This thesis reports the results of light-scattering measurements and visual investigations of critical phenomena in the complex mixture 1-propanol (1P) + water (W) + potassium chloride (KCl) which has a special critical point (or a special thermodynamic state) known as the double critical point (DCP). The main theme of the thesis is the critical behavior on approaching a special critical point (i.e., the DCP) in a complex or associating mixture in contrast with that in simple, nonassociating mixtures. The asymptotic critical behavior in complex or associating fluids, such as polymer solutions and blends, ionic and nonionic micellar solutions, microemulsions, aqueous and nonaqueous electrolyte solutions, protein solutions, etc., is now commonly accepted to belong to the 3D-Ising universality class. However, the temperature range of the asymptotic regime in these fluids, with universal behavior, has a nonuniversal width and is, in general, smaller than that in simple or nonassociating fluids. In complex mixtures, which are made up of relatively large molecules or particle clusters of mesoscopic range, the coupling between the conventional correlation length of the critical fluctuations ( ξ) and an additional length scale associated with the mesoscale structures (ξD) is known to modify the approach towards the universal nonclassical critical behavior near their critical points. Nevertheless, the generality of this approach needs to be confirmed. There are also instances of a pure classical or close to classical behavior being observed in the critical domain of complex mixtures, although recent experimental results contradict the earlier observations. Therefore, further experimental evidences than that presently available are necessary before one can say how far the analogy between simple and complex fluids can be pushed. Variations in the effective dielectric constant of a mixture have been known to affect the critical behavior. Furthermore, we anticipate the presence of special critical points in complex mixtures to cause nontrivial modifications in the approach towards the universal asymptotic critical behavior. Special thermodynamic states are characterized by critical fluctuations with exceptionally large correlation length, and are displayed by multicomponent liquid mixtures, in which there are a multitude of thermodynamic paths by which a critical point can be approached, and offers rich information about the critical phenomena. These issues are being addressed in this research work. This thesis is organized into 7 Chapters. Chapter 1 begins with an account of the historical development of the field of critical point phenomena with a brief introduction to critical phenomena in simple fluids. Critical phenomena observed in various complex systems such as aqueous and nonaqueous ionic fluids, polymer solutions and blends, micellar and microemulsion systems, etc., are discussed, with particular attention to investigations into crossover from Ising to mean-field critical behavior observed in these systems, which are relevant to the present work. Theoretical attempts at modeling ionic criticality are cited and summarized. This is followed by a discussion of re-entrant phase transitions in multicomponent liquid systems. An account of the various types of special critical points, such as double critical point, critical double point, critical inflection point, quadruple critical point, etc., highlighting the critical behavior on approaching these special critical points, and some of the models of reentrant miscibility are briefly given. The Chapter ends with a statement on the goals of the present research work. Chapter 2 describes the instrumentation developed and the data acquisition procedures adopted for the study. Details of the thermostats and precision temperature controllers used for visual and light-scattering measurements are provided. The important design considerations relating to the achievement of a high degree of temperature stability (~ ±1 mK in the range 293-383 K) are elucidated clearly. The temperature sensors used in the present experiments and their calibration procedures are discussed. The light-scattering instrumentation is discussed in depth. The problems associated with the light-scattering techniques when it is used to study critical point phenomena, and the strategies adopted to overcome them are discussed. The sample cells used for visual investigations and light- scattering experiments, along with the procedure adopted for cleaning and filling of sample cells are also described. Chapter 3 essentially deals with the characterization of the system 1P + W + KCl. It begins with a brief introduction to the critical behavior in complex mixtures, and the motivation behind choosing the present system. The phase behavior in the present mixture, the generation of the coexistence curves and the line of critical points in the mixture, and the method used for preparation of the samples are described. The criticality of the samples is judged by the equal volume phase separation criterion through visual investigations. Addition of a small amount of salt (i.e., KCl) to the 1P + W solution induces phase separation in the mixture as a result of a salting-out process. Decreasing the salt concentration has the same effect as that of increasing pressure on the liquid-liquid demixing of this mixture. Therefore, KCl may be considered as an appropriate field variable analogous to pressure in this mixture. The mixture 1P + W + KCl exhibits reentrant phase transitions and has an array of lower (TL) and upper (TU) critical solution temperatures. It is found that the line of TL’s and TU’s, known as the line of critical points, merge (TU - TL = ΔT → 0) to form a special thermodynamic state known as the DCP. The DCP is approached as close as 509 mK (i.e., ΔT ~ 509 mK) in this work. An analysis of the critical line shows that it is roughly parabolic in shape, which is in consonance with the predictions of the lattice models and the Landau-Ginzburg theory of phase transition. In addition to the presence of a special critical point, various structure probing techniques like small angle X-ray scattering (SAXS), small angle neutron scattering (SANS), etc., indicate the presence of large-scale density inhomogeneities or clusters in 1P + W solution and its augmentation on adding small amount of KCl. Therefore, the present mixture provides a unique possibility to investigate the combined effects of molecular structuring as well as a special critical point on the critical behavior. Only a section of the coexistence surface of the mixture could be generated, owing to various experimental limitations and other problems inherent to the system. This limited further studies on the coexistence curves in the mixture. Chapter 4 reports the critical behavior of osmotic susceptibility in the present mixture. The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths by varying t [ =| (T - T TL)/ TL|] from the lower one-phase region. The light-scattering data analysis emphasizes the need for correction-to-scaling terms for a proper description of the data over the investigated t range. Renormalization of the critical exponents is observed as the critical line is approached along certain special paths. Experimental evidence for the doubling of the extended scaling exponent Δ1 near the DCP is shown. There is no signature of Fisher renormalization in the values of the critical exponents. The data analysis yields very large magnitudes for the correction amplitudes A1 and A2, with the first-correction amplitude A1 being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in the mixture. The magnitudes of the correction amplitudes are observed to increase gradually as TL approaches the DCP. The increasing need for extended scaling in the neighborhood of special critical points has been noted earlier in several aqueous electrolyte solutions, in polymer-solvent systems, etc. However, the magnitudes of the correction amplitudes were not as large as that in the present case. Analysis of the effective susceptibility exponent γeff in terms of t indicate that, for the TL far away from the DCP, γeff displays a nonmonotonic crossover from its single limit 3D Ising value (~ 1.24) towards its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value (~ 2.39) towards its nearly doubled mean-field value (~ 1.84) with increase in t. For the in-between TL’s, the limiting value of γeff in the asymptotic as well as nonasymptotic regimes gradually increases towards the DCP. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend towards shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover behavior to the mean-field limit extends well beyond t > 10¯2 for the TL’s studied. The crossover behavior is discussed in terms of the emergence of a new lengthscale ξD associated with the enhanced ion-induced clustering seen in the mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover is discussed in terms of the varying influence of the DCP on the critical behavior along the TL line. The discussion is extended to explain the observed critical behavior in various re-entrant systems having other special critical points. The extended renormalized Ising regime towards the DCP is also reflected in a decrease in the correlation length amplitude (ξ0) as TL approaches the DCP. It is observed that the first-correction amplitude A1 corresponding to fit using two correction terms becomes more negative as TL approaches the DCP, implying an increase in the value of the parameter ū of the crossover model [by Anisimov et al., Phys. Rev. Lett. 75, 3146 (1995)] as the DCP is approached. This increase in reflected in a trend towards a relatively sharp crossover behavior of γeff as TL shifts towards the DCP, i.e., towards the high temperature critical points. The significance of the field variable tUL in understanding different aspects of reentrant phase transitions is manifested in the present system as well. Analysis of the data in terms of tUL led to the retrieval of universal values of the exponents for all TL’s. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value towards a value slightly lower than its nonasymptotic mean-field value of 1. The limited (TL _ T) range restricted such a behavior of the effective exponent (in terms of t as well as tUL) for the lowest TL. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic, high tUL region, as foreseen earlier in micellar systems. The effective susceptibility exponent in terms of tUL also indicates an increase in the sharpness of crossover towards the high temperature TL’s. An increase in the sharpness of crossover with polymer chain length has been observed in polymer solutions. Therefore, our results suggest the need for further composition and temperature-dependent study of molecular structuring in the present mixture. There is also a large decrease in the dielectric constant of the mixture towards the high temperature TL’s. In Chapter 5 the light-scattering measurements are performed on approaching the DCP along the line of the upper critical solution temperatures (i.e., TU’s), by varying t [ = (T - TU )/ TU ] from the high temperature one-phase region in the mixture. A trend towards shrinkage in the simple scaling region is observed as TU shifts away from the DCP. Such a trend was not visible in the data analysis of the TL’s using the correction terms, due to the varying (TL - T) ranges. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in the mixture. As with the TL’s, for the TU closest to the DCP, γeff displays a nonmonotonic crossover from its 3D-Ising value towards its nearly doubled mean-field value with increase in t. While for that far away from the DCP, γeff displays a nonmonotonic crossover from its single limit Ising value towards a value slightly lower than its mean-field value of 1 with increase in t. The limited (TL – T) range restricted such a behavior of γeff for the TL far away from the DCP, This feature of γeff in the nonasymptotic, high t region is yet again interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from below. Unlike TL’s, the crossover behavior in the present case is pronounced and more sharp for all TU’s. However, the variation in the width of the renormalized Ising regime on approaching the DCP along the TU line is quite similar to that observed along the TL line. The crossover behavior is attributed to the strong ion-induced structuring seen in the mixture, while the observed trend in the crossover as TU shifts towards/away from the DCP is attributed to the varying influence of the DCP. The influence of the DCP on the critical behavior along the TU (or TL) line decreases as TU (or TL) shifts away from the DCP. Our observations indicate an increase in the sharpness of crossover as the critical temperature shifts from TL towards TU, or in other words, as the critical point shifts towards higher temperatures. SANS measurements on the present mixture indicate no difference in the growth of mesoscale clusters in the lower and upper one-phase regions in the mixture. Hence, the observed increase in the sharpness of crossover towards the TU’s is very puzzling. The dielectric constant of the major constituent (i.e., water, ~ 62 %) of the present mixture decreases from around 80 to 63 as the critical temperature shifts from TL towards TU. Therefore, our results suggest the need to look at the crossover phenomena probably from two perspectives, namely, the solvent or dielectric effect and the clustering effect. The increase in the sharpness of the crossover behavior on approaching the high temperature critical points is probably related to the macroscopic property of the mixture, i.e., to the decrease in the dielectric constant of the mixture, while the actual nonmonotonic character of the crossover behavior is related to the microscopic property of the mixture, i.e., to the clustering effects, the extent of which determines the width of the asymptotic critical domain. However, this conclusion is somewhat subtle and calls for rigorous theoretical and experimental efforts to unravel the exact dependence of the crossover behavior on the dielectric constant. Analysis using the field variable tUL in lieu of the conventional variable t led to the retrieval of unique, universal exponents for all TU’s irrespective of the ΔT value. For all TU’s, the effective susceptibility exponent in terms of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value towards a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis of the effective exponent for the TU far away from the DCP. Like with the TL’s, the crossover behavior extends over nearly the same tUL range for the TU’s studied. However, the crossover is again sharper when compared to the TL’s. Chapter 6 reports light-scattering measurements (by heating as well as cooling) on a non phase-separating 1P + W + KCl mixture in the vicinity of the DCP. The results indicate that despite the lack of phase-separation or critical points, critical-phenomena-like fluctuations can still occur in homogeneous mixtures if they reside in some other direction than temperature or composition (like, pressure or salt concentration) of the phase diagram. Unlike earlier studies on non phase-separating mixtures, our results indicate a crossover behavior of the effective susceptibility exponent, in addition to the power-law behavior. Chapter 7 sums up the major findings of the work reported in this thesis. It also presents a range of open problems that need to be explored further in order to fully understand the results that are reported in this thesis, especially, regarding the exact dependence of dielectric constant of the mixture on the character of the crossover behavior.

Elastic properties of carbon nanotubes (CNT), boron nitride nanotubes (BNNT), double stranded DNA (dsDNA), paranemic-juxtapose crossover (PX-JX) DNA and dendrimer bound DNA are discussed in this thesis. Structural phase transitions of nucleic acids induced by external force, carbon nanotubes and graphene substrate are also studied extensively. Electrostatic interactions have a strong effect on the elastic properties of BNNTs due to large partial atomic charges on boron and nitrogen atoms. We have computed Young’s modulus (Y ) and shear modulus (G) of BNNT and CNT as a function of the nanotube radius and partial atomic charges on boron and nitrogen atoms using molecular mechanics calculation. Our calculation shows that Young’s modulus of BNNTs increases with increase in magnitude of the partial atomic charges on B and N atoms and can be larger than the Young’s modulus of CNTs of same radius. Shear modulus, on the other hand depends weakly on the magnitude of partial atomic charges and is always less than the shear modulus of the CNT. The values obtained for Young’s modulus and shear modulus are in excellent agreement with the available experimental results. We also study the elasticity of dsDNA using equilibrium fluctuation methods as well as nonequilibrium stretching simulations. The results obtained from both methods quantitatively agree with each other. The end-to-end length distribution P(ρ) and angle distribution P(θ) of the dsDNA has a Gaussian form which gives stretch modulus (γ1) to be 708 pN and persistence length (Lp) to be 42 nm, respectively. When dsDNA is stretched along its helix axis, it undergoes a large conformational change and elongates about 1.7 times its initial contour length at a critical force. Applying a force perpendicular to the DNA helix axis, dsDNA gets unzipped and separated into two single-stranded DNA (ssDNA). DNA unzipping is a fundamental process in DNA replication. As the force at one end of the DNA is increased the DNA starts melting above a critical force depending on the pulling direction. The critical force fm , at which dsDNA melts completely decreases as the temperature of the system is increased. The melting force in the case of unzipping is smaller compared to the melting force when the dsDNA is pulled along the helical axis. In the case of melting through unzipping, the double-strand separation has jumps which correspond to the different energy minima arising due to sequence of different base-pairs. Similar force-extension curve has also been observed when crossover DNA molecules are stretched along the helix axis. In the presence of mono-valent Na+ counterions, we find that the stretch modulus (γ1 ) of the paranemic crossover (PX) and its topoisomer juxtapose (JX) DNA structure is significantly higher (30 %) compared to normal B-DNA of the same sequence and length. When the DNA motif is surrounded by a solvent of divalent Mg2+ counterions, we find an enhanced rigidity compared to in Na+ environment due to the electrostatic screening effects arising from the divalent nature of Mg2+ counterions. This is the first direct determination of the mechanical strength of these crossover motifs which can be useful for the design of suitable DNA motifs for DNA based nanostructures and nanomechanical devices with improved structural rigidity. Negatively charged DNA can be compacted by positively charged dendrimer and the degree of compaction is a delicate balance between the strength of the electrostatic interaction and the elasticity of DNA. When the dsDNA is compacted by dendrimer, the stretch modulus, γ1 and persistence length, Lp decreases dramatically due to backbone charge neutralization of dsDNA by dendrimer. We also study the effect of CNT and graphene substrate on the elastic as well as adsorption properties of small interfering RNA (siRNA) and dsDNA. Our results show that siRNA strongly binds to CNT and graphene surface via unzipping its base-pairs and the propensity of unzipping increases with the increase in the diameter of the CNTs and is maximum on graphene. The unzipping and subsequent wrapping events are initiated and driven by van der Waals interactions between the aromatic rings of siRNA nucleobases and the CNT/graphene surface. However, dsDNA of the same sequence undergoes much less unzipping and wrapping on the CNT/graphene due to smaller interaction energy of thymidine of dsDNA with the CNT/graphene compared to that of uridine of siRNA. Unzipping probability distributions fitted to single exponential function give unzipping time (τ) of the order of few nanoseconds which decrease exponentially with temperature. From the temperature variation of unzipping time we estimate the free energy barrier to unzipping. We have also investigated the binding of siRNA to CNT by translocating siRNA inside CNT and find that siRNA spontaneously translocates inside CNT of various diameters and chiralities. Free en- ergy profiles show that siRNA gains free energy while translocating inside CNT and the barrier for siRNA exit from CNT ranges from 40 to 110 kcal/mol depending on CNT chirality and salt concentration. The translocation time τ decreases with the increase of CNT diameter having a critical diameter of 24 A for the translocation. After the optimal binding of siRNA to CNT/graphene, the complex is very stable which can serve as siRNA delivery agent for biomedical applications. Since siRNA has to undergo unwinding process in the presence of RNA-induced silencing complex, our proposed delivery mechanism by single wall CNT possesses potential advantages in achieving RNA interference (RNAi).

[pt] A investigação da geometria quântica em semicondutores e isoladores tornou-se significativa devido às suas implicações nas características dos materiais. A noção de geometria quântica surge considerando a métrica quântica do estado de Bloch da banda de valência, que é definido a partir da sobreposição dos estados de Bloch em momentos ligeiramente diferentes. Ao integrar a métrica quântica em toda a zona de Brillouin, introduzimos uma quantidade que chamamos de número de fidelidade, que significa a distância média entre estados de Bloch adjacentes. Além disso, apresentamos um formalismo para expressar o número de fidelidade como um marcador de fidelidade local no espaço real que pode ser definido em qualquer sítio da rede. O marcador pode ser calculado diretamente diagonalizando o hamiltoniano da rede que descreve o comportamento das partículas na rede. Posteriormente, o conceito de número e marcador de fidelidade é estendido para temperatura finita utilizando a teoria de resposta linear, conectando-os a medições experimentais que envolvem analisar o poder de absorção óptica global e local quando o material é exposto à luz linearmente polarizada. Particularmente para materiais bidimensionais, a opacidade do material permite a determinação direta do número de fidelidade espectral, permitindo a detecção experimental do número de fidelidade. Finalmente, um marcador de fidelidade não local é introduzido considerando a divergência da métrica quântica. Este marcador é postulado como um indicador universal de transições de fase quântica, assumindo que o momento cristalino permanece um número quântico válido. Este marcador não local pode ser interpretado como uma função de correlação dos estados de Wannier, que são funções de onda localizadas que descrevem estados eletrônicos em um cristal. A generalidade e aplicabilidade destes conceitos são demonstradas através da investigação de vários isoladores topológicos e transições de fase topológicas em diferentes dimensões. Essas descobertas elaboram o significado dessas quantidades e sua conexão com vários fenômenos fundamentais na física da matéria condensada. / [en] The investigation of quantum geometry in semiconductors and insulators has become significant due to its implications for material characteristics. The notion of quantum geometry arises by considering the quantum metric of the valence-band Bloch state, which is defined from the overlap of the Bloch states at slightly different momenta. By integrating the quantum metric through-out the Brillouin zone, we introduce a quantity that we call fidelity number, which signifies the average distance between adjacent Bloch states. Furthermore, we present a formalism to express the fidelity number as a local fidelity marker in real space that can be defined on every lattice site. The marker can be calculated directly by diagonalizing the lattice Hamiltonian that describes particle behavior on the lattice. Subsequently, the concept of the fidelity number and marker is extended to finite temperature using linear-response theory, connecting them to experimental measurements which involves analyze the global and local optical absorption power when the material is exposed to linearly polarized light. Particularly for two-dimensional materials, the material s opacity enables straightforward determination of the fidelity number spectral, allowing for experimental detection of the fidelity number. Finally, a nonlocal fidelity marker is introduced by considering the divergence of the quantum metric. This marker is postulated as a universal indicator of quantum phase transitions, assuming the crystalline momentum remains a valid quantum number. This nonlocal marker can be interpreted as a correlation function of Wannier states, which are localized wave functions describing electronic states in a crystal. The generality and applicability of these concepts are demonstrated through the investigation of various topological insulators and topological phase transitions across different dimensions. These findings elaborate the significance of these quantities and their connection to various fundamental phenomena in condensed matter physics.

In the study of strongly interacting condensed-matter systems controlled microscopic theories hold a key position. Spin-wave theory, large-N expansion, and $epsilon$-expansion are some of the few successful cornerstones. In this doctoral thesis work, we have developed a novel large-$d$ expansion method, $d$ being the spatial dimension, to study model Hamiltonians hosting a quantum phase transition between a paramagnet and a magnetically ordered phase. A highlight of this technique is that it can consistently describe the entire phase diagram of the above mentioned models, including the quantum critical point. Note that most analytical techniques either efficiently describe only one of the phases or suffer from divergences near the critical point. The idea of large-$d$ formalism is that in this limit, non-local fluctuations become unimportant and that a suitable product state delivers exact expectation values for local observables, with corrections being suppressed in powers of $1/d$. It turns out that, due to momentum summation properties of the interaction structure factor, all diagrams are suppressed in powers of $1/d$ leading to an analytic expansion. We have demonstrated this method in two important systems namely, the coupled-dimer magnets and the transverse-field Ising model. Coupled-dimer magnets are Heisenberg spin systems with two spins, coupled by intra-dimer antiferromagnetic interaction, per crystallographic unit cell (dimer). In turn, spins from neighboring dimers interact via some inter-dimer interaction. A quantum paramagnet is realized for a dominant intra-dimer interaction, while a magnetically ordered phase exists for a dominant (or of the same order as intra-dimer interaction) inter-dimer interaction. These two phases are connected by a quantum phase transition, which is in the Heisenberg O(3) universality class. Microscopic analytical theories to study such systems have been restricted to either only one of the phases or involve uncontrolled approximations. Using a non-linear bond-operator theory for spins with S=$1/2$, we have calculated the $1/d$ expansion of static and dynamic observables for coupled dimers on a hypercubic lattice at zero temperature. Analyticity of the $1/d$ expansion, even at the critical point, is ensured by correctly identifying suitable observables using the mean-field critical exponents. This method yields gapless excitation modes in the continuous symmetry broken phase, as required by Goldstone\'s theorem. In appropriate limits, our results match with perturbation expansion in small ratio of inter-dimer and intra-dimer coupling, performed using continuous unitary transformations, as well as the spin-wave theory for spin-$1/2$ in arbitrary dimensions. We also discuss the Brueckner approach, which relies on small quasiparticle density, and derive the same $1/d$ expansion for the dispersion relation in the disordered phase. Another success of our work is in describing the amplitude (Higgs) mode in coupled-dimer magnets. Our novel method establishes the popular bond-operator theory as a controlled approach. In $d=2$, the results from our calculations are in qualitative agreement with the quantum Monte Carlo study of the square-lattice bilayer Heisenberg AF spin-$1/2$ model. In particular, our results are useful to identify the amplitude (Higgs) mode in the QMC data. The ideas of large-$d$ are also successfully applied to the transverse-field Ising model on a hypercubic lattice. Similar to bond operators, we have introduced auxiliary Bosonsic operators to set up our method in this case. We have also discussed briefly the bilayer Kitaev model, constructed by antiferromagnetically coupling two layers of the Kitaev model on a honeycomb lattice. In this case, we investigate the dimer quantum paramagnetic phase, realized in the strong inter-layer coupling limit. Using bond-operator theory, we calculate the mode dispersion in this phase, within the harmonic approximation. We also conjecture a zero-temperature phase diagram for this model.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Low-dimensional materials are known to undergo phase transitions to differently or- dered states, when cooled to lower temperatures. These phases often show a periodic modulation of the charge density (called a charge density wave – CDW) coupled with a periodic perturbation of the crystal lattice (called a periodic lattice distortion – PLD). Although many experiments have been performed and much has been learnt about CDW phases in low-dimensional materials, the reasons for their existence are still not fully understood yet. Many processes, involving either strong electron–electron or electron–lattice coupling, have been observed which all might play a role in explaining the formation of different phases under different conditions. With the availability of femtosecond lasers it has become possible to study materials under highly nonequilibrium conditions. By suddenly introducing a known amount of energy into the system, the equilibrium state is disturbed and the subsequent relax- ation processes are then observed on timescales of structural and electronic responses. These experiments can deliver valuable information about the complex interactions between the different constituents of condensed matter, which would be inaccessible under equilibrium conditions. We use time resolved electron diffraction to investigate the behaviour of a CDW system perturbed by a short laser pulse. From the observed changes in the diffraction patterns we can directly deduce changes in the lattice structure of our sample. A femtosecond electron diffraction setup was developed at the Laser Research In- stitute in Stellenbosch, South Africa. Short laser pulses produce photo electrons which are accelerated to an energy of 30 keV. Despite space charge broadening effects, elec- tron pulses shorter than 500 fs at sample position can be achieved. Technical details of this system and its characterisation as well as sample preparation techniques and analysis methods are described in detail in this work. Measurements on two members of the quasi-two-dimensional transition metal di- chalcogenides, namely 4Hb-TaSe2 and 1T-TaS2, are shown and discussed. Both show fast (subpicosecond) changes due to the suppression of the PLD and a rapid heating of the lattice. When the induced temperature rise heats the sample above a phase tran- sition temperature, a complete transformation into the new phase was observed. For 4Hb-TaSe2 we found that the recovery to the original state is significantly slower if the PLD was completely suppressed compared to only disturbing it. On 1T-TaS2 we could not only study the suppression of the original phase but also the formation of the higher energetic CDW phase. Long (100 ps) time constants were found for the tran- sition between the two phases. These suggest the presence of an energy barrier which has to be overcome in order to change the CDW phase. Pinning of the CDW by de- fects in the crystal structure result in such an energy barrier and consequently lead to a phase of domain growth which is considerably slower than pure electron or lattice dynamics. / AFRIKAANSE OPSOMMING: Dit is bekend dat lae-dimensionele materie fase oorgange ondergaan na anders ge- ori¨enteerde toestande wanneer afgekoel word tot laer temperature. Hierdie fases toon dikwels ’n periodiese modulasie van die elektron digtheid (genoem ’n “charge density wave” – CDW), tesame met ’n periodiese effek op die kristalrooster (genoem ’n “peri- odic lattice distortion” – PLD). Alhoewel baie eksperimente al uitgevoer is en al baie geleer is oor hierdie CDW fase, is die redes vir hul bestaan nog steeds nie ten volle verstaan nie. Baie prosesse, wat of sterk elektron–elektron of elektron–fonon interaksie toon, is al waargeneem en kan ’n rol speel in die verduideliking van die vorming van die verskillende fases onder verskillende omstandighede. Met die beskikbaarheid van femtosekonde lasers is dit nou moontlik om materie onder hoogs nie-ewewig voorwaardes te bestudeer. Deur skielik ’n bekende hoeveel- heid energie in die stelsel in te voer, word die ewewigstaat versteur en word die daar- opvolgende ontspanning prosesse waargeneem op die tydskaal van atomies struktu- rele en elektroniese bewiging. Hierdie eksperimente kan waardevolle inligting lewer oor die komplekse interaksies tussen die verskillende atomiese komponente van ge- kondenseerde materie, wat ontoeganklik sou wees onder ewewig voorwaardes. Ons gebruik elektrondiffraksie met tyd resolusie van onder ’n pikosekonde om die gedrag van ’n CDW stelsel te ondersoek nadat dit versteur is deur ’n kort laser puls. Van die waargenome veranderinge in die diffraksie patrone kan ons direk aflei watse veranderinge die kristalstruktuur van ons monster ondergaan. ’n Femtosekonde elektronendiffraksie opstelling is ontwikkel by die Lasernavors- ingsinstituut in Stellenbosch, Suid-Afrika. Kort laser pulse produseer foto-elektrone wat dan na ’n energie van 30 keV versnel word. Ten spyte van Coulomb afstoting ef- fekte, kan elektron pulse korter as 500 fs by die monster posisie bereik word. Tegniese besonderhede van hierdie opstelling, tegnieke van die voorbereiding van monsters asook analise metodes word volledig in hierdie tesis beskryf. Metings op twee voorbeelde van kwasi-tweedimensionele semi-metale, naamlik 4Hb-TaSe2 en 1T-TaS2, word gewys en bespreek. Beide wys ’n vinnige (subpikosekon- de) verandering as gevolg van die versteuring van die PLD en ’n vinnige verhitting van die kristalrooster. Wanneer die ge¨ınduseerde temperatuur bo die fase oorgang tempe- ratuur styg, is ’n volledige transformasie na die nuwe fase waargeneem. Vir 4Hb-TaSe2 het ons gevind dat die herstelling na die oorspronklike toestand aansienlik stadiger is as die PLD heeltemal viernietig is in vergelyking met as die PLD net versteur is. Met 1T-TaS2 kon ons nie net alleenlik die vernietiging van die oorspronklike fase sien nie, maar ook die vorming van ’n ho¨er energie CDW fase. Lang (100 ps) tydkonstante is gevind vir die oorgang tussen die twee fases. Hierdie dui op die teenwoordigheid van ’n energie-versperring wat eers oorkom moet word om die CDW fase voledig te ver- ander. Vaspenning van die CDW deur defekte in die kristalstruktuur veroorsaak so’n energie versperring en gevolglik lei dit tot ’n fase van groeiende CDW gebiede wat heelwat stadiger as pure elektron of kritalrooster dinamika is.

<p>In this work, we study two important themes in the physics of the interacting one-dimensional (1D) electron gas: the transition from one-dimensional to higher dimensional behavior, and the role of inhomogeneity. The interplay between interactions, reduced dimensionality, and inhomogeneity drives a rich variety of phenomena in mesoscopic physics. In 1D, interactions fundamentally alter the nature of the electron gas, and the homogeneous 1D electron gas is described by Luttinger Liquid theory. We use Quantum Monte Carlo methods to study two situations that are beyond Luttinger Liquid theory --- the quantum phase transition from a linear 1D electron system to a quasi-1D zigzag arrangement, and electron localization in quantum point contacts. </p><p>Since the interacting electron gas has fundamentally different behavior in one dimension than in higher dimensions, the transition from 1D to higher dimensional behavior is of both practical and theoretical interest. We study the first stage in such a transition; the quantum phase transition from a 1D linear arrangement of electrons in a quantum wire to a quasi-1D zigzag configuration, and then to a liquid-like phase at higher densities. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal; then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase; and, finally, the electrons form a disordered liquid-like phase. We show that the linear to zigzag phase transition occurs even in narrow wires with strong quantum fluctuations, and that it has characteristics which are qualitatively different from the classical transition.</p><p>Experiments in quantum point contacts (QPC's) show an unexplained feature in the conductance known as the ``0.7 Effect''. The presence of the 0.7 effect is an indication of the rich physics present in inhomogeneous systems, and we study electron localization in quantum point contacts to evaluate several different proposed mechanisms for the 0.7 effect. We show that electrons form a Wigner crystal in a 1D constriction; for sharp constriction potentials the localized electrons are separated from the leads by a gap in the density, while for smoother potentials, the Wigner crystal is smoothly connected to the leads. Isolated bound states can also form in smooth constrictions if they are sufficiently long. We thus show that localization can occur in QPC's for a variety of potential shapes and at a variety of electron densities. These results are consistent with the idea that the 0.7 effect and bound states observed in quantum point contacts are two distinct phenomena.</p> / Dissertation

When cutting an ice from lakes and ponds gaseous phase displays often ubiquitous bubble textures along the ice thickness. The occurrence of bubbles (enclosures filled with the gas) in ice relates to a content of the dissolved gas in the lake/pond water prior to freezing over the surface. When water freezes, dissolved gases are rejected and redistributed at the ice-water interface, depending on the saturation ratio between the gas and water. If the concentration of dissolved gases surpasses a critical value (as freezing progresses), the water at the interface becomes supersaturated, and gas bubbles nucleate and grow to a visible size along the interface. The bubbles generated at the ice-water interface are either incorporated into the ice crystal as the ice-water interface advances, thus forming gas pores in the ice, or released from the interface. If there is incorporation or release is determined by several factors. The bubbles nucleated at the advancing ice-water interface may be characterized by concentration, shape, and size, which depend on growth rate of ice, the amount of gases dissolved in water, and the particulate content of water. This work focused on the relation between growth rates of the ice and the occurrence of bubbles in the pond ice. I monitored the temperature of the ice formed...

Syftet med denna undersökning är att undersöka hur undervisningen om partikelmodellen bedrivs i årskurserna 4–6 och hur undervisningen utformas. Studien genomfördes med hjälp av kvalitativt inriktade intervjuer med fem olika lärare som undervisar inom No-ämnena i de aktuella årskurserna. Resultatet visar att alla fem lärarna undervisar om fasövergångar och materians byggstenar, men att lärarna fördjupar sig inom olika delar av dessa områden.  Lärarna i undersökningen väljer olika undervisningsmetoder när de undervisar om partikelmodellen: Traditionell undervisning, hypoteser, datoranimeringar, laborationer, dramatiseringar och användning av konkret material. / The purpose with this paper has been to examine how the education about the particle model in grades 4–6 is conducted and how the education is carried out. The study was carried out with the help of qualitatively directed interviews with five teachers that teach in the science subjects in the grades in question. The results show that all five teachers teach about, phase transitions and the building blocks of matter, but choose to immerse in different parts of these subjects. The teachers choose different teaching methods to teach about the particle model: Traditional teaching, hypotheses, computer animations, laboratory, dramatization and use of concrete materials.

Misturas liotrópicas de laurato de potássio (KL)/ sulfato de potássio (K2SO4)/ álcool (CnH2n+1OH)/ água (H2O) apresentam fases no estado líquido cristalino nemático. Essas fases nemáticas foram colesterizadas através da adicão do agente quiral brucina à mistura. Este estudo foi realizado mantendo as frações molares de todos os constituintes das misturas constantes e variando o comprimento da mol´ecula de álcool entre oito (1-octanol) e dezesseis (1-hexadecanol) átomos de carbono. Três fases colestéricas foram identificadas: ChD (colestérica discótica), ChB (colestérica biaxial) e ChC (colestérica calamítica). O diagrama de fases foi construído em função do número de átomos de carbono n na molécula do álcool. As transições entre as fases colestéricas foram investigadas por medições das birrenfringências ópticas usando microscopia óptica de luz polarizada. As misturas com 9 n 12 apresentaram as três fases colestéricas como função da temperatura e uma região de crossover entre as fases ChD e ChB, com comprimento de correlação a temperatura nula maior do que as dimensões micelares típicas. Misturas com n=8 e n=13 apresentaram transição de fase de primeira ordem entre as fases ChD e ChC, sem a presença da fase ChB intermediária a elas. As misturas com n=14, 15 e 16 apresentaram somente a fase ChC como função da temperatura. Os resultados foram interpretados como consequência da nanosegregação das moléculas de álcool nas micelas com relação às moléculas do anfifílico principal. / Lyotropic mixtures of potassium laurate (KL)/ potassium sulphate (K2SO4)/ alcohol (CnH2n+1OH)/ water (H2O) present nematic liquid crystal phases. These nematic phases were cholesterized by the doping of the mixtures with the chiral agent brucine. This study was conducted by keeping constant the molar fractions of all constituents of the mixtures and varying the length of the alcohol molecule between eight (1-octanol) and sixteen (1-hexadecanol) carbon atoms. Three cholesteric phases were identified: ChD (discotic cholesteric), ChB (biaxial cholesteric), and ChC (calamitic cholesteric). The phase diagram was constructed as a function of the number of carbon atoms n in the alcohol molecule. The cholesteric-cholesteric phase transitions were investigated by measurements of the optical birefringences via polarized light microscopy. The mixtures with 9 n 12 presented the three cholesteric phases as a function of temperature and a crossover between the ChD and ChB phases, with a bare correlation length larger than the typical micellar dimensions. Mixtures with n =8 and n =13 exhibited first order phase transitions among the ChD and the ChC phases, without the presence of the intermediate ChB phase. Mixtures with n =14, 15 and 16 showed only the ChC phase as a function of temperature. These results were interpreted as a consequence of the nanosegregation of the alcohol molecules in the micelles with respect to the main amphiphilic molecules.

Este trabalho visou o estudo da resposta óptica não-linear de cristais líquidos liotrópicos nas fases isotrópicas e nemática calamítica e nas vizinhanças das transições de fase nemática calamítica isotrópica e nemática calamítica nemática biaxial. Para este estudo foi utilizada, fundamentalmente, a técnica de varredura Z. Os resultados obtidos indicam que o efeito não-linear em cristais líquidos liotrópicos esta ligado à presença de micelas na mistura e que a anisometria de micela tem influencia na resposta observada. Foi observado ainda que a presença de ferrofluido na mistura, mesmo em pequenas quantidades, causa um grande aumento na absorção óptica da amostra e consequentemente da resposta não-linear. O comportamento do índice de refração não-linear (n IND.2) em função da temperatura nas vizinhanças da transição da fase nemática calamítica para nemática biaxial apresenta um crescimento expressivo de (n IND.2). Nas vizinhanças da transição nemática calamítica para isotrópica esse efeito não foi observado. / This work has been focused on the study of the optical nonlinear response of lyotropic liquid crystals in the isotropic and nematic calamitic phases and in the neighborhood of the nematic calamitic isotropic and nematic calamitic nematic biaxial phase transitions. The basic technique we used is Z-scan. The results obtained indicated that the nonlinear effect in lyotropic liquid crystals is related to the presence of micelles in the mixture and the micelle anisotropy has influence on the observed response. Is has also been observed that the presence of ferrofluid in the mixture, even in small quantities, causes a large raise in the sample optical absorption and consequently in the nonlinear response. The behavior of the nonlinear refractive index (n IND.2) as function of temperature in the neighborhood of the nematic calamitic to nematic biaxial phase transition shows as expressive n IND.2 raise. This behavior has not been observed in the neighborhood of the nematic calamitic to isotropic phase transition.