensions de smectites ayant un déficit de charge tétraédrique. L’effet de la localisation de la charge sur le comportement colloïdal a été déterminée à l’aide de la diffusion des rayons X aux petits angles (SAXS) et par des mesures rhéologiques. La nature des interactions électrostatiques dans ces suspensions est purement répulsive et rejette l’idée d’une structure tridimensionnelle de type « château de carte ». Cependant, les smectites ayant un déficit de charge tétraédrique sont plus répulsives et ont des propriétés viscoélastiques plus faibles que celles ayant un déficit octaédrique. Il a également été montré que la dépendance en taille de particules de la position de la transition sol-gel était liée à une statistique de piégeage hydrodynamique des plaquettes d’argile. Finalement, l’application de champs externes (électrique et magnétique) a permis d’obtenir l’alignement de la phase nématique tandis que dans la phase isotrope, le champ électrique induit un ordre antinématique parfait. Afin de préserver l’ordre induit, ces suspensions ont été polymérisées sous champ permettant l’obtention de nanocomposites orientées et structurés
The aim of this work is to study sol-gel and isotropic-nematic phases transitions in suspensions of dioctahedral smectites depending on the morphology and mineralogical nature of clays. Although all the systems studied exhibit a sol-gel at low volume fraction, the liquid-crystalline isotropic-nematic transition could be identified only in the case of smectites with tetrahedral charge deficit. The effect of charge location on the colloidal behavior was determined using small-angle X-ray scattering (SAXS) and rheological measurements. The nature of electrostatic interactions in these suspensions is purely repulsive and rejects the idea of the so-called “house of card” network. However, smectites with a charge deficit located in the tetrahedron are more repulsive and their viscoelastic properties are lower than octahedrally substituted clays. It was also shown that the particle size dependence of the volume fraction corresponding to the sol-gel transition c was related to a simple statistical hydrodynamic trapping of clay platelets. Finally, the application of external fields (electric and magnetic) has resulted in the alignment of the nematic phase while in the isotropic phase, the electric field induces a perfect antinematic order. To preserve the induced alignment, these suspensions were polymerized under the field to obtain perfectly aligned and patterned nanocomposites

Orientadores: Ricardo Antonio Mosna, Guillermo Gerardo Cabrera Oyarzun
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
Made available in DSpace on 2018-08-26T12:57:50Z (GMT). No. of bitstreams: 1 Souza_IbereOliveiraKuntzde_M.pdf: 20917156 bytes, checksum: bb95eeb451fb153542f18a4c8e165528 (MD5) Previous issue date: 2015
Resumo: Nesse trabalho estudamos configurações geométricas de um cristal líquido bidimensional sobre substratos curvos. Em particular, estamos interessados na fase esmética-A desses materiais, em que as suas moléculas são organizadas em camadas. Isso é interessante pois grande parte das propriedades de um cristal líquido, como as propriedades ópticas e elásticas, é afetada pela curvatura do seu substrato. Diferentemente dos esméticos no plano euclidiano, em superfícies curvas a presença de curvatura gaussiana dá origem a defeitos topológicos e grain boundaries na estrutura dos esméticos. Mostrarei essa interação entre curvatura e defeitos topológicos em algumas superfícies no limite em que a contribuição à energia devido a compressão das camadas é muito maior do que as contribuições provenientes de outros tipos de deformação. Nesse regime, o estado de menor energia é obtido quando as camadas esméticas são igualmente espaçadas. Isso faz com que o vetor diretor siga as geodésicas da superfície, o que leva a uma interessante analogia entre esméticos e óptica geométrica. Além disso, é bem conhecido na comunidade de óptica que lentes planas de índice de refração não-uniformes podem ser tratadas como superfícies curvas, cujas geodésicas se propagam da mesma forma que a luz se propaga na lente. Com isso, pode-se fabricar, em princípio, superfícies com propriedades ópticas específicas e, dessa forma, construir texturas esméticas com diferentes defeitos e singularidades a partir da extensa literatura conhecida de lentes
Abstract: We study geometrical configurations of liquid crystals defined on curved bidimensional substrates. We are particularly interested in the smectics-A phase, whose molecules are organized in layers. This is an interesting problem since many of the liquid crystal characteristics, such as its optical and elastic properties, are affected by the curvature of its substrate. Differently from the planar case, in curved surfaces the presence of Gaussian curvature induces topological defects and grain boundaries in the smectic structure. We will illustrate this interplay between curvature and topological defects for different surfaces in the limit where the energy contribution due to the compression of the layers is much larger than the contributions from other types of deformations. At this regime, the ground state is obtained when the smectic layers are uniformly spaced. In this case the normals to the layers follows geodesics of the surface. This leads to an interesting analogy between smectics and geometric optics. Moreover, it is well known in the optics community that flat lenses with nonuniform refractive index can be treated as curved surfaces, where their geodesics propagate in the same way that light propagates in the lens. Therefore, one can manufacture, in principle, surfaces with specific optical properties and construct smectic textures with different topological defects and singularities by using the extensive literature of known lenses
Mestrado
Física
Mestre em Física

Die vorliegende Arbeit befasst sich mit der Synthese und der Untersuchung von Struktur-Eigenschaftsbeziehungen neuartiger V-förmiger, formstabiler Mesogene zur Realisierung biaxial nematischer Mesophasen (Nb). Alle synthetisierten Verbindungen besitzen ein formtreues Oligo(phenylenethinylen)-Grundgerüst, an welches laterale Alkyloxyketten und verschiedene terminale Substituenten (z. B. -CN, O(CH2)nCOOEt, Pyridyle) angebunden wurden. Durch dieses spezielle Design erhält man ausschließlich nematische und keine höher geordneten flüssigkristallinen Phasen. Durch den Einsatz verschiedener zentraler heterozyklischer Kernbausteine konnten erfolgreich Öffnungswinkel zwischen 108.9° und 160° realisiert werden. Dabei zeigen Thiadiazolderivate stets enantiotrope Mesophasen, wobei im Hochtemperaturbereich eine uniaxiale Phase mit biaxialen Aggregaten vorliegt. Beim Abkühlen konnte bei etwa 50 °C mittels Polarisationsmikroskopie und dielektrischer Spektroskopie ein Übergang in die Nb-Phase nachgewiesen werden. Die erstmalige Beobachtung eines direkten Übergangs von der isotropen Phase in die Nb-Phase gelang durch den Einsatz von Benzo[1,2-b:4,3-b]dithiophen als Kernbaustein.

Après une importante bibliographie concernant les phases lyotropes et les techniques cryogéniques en microscopie électronique, l'auteur expose les résultats de ses observations en cryofracture sur les systèmes du titre. Description de la transition lamellaire-nématique et comparaison aux modèles présentés par d'autres auteurs. Discussion de la validité de la technique de cryofracture pour ce type de systèmes

Compounds which exhibit liquid crystal phases have been widely used in display technology. The majority of display applications utilize the nematic liquid crystal phase, which is a liquid-like phase which has partial orientational order at the molecular level. The nematic phase exhibits birifringence which can be manipulated through the application of an external field. Subsequently, all liquid crystal-based display technology utilizes the application of an external field to ???switch??? or tune the optical properties of a nematic domain into a desired optical state. In addition to an external field, the geometry and surface interactions of the liquid crystal domain must be precisely controlled in order for the display to operate properly. Liquid crystal displays (LCDs) utilize a rectangular domain, or pixel, within which the nematic domain is exposed to surface anchoring conditions that result in a twist of the nematic alignment through the thickness of the domain. In this work, a different type of liquid crystal domain that is elliptic is studied which is formed through ???bottom-up??? techniques, such as phase separation of a liquid crystal/polymer mixture to form a polymer-dispersed liquid crystal (PDLC) composite. Nematic domains within PDLCs are spheroidal, as opposed to rectangular for a pixel, and thus exhibit substantially different behaviour in the presence of an external field. The fundamental difference between spheroidal and rectangular nematic domains is that the former requires the presence of defects in nematic order while the latter does not. The overall objective of this work is to study, for a simplified elliptic cylinder domain, the formation of the nematic domain, the resulting domain texture in the presence of an external field, and the domain texture following release of the external field. These three states are directly related to applications of PDLC films as optical functional materials, where an external (electric) field is used to manipulate the optical properties of the film. The effects of geometry (aspect ratio), surface anchoring, and external field strength are studied through a simulation-based approach using the Landau-de Gennes theory of the nematic phase.

碩士
淡江大學
化學學系碩士班
99
It was proposed by theory that biaxial liquid crystals are predicted to exhibit significantly shorter switching time than uniaxial ones used in liquid crystal displays. In this thesis, modify the structural and incorporate a polar group onto cross-like and disc-like mesogens for the generation of biaxial nematic phases with stronger intermolecular dipole interaction. Their biaxiallity was envestigated and verified by conoscopic and X-ray diffraction studies.

碩士
淡江大學
化學學系碩士班
100
The aim of this thesis is to explore the synthesis and liquid crystal properties of hexabenzocoronene and hexakis(phenylethynyl)benzene. The first part includes the design and synthesis of hexa-peri-hexabenzocoronene-(HBC)-based derivatives. It was attempted to introduce cyclohexyl group in a C3 symmetry manneto increasee effective interdisc contact area for higher charge mobility intra-columnar. The second part discusses the chiral amplification effect by introducing various number of chiral side chains onto hexakis(phenylethynyl)benzene. The results by circular dichroism (CD) spectroscopy indicate a liner relationship between the number of chiral chains and the minimum chiral dopants are determined. The third part explores the influence on supra-structures by replacing a alkylphenyl with a a polar cyanophenyl or a cyanobiphenyl group onto the discotic nematogenic hexaynylphenylbenzene. The polar cyano group in either case induced the columnar molecular packing.

Condensed matter physics provides us with an opportunity to explore a large variety of systems with diverse properties. Central to the understanding of these systems is a characterization of the nature of their ground states and low energy excitation. Often, such systems show various forms of emergent properties that are absent in the microscopic level. Identification of such emergent phases of condensed matter form an important avenue of research in the field. In this thesis example of such phases and their associated phase transitions have been studied. The work presented here may be broadly divided into two themes: construction of the theoretical framework for understanding materials already studied experimentally, and, trying to provide new theoretical avenues which may be relevant for understanding future experiments. In these studies we shall explore some unconventional phases and phase transitions that may occur in condensed matter systems. A comprehensive understanding of the properties of such unconventional phases and phase transitions is important in the context of the large array of experimentally studied materials that regularly defy conventional wisdom in more than one way. The thesis consists of two distinct parts. In the first part we study three problems in frustrated magnets. The second part consists of studies of the tunnelling spectroscopy of metal-insulator-superconductor junctions in graphene. Studies in frustrated magnets have opened up the possibility of existence of a whole range of phases beyond the already known magnetically ordered ones. Some of these new phases, like the spin nematic or the valence bond solid, display some other conventional order themselves. Others, like the much sort after spin liquid phases displays a whole new kind of order that cannot be captured through the celebrated Landau’s classification of phases on the basis of symmetry breaking and associated order parameters. The phase transitions in these systems are also equally interesting and lead to intriguing possibilities that demand new modes of analysis. In this part of the thesis we shall study the different properties of three magnets with spin-1/2, 1 and 3/2 respectively. We start by providing an introduction to frustrated spin systems in Chapter [1]. The origin of antiferromagnetic interactions in Mott insulators is discussed and the concept of frustration of magnetic interaction is explained. We also point out the causes that may destroy magnetic order in spin systems, particularly the role of quantum fluctuations in presence or absence of magnetic frustration. This is followed with a brief outline of various magnetically ordered and disordered ground states with particular emphasis on the description of the later. We also give a brief outline of various properties of such phases and associated quantum phase transitions particularly noting the influences of quantum interferences encoded in the Berry phase terms. A brief description of the finite temperature properties is also provided. We end an outline of various experimentally relevant compounds that requires comprehensive understanding, some of which have been addressed in this thesis. In Chapter [2] we study the properties of a spin-nematic state in context of the recently discovered spin-1 Mott insulator Nickel Gallium Sulphide (NiGa2S4). This isotropic triangular lattice compound shows no spin ordering till low temperatures. We propose that it may have a particular type of spin-nematic ground state and explain the experimentally observed properties of the compound on the basis of our proposal. Starting from a two band Hubbard model description, relevant for the compound, we derive the Bilinear Biquadratic spin Hamiltonian. We then show, within mean field theory, that this Hamiltonian describes a transition from the spiral state to a ferro-nematic state as a function of the ratio of bilinear and biquadratic couplings. We also study the possible effects of small pinning disorder andmagnetic field and suggest experiments that can possibly distinguish the proposed nematic state from others. In Chapter [3] we explore the effects of the magneto-elastic coupling in the spin-3/2 B-site chromite spinel Cadmium Chromite (CdCr2O4). In this compound the spins form a pyrochlore lattice. Nearest neighbour spins interact antiferromagnetically. Due to frustration the system does not order at low temperatures and instead goes into a classical spin liquid state. Such a cooperative paramagnet is very susceptible to external perturbations which may relieve their frustration. In CdCr2O4, at lower temperatures the magnetic frustration is relieved by distorting the lattice through a first order magnetoelastic transition. Thus the compound presents a case where the relevant perturbation to the frustrated spin interactions is provided by spin-phonon coupling. An effect of such perturbations on a cooperative paramagnet is of general interest and all aspects of this are not understood presently. We take the initial step of characterizing the spin-phonon interaction in detail. Based on recent sound velocity experiments, we construct a microscopic theory for the sound velocity renormalization due to the spin-phonon coupling and explain the recent experimental data obtained by S. Zherlitsyn et al. using our theory we can explain the dependence of the sound velocity on temperature as well as magnetic field. We also construct a Landau theory to explain (qualitatively) the behaviour of sound velocity across the magneto-structural transition. Further, we discuss the effects due to the small Dzyaloshinskii-Moriya interaction that may be present in these compounds. In Chapter [4] we study the possibility of a direct second order quantum phase transition from spiral to dimer phase in two dimensional antiferromagnets. Such transitions between phases with incompatible symmetries are forbidden within conventional Landau Ginzburg-Wilson paradigm of critical phenomena. Early works showed that when the spiral is destroyed by long wavelength fluctuations a fractionalized Z2 spin liquid is obtained. In this work we show an alternative way–the quantum destruction of the spiral magnet. We argue that, when the defects of the spiral phase proliferate and condense, their associated Berry phase automatically leads to dimerization. We apply our theory to study concrete lattice models where such transitions may be observed. This transition is an example of a Landau forbidden deconfined quantum phase transition. The proposed critical theory is naturally written in terms of fractional degrees of freedom which emerge right at the critical point. These fractional particles interact with each other through emergent gauge fields and are deconfined right at the critical point (but are confined in either of the two adjoining phases). We argue, based on existing results, that the monopoles of the gauge field are dangerously irrelevant right at the critical point rendering the later noncompact. The critical point is characterized by an emergent global U (1) conservation law that is absent in the microscopic model, a typical feature of a deconfined quantum critical point. The resultant field theory belongs to the class of anisotropic NCCP3 class which may be studied numerically in future to understand its critical properties. In modern condensed matter physics the emergence of new and novel phases of matter have often been associated with the presence of strong correlations. Indeed, strongly correlated systems seem to harbour in them the potential to realize some of the most unconventional and exotic emergent phases of matter. However in graphene, which is a single layer of graphite, the emergence of novel properties, as present experiments suggest, is due to its unique band structure and not a fallout of intricate correlation effects. Band structure studies of graphene suggest that the material is a zero gap semiconductor with the low energy excitations resembling massless Dirac quasi-particles. The consequence of this is immediate and interesting. It has lead to the possibility of exploring the physics of relativistic fermions in two spatial dimensions and much of this has been studied with great vigour in the last five years. In our studies, presented in Chapter [5], we explore one of the many consequence of this emergent Dirac structure of the low energy quasi-particles, namely the properties of metal-insulator-superconductor junctions of graphene. The twin effect of Klein tunneling of Dirac fermions (and associated transmission resonances) and Andreev reflection (both specular and retro) sets them aside from their conventional counterparts. The graphene normal metal-insulator-superconductor (NIS) junctions show strikingly different properties like oscillations in the sub-gap tunneling conductance as a function of both barrier strength and width. We make a detailed study of this for arbitrary barrier strengths and widths with and without Fermi-surface mismatch between the normal and the superconducting sides. The amplitude of these oscillations are maximum for aligned Fermi surface and vanishes for large Fermi surface mismatch. We provide an understanding for this unconventional behaviour of graphene NIS junctions. We also suggest experimental tests for our theory. Such experimental verification will reveal one more remarkable emergent property in a condensed matter system.

Condensed matter physics provides us with an opportunity to explore a large variety of systems with diverse properties. Central to the understanding of these systems is a characterization of the nature of their ground states and low energy excitation. Often, such systems show various forms of emergent properties that are absent in the microscopic level. Identification of such emergent phases of condensed matter form an important avenue of research in the field. In this thesis example of such phases and their associated phase transitions have been studied. The work presented here may be broadly divided into two themes: construction of the theoretical framework for understanding materials already studied experimentally, and, trying to provide new theoretical avenues which may be relevant for understanding future experiments. In these studies we shall explore some unconventional phases and phase transitions that may occur in condensed matter systems. A comprehensive understanding of the properties of such unconventional phases and phase transitions is important in the context of the large array of experimentally studied materials that regularly defy conventional wisdom in more than one way. The thesis consists of two distinct parts. In the first part we study three problems in frustrated magnets. The second part consists of studies of the tunnelling spectroscopy of metal-insulator-superconductor junctions in graphene. Studies in frustrated magnets have opened up the possibility of existence of a whole range of phases beyond the already known magnetically ordered ones. Some of these new phases, like the spin nematic or the valence bond solid, display some other conventional order themselves. Others, like the much sort after spin liquid phases displays a whole new kind of order that cannot be captured through the celebrated Landau’s classification of phases on the basis of symmetry breaking and associated order parameters. The phase transitions in these systems are also equally interesting and lead to intriguing possibilities that demand new modes of analysis. In this part of the thesis we shall study the different properties of three magnets with spin-1/2, 1 and 3/2 respectively. We start by providing an introduction to frustrated spin systems in Chapter [1]. The origin of antiferromagnetic interactions in Mott insulators is discussed and the concept of frustration of magnetic interaction is explained. We also point out the causes that may destroy magnetic order in spin systems, particularly the role of quantum fluctuations in presence or absence of magnetic frustration. This is followed with a brief outline of various magnetically ordered and disordered ground states with particular emphasis on the description of the later. We also give a brief outline of various properties of such phases and associated quantum phase transitions particularly noting the influences of quantum interferences encoded in the Berry phase terms. A brief description of the finite temperature properties is also provided. We end an outline of various experimentally relevant compounds that requires comprehensive understanding, some of which have been addressed in this thesis. In Chapter [2] we study the properties of a spin-nematic state in context of the recently discovered spin-1 Mott insulator Nickel Gallium Sulphide (NiGa2S4). This isotropic triangular lattice compound shows no spin ordering till low temperatures. We propose that it may have a particular type of spin-nematic ground state and explain the experimentally observed properties of the compound on the basis of our proposal. Starting from a two band Hubbard model description, relevant for the compound, we derive the Bilinear Biquadratic spin Hamiltonian. We then show, within mean field theory, that this Hamiltonian describes a transition from the spiral state to a ferro-nematic state as a function of the ratio of bilinear and biquadratic couplings. We also study the possible effects of small pinning disorder andmagnetic field and suggest experiments that can possibly distinguish the proposed nematic state from others. In Chapter [3] we explore the effects of the magneto-elastic coupling in the spin-3/2 B-site chromite spinel Cadmium Chromite (CdCr2O4). In this compound the spins form a pyrochlore lattice. Nearest neighbour spins interact antiferromagnetically. Due to frustration the system does not order at low temperatures and instead goes into a classical spin liquid state. Such a cooperative paramagnet is very susceptible to external perturbations which may relieve their frustration. In CdCr2O4, at lower temperatures the magnetic frustration is relieved by distorting the lattice through a first order magnetoelastic transition. Thus the compound presents a case where the relevant perturbation to the frustrated spin interactions is provided by spin-phonon coupling. An effect of such perturbations on a cooperative paramagnet is of general interest and all aspects of this are not understood presently. We take the initial step of characterizing the spin-phonon interaction in detail. Based on recent sound velocity experiments, we construct a microscopic theory for the sound velocity renormalization due to the spin-phonon coupling and explain the recent experimental data obtained by S. Zherlitsyn et al. using our theory we can explain the dependence of the sound velocity on temperature as well as magnetic field. We also construct a Landau theory to explain (qualitatively) the behaviour of sound velocity across the magneto-structural transition. Further, we discuss the effects due to the small Dzyaloshinskii-Moriya interaction that may be present in these compounds. In Chapter [4] we study the possibility of a direct second order quantum phase transition from spiral to dimer phase in two dimensional antiferromagnets. Such transitions between phases with incompatible symmetries are forbidden within conventional Landau Ginzburg-Wilson paradigm of critical phenomena. Early works showed that when the spiral is destroyed by long wavelength fluctuations a fractionalized Z2 spin liquid is obtained. In this work we show an alternative way–the quantum destruction of the spiral magnet. We argue that, when the defects of the spiral phase proliferate and condense, their associated Berry phase automatically leads to dimerization. We apply our theory to study concrete lattice models where such transitions may be observed. This transition is an example of a Landau forbidden deconfined quantum phase transition. The proposed critical theory is naturally written in terms of fractional degrees of freedom which emerge right at the critical point. These fractional particles interact with each other through emergent gauge fields and are deconfined right at the critical point (but are confined in either of the two adjoining phases). We argue, based on existing results, that the monopoles of the gauge field are dangerously irrelevant right at the critical point rendering the later noncompact. The critical point is characterized by an emergent global U (1) conservation law that is absent in the microscopic model, a typical feature of a deconfined quantum critical point. The resultant field theory belongs to the class of anisotropic NCCP3 class which may be studied numerically in future to understand its critical properties. In modern condensed matter physics the emergence of new and novel phases of matter have often been associated with the presence of strong correlations. Indeed, strongly correlated systems seem to harbour in them the potential to realize some of the most unconventional and exotic emergent phases of matter. However in graphene, which is a single layer of graphite, the emergence of novel properties, as present experiments suggest, is due to its unique band structure and not a fallout of intricate correlation effects. Band structure studies of graphene suggest that the material is a zero gap semiconductor with the low energy excitations resembling massless Dirac quasi-particles. The consequence of this is immediate and interesting. It has lead to the possibility of exploring the physics of relativistic fermions in two spatial dimensions and much of this has been studied with great vigour in the last five years. In our studies, presented in Chapter [5], we explore one of the many consequence of this emergent Dirac structure of the low energy quasi-particles, namely the properties of metal-insulator-superconductor junctions of graphene. The twin effect of Klein tunneling of Dirac fermions (and associated transmission resonances) and Andreev reflection (both specular and retro) sets them aside from their conventional counterparts. The graphene normal metal-insulator-superconductor (NIS) junctions show strikingly different properties like oscillations in the sub-gap tunneling conductance as a function of both barrier strength and width. We make a detailed study of this for arbitrary barrier strengths and widths with and without Fermi-surface mismatch between the normal and the superconducting sides. The amplitude of these oscillations are maximum for aligned Fermi surface and vanishes for large Fermi surface mismatch. We provide an understanding for this unconventional behaviour of graphene NIS junctions. We also suggest experimental tests for our theory. Such experimental verification will reveal one more remarkable emergent property in a condensed matter system.

Dziesięć chiralnych estrów z ciekłokrystalicznych szeregów 3FmXiPhX2 (m = 2, 4, 5, 6, 7; X1, X2 = H, F) przebadano komplementarnymi metodami eksperymentalnymi i obliczeniowymi pod kątem wpływu struktury molekularnej na przemiany fazowe i właściwości fizyczne. W oparciu o obliczenia kwantowo-mechaniczne dla izolowanych molekuł (metodą DFT i pół-empiryczną metodą AM1) zdefiniowano poprawkę na nieliniowy kształt molekuł, przetestowano jej cztery warianty oraz wykazano, że jej wprowadzenie umożliwia wyznaczenie wartości nasycenia kąta pochylenia tego typu molekuł w oparciu o pomiary dyfrakcyjne. Wyniki przeprowadzonych obliczeń DFT wykorzystano również do analizy widm w podczerwieni dla związku 3F2HPhF. Zbadano polimorfizm faz smektycznych i krystalicznych, a dla wybranych homologów (3FmHPhF i 3FmFPhF, m = 5 i 7) przeprowadzono badania kinetyki krystalizacji. Wyznaczono temperaturowe zależności spontanicznej polaryzacji, czasu przełączania, lepkości rotacyjnej, grubości warstw smektycznych, kąta pochylenia molekuł oraz średnią odległość między molekułami i długość korelacji w warstwach smektycznych. Zidentyfikowano procesy relaksacyjne w fazach smektycznych (proces Goldstone'a, proces miękki, fazon ferroelektryczny, fazon antyferroelektryczny, proces domenowy, proces alfa). Na podstawie temperaturowej zależności czasu relaksacji procesu alfa określono wartość parametru kruchości dla homologów 3FmHPhF (m = 5, 6, 7), występujących w zeszklonej fazie SmC*A.
An influence of the molecular structure on the phase sequence and physical properties of ten chiral liquid crystalline esters of the 3FmXiPhX2 series (m = 2, 4, 5, 6, 7; X1, X2 = H, F) were studied by complementary experimental and computational methods. Based on quantum-mechanical computations (by DFT and semi-empirical AM1 method) a correction for the nonlinear shape of the molecules was proposed, its four different definitions were tested and it was shown that the saturated values of the tilt angle of molecules can be successfully estimated based on X-ray diffraction as long as the shape-related correction is considered. The DFT results were also used to analyze the FT-IR spectra of the 3F2HPhF compound. Polymorphism of liquid crystalline and crystalline phases were investigated, moreover the kinetics of the crystallization process were studied for chosen homologues (3FmHPhF and 3FmFPhF, m = 5, 7). The temperature dependencies of the spontaneous polarisation, the switching time, the rotational viscosity, the smectic layer thickness, the tilt angle as well as the average distances between molecules and the correlation length within smectic layers were determined. Relaxation processes in the smectic phases were identified (as the Goldstone mode, soft mode, ferroelectric phason, antiferroelectric phason, domain mode and alpha mode). For three 3FmHPhF homologues (m = 5, 6, 7), exhibiting the vitrified SmC*A phase, the fragility parameter was determined based on the temperature dependence of relaxation time of the alpha mode.