Doctor of Philosophy / Department of Physics / Christopher M. Sorensen / Nano-size materials are new materials in an intermediate state between the bulk and atomic or molecular states. Nanoparticles in colloidal solution and their assemblies have the great attention of researchers to investigate the novel fundamental properties and numerous applications. In this dissertation, we investigated the solubility phase transition behavior of gold nanoparticles in colloidal solution. We used the nearly monodisperse gold nanoparticles synthesized by either the inverse micelle or the solvated metal atom dispersion methods followed by digestive ripening. The gold nanoparticles were ligated with alkyl chains, which were dodecanethiol, decanethiol, or octanethiol for individual samples. They dispersed in toluene or t-butyl toluene like large molecules at room temperature. In analogy to molecular solutions, the colloidal solution had thermally reversible phase transitions between a dissolved phase of dispersed single nanoparticles and dispersed-aggregation co-existing phase. A more polar solvent, 2-butanone, was added to the colloidal solution for changing the solubility of gold nanoparticles and adjusting the phase transition temperatures to accessible temperatures. Superclusters formed by the nanoparticles when the colloidal solutions were quenched from a one-phase regime at high temperature to a two-phase regime at low temperature. Solubility phase diagrams were obtained for gold nanoparticles with different ligands in the mixtures of different ratios of 2-butanone and toluene or t-butyl toluene. The explanation from classical ideal solution theory gave the fusion enthalpy of superclusters. Temperature quenches from the one-phase to the two-phase regime yielded superclusters of the nanoparticle solid phase with sizes that depended on the quench depth. Classical nucleation theory was used to describe these sizes using a relative small value of the surface tension for the nanoparticle solid phase. This value is consistent with molecule size scaling of the surface tension. In total these results show that the solubility behavior of nanoparticles in colloidal solution is similar to the behavior in molecular solutions.

In recent years, both hafnia and zirconia have been looked at closely in the quest for a high permittivity gate dielectric to replace silicon dioxide in advanced metal oxide semiconductor field effect transistors (MOSFET). Hafnium dioxide or HfO2 is chosen for its high dielectric constant (five times that of SiO2) and compatibility with stringent requirements of the Si process. As deposited, thin hafnia films are typically amorphous but turn polycrystalline after a post-deposition anneal. To control the phase composition in hafnia films understanding of structural phase transitions is a first step. In this dissertation using first principles methods we consider three phase transitions of hafnia and zirconia: monoclinic to tetragonal, tetragonal to cubic and amorphous to crystalline. Because the high surface to volume ratio in hafnia films and powders plays an important role in phase transitions, we also study the surface properties of hafnia. We discuss the mechanisms of various phase transitions and theoretically estimate the transition temperatures. We find two types of amorphous hafnia and show that they have different structural and electronic properties. The small energy barrier between the amorphous and crystalline structures is found to cause the low crystallization temperature. Moreover, we calculate work functions and surface energies for hafnia surfaces and show the surface suppression of the phase transitions. / text

In this thesis several classes of directed paths are considered as models of linear polymers in a dilute solution. We obtain the generating functions for each model by considering factorization arguments. Information about the polymer behaviour can be extracted from the singularity structure of the associated generating functions. By using modified versions of these models we study the adsorption and localization of polymer molecules, the behaviour of polymers subject to a tensile force, the effects of stiffness, as well as the behaviour of polymers in confined geometries. In each of these situations the resulting generating functions contain at least two physical singularities. We identify the phase transitions in these systems by a changeover in the dominant singularity of the generating function. In the study of localization and polymers subject to a force, we utilize both homopolymer and random copolymer models. For copolymers, the physically relevant properties are obtained by considering a quenched average of the free energy over all possible monomer sequences. This procedure is intractable even for the simplest models. By considering the Morita approximation for several walk models we obtain results which give a bound on the corresponding features of the quenched system. We use a mapping between a simple model of duplex DNA and an adsorbing Motzkin path in order to study the mechanical unzipping of duplex DNA. From this model, we obtain force-temperature diagrams which show re-entrant behaviour of the force. We also develop a simple low temperature theory to describe the behaviour of the force close to T=0 and find that the shape of the force-temperature curve is associated with entropy in the ground state of the system. We consider the effect of stiffness on polymer adsorption and find that the phase transition is second order for all finite stiffness parameters. For systems of polymers in confined geometries, we find that the behaviour of the polymer depends on the distance between the confining surfaces and the associated interactions with each surface. In this problem, there exist regimes where the polymer exerts a force on the surfaces which can be attractive, repulsive or zero.

One of the most important problems in statistical mechanics is the measurement of free energies, these being the quantities that determine the direction of chemical reactions and--the concern of this thesis--the location of phase transitions. While Monte Carlo (MC) computer simulation is a well-established and invaluable aid in statistical mechanical calculations, it is well known that, in its most commonly-practised form (where samples are generated from the Boltzmann distribution), it fails if applied directly to the free energy problem. This failure occurs because the measurement of free energies requires a much more extensive exploration of the system's configuration space than do most statistical mechanical calculations: configurations which have a very low Boltzmann probability make a substantial contribution to the free energy, and the important regions of configuration space may be separated by potential barriers. We begin the thesis with an introduction, and then give a review of the very substantial literature that the problem of the MC measurement of free energy has produced, explaining and classifying the various different approaches that have been adopted. We then proceed to present the results of our own investigations. First, we investigate methods in which the configurations of the system are sampled from a distribution other than the Boltzmann distribution, concentrating in particular on a recently developed technique known as the multicanonical ensemble. The principal difficulty in using the multicanonical ensemble is the difficulty of constructing it: implicit in it is at least partial knowledge of the very free energy that we are trying to measure, and so to produce it requires an iterative process. Therefore we study this iterative process, using Bayesian inference to extend the usual method of MC data analysis, and introducing a new MC method in which inferences are made based not on the macrostates visited by the simulation but on the transitions made between them. We present a detailed comparison between the multicanonical ensemble and the traditional method of free energy measurement, thermodynamic integration, and use the former to make a high-accuracy investigation of the critical magnetisation distribution of the 2d Ising model from the scaling region all the way to saturation. We also make some comments on the possibility of going beyond the multicanonical ensemble to `optimal' MC sampling. Second, we investigate an isostructural solid-solid phase transition in a system consisting of hard spheres with a square-well attractive potential. Recent work, which we have confirmed, suggests that this transition exists when the range of the attraction is very small (width of attractive potential/ hard core diameter ~ 0.01). First we study this system using a method of free energy measurement in which the square-well potential is smoothly transformed into that of the Einstein solid. This enables a direct comparison of a multicanonical-like method with thermodynamic integration. Then we perform extensive simulations using a different, purely multicanonical approach, which enables the direct connection of the two coexisting phases. It is found that the measurement of transition probabilities is again advantageous for the generation of the multicanonical ensemble, and can even be used to produce the final estimators. Some of the work presented in this thesis has been published or accepted for publication: the references are G. R. Smith & A. D. Bruce, A Study of the Multicanonical Monte Carlo Method, J. Phys. A. 28, 6623 (1995). [reference details doi:10.1088/0305-4470/28/23/015] G. R. Smith & A. D. Bruce, Multicanonical Monte Carlo Study of a Structural Phase Transition, to be published in Europhys. Lett. [reference details Europhys. Lett. 34, 91 (1996) doi:10.1209/epl/i1996-00421-1] G. R. Smith & A. D. Bruce, Multicanonical Monte Carlo Study of Solid-Solid Phase Coexistence in a Model Colloid, to be published in Phys. Rev. E [reference details Phys. Rev. E 53, 6530–6543 (1996) doi:10.1103/PhysRevE.53.6530].

Abstract Layered inorganic-organic hybrid compounds have been widely studied as new potential sources of semiconductors and other optical devices. They simulate natural quantum well materials, where the inorganic part acts as semiconductors, separated by an organic part. This class of hybrid materials has no covalent bonds between the inorganic and organic parts; instead, weak hydrogen bonds and van der Waals forces bind and stabilise the overall structure. The inorganic part is made up of layers of corner-sharing metal halide octahedra, MX6, where the metal must be in a divalent state and the halides are Cl, Br or I. The 2-D layers extend infinitely in two directions and are separated themselves by layers of primary ammonium cations, with only one ammonium group at one end of the chain, [(R-NH3)2MX4], or two ammonium groups at either of the chain, [(H3N-R-NH3)MX4]. Due to its similarity to the cubic perovskite structure, this inorganic motif is referred to as "layered perovskite-type". Depending on the choice of the organic ammonium cation, the materials can display phase transitions and / or have optical and electronic properties. Various investigations of inorganic-organic hybrids have concentrated on the phase transitions of the hybrids of general formula [(CnH2n+1NH3)2MX4] and [(NH3CnH2nNH3)MX4] (n = 1-18; X = Cl, Br, I; M = Cu2+, Mn2+, Cd2+) to elucidate their mechanism. There are two types of displasive transitions, a minor one were small conformational changes within the alkylammonium chain occurs, and a major one, when the entire alkylammonium chain becomes disordered along its long axis. The interlayer spacing between the inorganic layers increases with temperature and during the major phase transition. The methods used to identify the temperatures and the enthalpies of the phase transitions are Differential Scanning Calorimetry (DSC); and Single Crystal X-ray Diffraction (SC-XRD) as well as Powder X-Ray Diffraction (P-XRD) to follow the structural changes. In contrast, only a few reports on investigations of the lead iodide hybrids, [(CnH2n+1NH3)2PbI4] were found in the literature, with only two single crystal structures previously reported. Due to the difficulty in growing good quality crystals, the previous studies on the lead iodide hybrids have been only researched using DSC and P-XRD. The phase transition behaviour has been found to show the same trends as the previous hybrids. The primary aim of this study was to follow the same phase transitions via SC-XRD, ideally single-crystal to single-crystal, and to determine the detailed structural changes with the hopes of elucidating their detailed phase transition mechanism. A secondary aim was to synthesize as many inorganic-organic hybrids as possible using a variety of primary ammonium cations to find different inorganic motifs apart from the layered perovskite-type. Other inorganic motifs can have purely corner-, edge or face-sharing octahedra or combinations thereof to give 2-D net-type networks or 1-D extended chains. The effect that the identity of the ammonium cation has on the type of inorganic motif and the effect on the detailed structural geometry within the inorganic motif are investigated. Examples of structural geometries within the layered perovskite-type inorganic motif that can differ from compound to compound are the relative positions of the inorganic and organic moieties; the N---H….X hydrogen bonding geometry between the halides and the ammonium group; and the relative positions of successive inorganic layers.

A função partição do modelo SOS é analisada, mostrando heuristicamente que acima da transição de rugosidade, TR, este modelo se torna essencialmente um problema unidimensional. Os resultados para a rugosidade superficial e calor específico são comparados com uma simulação Monte Carlo de uma rede mxm (m=20, 40, 80, 100). Um novo modelo SOS unidimensional é introduzido o qual mostra um bom acordo para regiões de altas e baixas temperaturas com o modelo SOS bidimensional. Foi dedicada atenção especial na estimativa da temperatura de transição pelo método Monte Carlo, a qual foi estabelecida como sendo TR= 0.80. Através de um aprimoramento no método Monte Carlo, aplicado a um sistema contendo 224 discos duros, obteve-se o loop de van der Waals, indicando assim, uma coexistência de fases para densidades entre 1.29 &#60 &#964 &#60 1.36. Este resultado até então, só tinha sido obtido através da técnica dinâmica molecular para 870 discos / The partition function of the SOS model is analysed and it is shown heuristically that above the roughening transition temperature, TR, this model becomes essentially na one-dimensional problem. The results for the surface roughness and surface specific heat are compared with a Monte Carlo simulation of a mxm lattice (m= 20, 40, 80, 100). A new one-dimensional SOS model is introduced wich shows a good agreement with the ordinary two dimensional SOS model for low and high temperatures. Especial attention was paid for the Monte Carlo estimation of the roughening transition temperature which was stablished as being TR= 0.80. Through na improvement in the choice of the most representative configurations in the Monte Carlo procedure, applied to a system containing 224 hard disks, it was possible to obtain the van der Waals-type loop curve, showing then, a fase coexistence in a density range 1.29 &#60 &#964 &#60 1.36. This result has so far only been obtained by molecular dynamic procedure for 870 disks

The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific analysis of each model individually. In this thesis, we propose a potential classification method for time-dependent dynamical systems, namely comparing the possible deformations of the original problem, and identifying dynamical systems which share the same deformation space. The specific model on which this procedure is developed is the Kuramoto model for interacting, disordered oscillators. Studied in the mean-field limit by a variety of methods, its associated synchronization phase transition appears as an appropriate model for cooperative phenomena ranging from coupled Josephson junctions to self-ordering patterns in biological and social systems. We investigate the geometric deformation of the dynamical system into the space of univalent maps of the unit disk, related to the Douady-Earle extension and the Denjoy-Wolff theory, and separately the algebraic deformation into the space of nonlinear sigma models for unitary operators. The results indicate that the Kuramoto model is representative for a large class of non-equilibrium synchronization models, with a rich phase-space diagram.

Metal organic frameworks have gained much attention due to their tunable pore sizes and very high surface areas. With the discovery many of these type materials the need has raised to look into new applications of theses porous frameworks. This thesis focuses on the synthesis of a new perovskite-type metal organic framework and measurement of its thermal conductivity in search of its applicability as a thermoelectric material. The second part of this work focuses on the synthesis of a metal organic framework incorporated with a Lewis pair for the first time. The optimum loading amount of the Lewis pair into the framework was also investigated.

Orientador: Edson Denis Leonel / Resumo: Nesse trabalho, utilizaremos um autômato celular para investigar o problema de roubos e furtos residenciais. A partir de regras e critérios pré-estabelecidos, definimos o comportamento da difusão da criminalidade em uma cidade como função do tempo e dos seus parâmetros de controle. Utilizando um tratamento estatístico da criminalidade, nossos resultados indicam uma possível transição entre fase endêmica, onde o crime existe porém em baixa ocorrência, e uma fase epidêmica, onde o crime é desenfreado. / Abstract: In this work, we will use a cellular automata to investigate the problem of residential robberies. Starting from a set of rules and criteria, the diffusion of the crime is investigated either as a function of time as well function of the control parameters. Using a statistical treatment our results indicate a possible phase transition between endemic, where crime exists but in low occurrence, and epidemic where crime is rampant. / Mestre

Biological membranes mainly constituent lipid molecules along with some proteins and steroles. The properties of the pure lipid bilayers as well as in the presence of other constituents (in case of two or three component systems) are very important to be studied carefully to model these systems and compare them with the realistic systems. Molecular dynamic simulations provide a good opportunity to model such systems and to study them at microscopic level where experiments fail to do. In this thesis we study the structural and dynamic properties of the pure phospholipid bilayers and the phase behavior of phospholipid bilayers when other constituents are present in them. Material and structural properties like area per lipid and area compressibility of the phospholipids show a big scatter in experiments. These properties are studied for different system sizes and it was found that the increasing undulations in large systems effect these properties. A correction was applied to area per lipid and area compressibility using the Helfrich theory in Fourier space. Other structural properties like order of the lipid chains, electron density and radial distribution functions are calculated which give the structure of the lipid bilayer along the normal and in the lateral direction. These properties are compared to the X-ray and neutron scattering experiments after Fourier transform. Thermodynamic properties like heat capacity and heat of melting are also calculated from derivatives of energies available in molecular dynamics. Heat capacity on the other hand include quantum effect and are corrected for that by applying quantum correction using normal mode analysis for a simple as well as ambiguous system like water. Here it is done for SPC/E water model. The purpose of this study is to further apply the quantum corrections on macromolecules like lipids by using this technique. Furthermore the phase behavior of two component systems (phospholipids/cholesterol) is also studied. Phase transition in these systems is observed at different cholesterol concentrations as a function of temperature by looking at different quantities (as an order parameter) like the order of chains, area per molecule and partial specific area. Radial distribution functions are used to look at the in plane structure for different phases having a different lateral or positional order. Adding more cholesterol orders the lipid chains changing a liquid disordered system into a liquid ordered one and turning a solid ordered system into a liquid ordered one. Further more the free energy of domain formation is calculated to investigate the two phasecoexistence in binary systems. Free energy contains two terms. One is bulk freeenergy which was calculated by the chemical potential of cholesterol moleculein a homogeneous system which is favorable for segregation. Second is thefree energy of having an interface which is calculated from the line tension of the interface of two systems with different cholesterol concentration which in unfavorable for domain formation. The size of the domains calculated from these two contributions to the free energy gives the domains of a few nm in size. Though we could not find any such domains by directly looking at our simulations. / <p>QC 20120913</p>