Phase transitions of the gelatin – water and agaroza - water systems have been studied using the cloud-point method. Phase diagrams of these systems are constructed at different values of pH of medium. It is shown that pH of medium influences on the melting temperature of gelatin and agaroza gels. / Методом точек помутнения изучены фазовые переходы в системах желатин – вода и агароза – вода. Построены фазовые диаграммы систем при разных pH среды в магнитном поле и вне поля. Установлено, что pH среды влияет на температуру плавления гелей желатина и агарозы.

Изучены фазовые переходы и структура систем: гидроксипропилцеллюлоза-вода и гидроксипропилцеллюлоза -вода-этанол. Показано, что с увеличением содержания этанола в смешанном растворители вода-этанол нижняя критическая температура растворения системы гидроксипропилцеллюлоза -вода-этанол повышается. При содержании эталона свыше 50% нижняя критическая температура растворения не обнаружена в диапазоне температур от 298 до 423 К. Определены размеры макромолекул и их ассоциатов для растворов гидроксипропилцеллюлозы в смешанном растворителе. / Phase transitions and the structure of the hydroxypropylcellulose-water and hydroxypropylcellulose-water-ethanol systems were studied. It has been shown that as the ethanol content in the water-ethanol mixed solvents increases, the lower critical solution temperature of the hydroxypropylcellulose-water-ethanol system increases. With the ethanol content of more than 50%, the lower critical solution temperature was not found in the temperature range from 298 to 423 K. The dimensions of macromolecules and their associations for hydroxypropylcellulose solutions in a mixed solvent were determined.

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<p> Block copolymers are a class of soft materials which can self-assemble into a variety of ordered structures. One method to induce new structures is the application of an external field such as an electric field. Previously, studies of the field-induced phase transitions are based on the assumption that the structural change follows certain symmetry pattern or simply using real-space numerical methods. The goal of the current project is to develop a simple analytic method to predict the structural change. Our approach is based on a linear response theory, in which the external field is taken as a perturbation and the lowest-order contribution to the solution is computed. We applied our method to the Landau-Brazovskii theory which is valid close to the order-disorder transition point of diblock copolymers. The result shows that there will be an additional term to the order parameter as a response to the external field. The structural change can be predicted by a new Fourier expansion of the order parameter. As an example, we examined the structural change of a body-centered cubic phase under an applied electric field.</p> / Thesis / Master of Science (MSc)

In this thesis we introduce a new quantity which we call the dynamic fidelity susceptibility (DFS). We show that it is relevant to out-of-equilibrium dynamics in many-particle quantum systems, taking the problem of an impurity in a Bosonic Josephson junction, and the transverse field Ising model, as examples. Both of these systems feature quantum phase transitions in their ground states and understanding the dynamics near such critical points is currently an active area of research. In particular, sweeping a system through a quantum critical point at finite speed leads to non-adiabatic dynamics. A simple theoretical tool for describing such a scenario is the celebrated Kibble-Zurek theory which predicts that the number of excitations is related to the speed of sweep via the phase transition’s critical exponents at equilibrium. Another theoretical tool, useful in describing the static properties of quantum phase transitions, is the fidelity susceptibility. Our DFS generalizes the concept of fidelity susceptibility to nonequilibrium dynamics, reproducing its results in the static limit, whilst also displaying universal scaling properties, akin to those found in Kibble-Zurek theory, in the non-adiabatic regime. Furthermore, we show that the DFS is the same quantity as the time-dependent quantum Fisher information which provides a measure of multi-partite entanglement, as well as being closely related to out-of-time-order correlators (OTOCs). / Thesis / Master of Science (MSc)

Sol-gel titania particles were investigated, primarily by optical techniques, by systematically varying synthesis, sample handling, and annealing variables. The material phases investigated were amorphous titania, anatase TiO2, and rutile TiO2. Annealing-induced phase transformations from amorphous TiO2 to anatase to rutile were studied by Raman scattering, infrared reflectivity, infrared absorption, x-ray diffraction, and electron energy-loss spectroscopy (EELS). Detailed experiments were carried out on the effects of annealing on the Raman and infrared spectra of anatase nanocrystals. The frequencies of the zone-center transverse optical (TO) and longitudinal-optical (LO) phonons of anatase were determined and were used in analyzing the results obtained on composites consisting of annealed solgel particles. The TO and LO frequencies of anatase were obtained from polarization-dependent far-infrared reflectivity measurements on single crystals. These results, which determined the dielectric functions of anatase, were used to explain infrared (IR) reflectivity spectra of titania nanoparticles pressed into pellets, as well as the grazing-incidence IR reflectivity observed for titania thin films. Because of the polycrystalline character of the titania nanoparticles, the surface roughness of the pressed pellets, and the island-structure character of the thin films, effective-medium theories (appropriate for composites) were used, along with the anatase dielectric functions, to interpret the experimental results. The titania nanoparticles were prepared by the hydrolysis/condensation of Ti(OC2H5)4. A polymeric steric stabilizer was used in the sol-gel synthesis in order to prevent continued agglomeration during the condensation process. This yielded particles with a relatively narrow size distribution. The amount of water used in the reaction determines the final particle size. Particles as small as 80 nm and as large as 300 nm were used throughout this work. From the colloidal suspension, loose powders, pressed pellets, and thin films were formed. These samples were subjected to different annealing processes at temperatures ranging from room temperature up to 1000 C. Two different annealing atmospheres were used: air (oxygen-containing) and argon (no oxygen). The amorphous to anatase transformation was followed by in-situ IR transmission measurements carried out during annealing. The particles as prepared are amorphous and the anatase phase could be detected, using this sensitive IR technique, at temperatures as low as 150 C. This phase transition was shown to be particle size dependent. It was also shown that introducing the stabilizer by means of the alkoxide flask instead of the water flask (during the sol-gel synthesis) decreases the anatase to rutile transformation temperature. Loose powders were found to transform more readily than dense pellets, while island-structure films were found to be the hardest to transform. Even at 1000 C, most of these films did not transform to rutile. X-ray diffraction experiments were used to determine nanocrystal sizes in anatase samples obtained by air and argon anneals at temperatures from 300 to 800 C. A correlation was found between Raman band shape (peak position and linewidth) and crystallite size, but this correlation was different for air anneals and for argon anneals. These experiments called for an interpretation based on a stoichiometric effect rather than a finite size effect. Based on this interpretation, the as-prepared particles are slightly oxygen-deficient, with a stoichiometry corresponding to TiO1.98. In the electron energy-loss experiments, a special data-analysis technique was used to extract the EELS spectrum of the titania nanoparticles from the observed substrate-plus-particles signal. This technique successfully resolved the titania absorption-edge peak. Which was found to be momentum independent. For low electron momentum, the results were consistent with the reported optical absorption edge. / Ph. D.

Thesis advisor: Xiao Chen / The development of highly controllable quantum coherent simulators such as superconducting qubits and Rydberg atom arrays has stimulated the study of non-equilibrium quantum dynamics, opening the door to exciting topics including dynamical phase transitions, thermalization, transport, and quantum error correction. This thesis addresses various questions from non-equilbrium quantum dynamics, with a concentration on measurement-induced phase transitions (MIPT), adaptive dynamics with feedback mechanism, and Hilbert space fragmentation. In the first part, we study the hybrid quantum automaton (QA) circuits with different symmetries subject to local composite measurements. For $\mathbb{Z}_2$-symmetric hybrid QA circuits, there exists an entanglement phase transition from a volume-law phase to a critical phase by varying the measurement rate. The special feature of QA circuits enables us to interpret the entanglement dynamics in terms of a stochastic particle model. With the help of this stochastic model, we further investigate the entanglement fluctuations and quantum error correcting property of the volume-law phase in QA circuits with no symmetry, and study the entanglement dynamics in QA circuits with U(1) symmetry. Despite being a hallmark of non-unitary quantum dynamics, MIPT is absent in the density matrix averaged over measurement outcomes. In the second part, we introduce an adaptive quantum circuit subject to measurements with feedback. The feedback is applied according to the measurement outcome and steers the system towards a unique state above certain measurement threshold. We show that there exists an absorbing phase transition in both quantum trajectories and quantum channels. In the end, we turn to the phenomenon of Hilbert space fragmentation (HSF), whereby dynamical constraints fragment Hilbert space into many disconnected sectors, providing a simple mechanism by which thermalization can be arrested. However, little is known about how thermalization occurs in situations where the constraints are not exact. To study this, we consider a situation in which a fragmented 1d chain with pair-flip constraints is coupled to a thermal bath at its boundary. For product states quenched under Hamiltonian dynamics, we numerically observe an exponentially long thermalization time, manifested in both entanglement dynamics and the relaxation of local observables. To understand this, we study an analogous model of random unitary circuit dynamics, where we rigorously prove that the thermalization time scales exponentially with system size. Slow thermalization in this model is shown to be a consequence of strong bottlenecks in configuration space, demonstrating a new way of producing anomalously slow thermalization dynamics. / Thesis (PhD) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Condensed matter systems undergoing phase transitions rarely allow exact solutions. The presence of disorder renders the situation  even worse but collective Monte Carlo methods and parallel algorithms allow numerical descriptions. This thesis considers classical phase transitions in disordered spin systems in general and in effective models of superfluids with disorder and novel interactions in particular. Quantum phase transitions are considered via a quantum to classical mapping. Central questions are if the presence of defects changes universal properties and what qualitative implications follow for experiments. Common to the cases considered is that the disorder maps out correlated structures. All results are obtained using large-scale Monte Carlo simulations of effective models capturing the relevant degrees of freedom at the transition. Considering a model system for superflow aided by a defect network, we find that the onset properties are significantly altered compared to the $\lambda$-transition in $^{4}$He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario. For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent $z=1.8 \pm 0.05$ contradicting the long standing result $z=d$. Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role. Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations. / <p>QC 20150306</p>

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.