We present a new approach to solid solution thermodynamics using the concept of cell theory. We looked particularly at the influence of packing effects on freezing. To isolate this contribution we studied substitutionally ordered and substitutionally disordered binary hard sphere solid solutions. The absence of long range interactions makes the influence of inhomegeneities in composition and molecular sizes readily measurable. Such mixtures not only exhibit a freezing transition but the shape of the pressure-composition phase diagram depends drastically on the size difference between particles. Our predictions agree well with available Monte Carlo simulation results. In the case of substitutionally disordered binary hard sphere mixtures our predictions also agree with the Hume-Rothery rule which states that a substitutionally disordered binary alloy cannot exist for size differences greater than 15%. This approach is also capable of predicting the formation of some compounds such as AB (NaCl structure) $AB\sb2$ $(AlB\sb2$ structure) and $AB\sb{13}$ $(NaZn\sb{13}$ structure) as well as their domain of stability in terms of molecular size differences. The similarity between the solid-fluid phase diagrams we obtained in the case of binary hard sphere mixtures and that of binary organic systems is a sign that packing effects may actually play a much more important role in the freezing of real mixtures than what was previously believed. To investigate this question and broaden the applicability of our approach we added attractive forces in the form of a 12-6 Lennard-Jones potential to our model. Predictions for the pure component were in good agreement with published simulation results, especially when correlations between the motions of the particles were considered. In the binary case such correlations were not included for simplicity. Preliminary results obtained at constant pressure indicate that the size ratio of the particles dictates the overall shape of the solid-fluid phase diagram while the effect of attractive interactions is to position the diagram in terms of temperature. In addition, the equilibrium lines are relatively insensitive to pressure. A comparison with experimental data for methane and rare gas mixtures was done and yielded good qualitative agreement.

Numerical simulation was used to analyze performance of Si$\sb{1-x}$Ge$\sb{x}$ pseudomorphic heterojunction bipolar transistors (PHBTs). Models for different material properties were developed and used in 2-D drift-diffusion-equations and 1-D hydrodynamic-equations simulation programs. N-p-N and P-n-P PHBTs were analyzed. For N-p-N PHBTs both metal- and poly-Si-emitter contacts were investigated. The figures of merit used are unity current gain frequency f$\sb{T}$ and maximum frequency of oscillation f$\sb{max}$. In all cases analyzed, Si$\sb{1-x}$Ge$\sb{x}$ offers significant advantages over equivalent Si devices: metal emitter N-p-N Si$\sb{1-x}$Ge$\sb{x}$ devices can have f$\sb{T}$ up to two to three times higher than Si; poly-Si emitter N-p-N Si$\sb{1-x}$Ge$\sb{x}$ up to 50% or more higher f$\sb{T}$; P-n-P metal-emitter Si$\sb{1-x}$Ge$\sb{x}$ devices shows similar improvements. f$\sb{max}$ is also improved in all devices, but not as much as f$\sb{T}$. Some devices are actually limited by their f$\sb{max}$ and not f$\sb{T}$ and to improve their performance, f$\sb{max}$ must be increased first by reducing parasitic resistances and capacitances.

Due to the presence of long-ranged electrostatic interactions, polyelectrolyte solutions are characterized by a length scale in addition to the radius of gyration and the correlation length, the Debye screening length. Contrasted to the behavior observed in neutral polymer solutions in which miscibility is controlled by molecular weight and temperature, the inverse-square Debye length additionally controls polyelectrolyte phase behavior. This thesis project experimentally investigated the influence of added barium chloride on both the collective and configurational properties of a model polyelectrolyte, sodium-poly (styrene sulfonate). Regarding the collective properties the crossover from mean field to Ising criticality close to the precipitation phase boundary was measured. This crossover was demonstrated for both salt-dependent and temperature-dependent thermodynamics. A mean field model qualitatively describes the collective behavior in polyelectrolyte solutions as a competition between a short-ranged chemical mismatch, governed by a Flory-Huggins interaction parameter, that disfavors miscibility and a repulsive screened-Coulombic interaction between monomers that favors miscibility. The addition of salt screens the electrostatic interaction such that it becomes short-ranged, leading to the observed precipitation at fixed temperature. Similarly, for a fixed salt concentration, the solvent quality is tuned and precipitation is observed upon lowering temperature. The configurational properties of labeled chains were also examined as a function of molecular weight, polymer concentration, and salt concentration. In solutions without any added salts, we observe scaling laws for low-ionic strength semidilute polyelectrolyte solutions in agreement with the double screening theory. These scaling laws, along with the adequate fits of the labeled chain structure factor with the Debye structure factor, highlight the concept of screening in semidilute solutions and polyelectrolytes obeys Gaussian chain statistics on length scales of the order of a renormalized Kuhn length. Significant coil contraction is measured upon the addition of the multivalent salt. Upon comparing the correlation length, the radius of gyration, and the Debye length, the radius of gyration remains the dominant length scale in the system, until a crossover is observed as the correlation length diverges and surpasses the labeled chain dimension with increased ionic strength. The double screening theory was applied to understand the dependence of size of the labeled chains as functions of polymer concentration and added multivalent salt. It was necessary to include the influence of ion-pairing into a salt-concentration de pendent degree of ionization. Such ion-pair formation is also necessary to calculate phase diagrams with better qualitative agreement with experimental data. These initial efforts should foster strong theoretical and simulation studies and further experimentation in the area of polyelectrolyte solutions.

This dissertation discusses the effects of shape anisotropy on the evolved microstructure of diblock copolymers at various levels. Due to chain connectivity and microphase separation, the diblock copolymers self-assemble into ellipsoidal grains of lamellar and cylindrical morphologies. A grain-structure related phenomenon, Excluded Volume Epitaxy (E.V.E.) is explored in Chapter 2. E.V.E. is a local, inter-grain azimuthal orientational correlations effect, which results from a combination of sporadic nucleation and impingement of growing anisotropic shaped grains. Due to E.V.E., the ellipsoidal grains have a propensity for similar orientations in a local neighborhood, despite complete absence of global orientation in the sample. Simulations and experiments have verified this effect. The Avrami kinetics of anisotropic shaped grains is discussed in Chapter 3. Traditionally Avrami equation is used to model the growth kinetics of volume filling isotropic shaped grains. The probabilistic nature of Avrami kinetics produces a coupling between the grain shape and Poisson distribution. The Poisson-shape coupling remains latent for isotropic grains but becomes operative for anisotropic grains in random orientations scheme leading to inhibited growth kinetics. For unidirectional orientation of anisotropic grains, the growth kinetics remains uninhibited due to absence of Poisson-shape coupling. For two-dimensional case in simultaneous and continuous nucleation regimes, the inhibited kinetics scales as L1/2 where L is the shape anisotropy. The blends of highly shape anisotropic nanoclay, montmorillonite (MMT) and lamellar poly(styrene-b-isoprene), PS-PI are discussed in Appendix A. Annealing and cooling is sufficient to produce long-range lamellar order at 1 wt % clay loading. However at 5 wt % clay loading, shear force is additionally required. This system reveals the effect of shape anisotropy on evolution of long-range order in clay-block copolymer blends. The effect of shape anisotropy of polymer chain in the context of rod-coil block copolymer is explored in Appendix B. Poly(styrene-b-1,3-cyclohexadiene), PS-PCHD self-assembles into core-shell cylinder structure, seen rarely in AB diblock copolymers. A rod-coil free energy model that incorporates liquid crystalline splay distortion energy in the rod phase is presented. In this model, the PCHD block is treated as rod to explain the stability of the core-shell cylinder structure.

Disordered materials, such as window glass, powders, gels, concentrated emulsions, differ tremendously in their microscopic detail, there is increasing evidence that they belong to a more general phenomenon known as jamming. The response of disordered materials to applied stresses is a particularly interesting but difficult problem with broad applications in many fields. Using confocal microscopy, we performed systematic and detailed measurements of inter-drop contact forces inside three-dimensional piles of frictionless liquid droplets. We found chain-like structures of contact forces called force chains and measured long-range correlations of the directions and magnitudes of large forces. These correlations arise from the tendency of two largest forces on a droplet to oppose one another. Furthermore, we found that piles whose height was comparable to the length of force chains exhibited greater strain hardening than did tall piles. Thus, we established a connection between the microscopic force network and the elastic response of meso- or macroscopic disordered materials. A statistical model that incorporates the force-balance constraint and that assumes random orientation of contacts, confirmed the tendency of two large forces on a grain to oppose each other, which leads to the formation of force chains in disordered materials. This model also provided direct insight into other issues, such as the role of friction, the effects of stress anisotropy, the difference between two-dimensional materials and three-dimensional materials. The numerical results obtained from the model are qualitatively consistent with earlier simulations and experiments.

No description available.

This thesis is a theoretical study of the effects of vibrational degrees of freedom on the polariton physics. The work is motivated by recent experiments, which show that by allowing light to strongly couple with organic matter (inside a microcavity), polariton condensation can occur at room temperature. We begin by introducing a model, which describes localised electronic excitations of molecules coupled to cavity photon modes. The additional feature is the coupling between electronic excitations and local vibrational modes of molecules. Investigations of equilibrium phase diagrams and absorption spectra of the system (with a single cavity mode and without disorder) have revealed that coupling to vibrational modes acts to suppress the effective light-matter strength, can give rise to a sequence of normal-condensed-normal transitions as a function of temperature, and can drive the phase transition first order. We have also found that despite the vibrational sidebands existing at energies below the lower polariton, they cannot result in condensation, though their admixture has been found in the state which acquires macroscopic occupation. Secondly, we focused on the effects of excitonic disorder and the possibility of the ground state reconfiguration in ultra-strong coupling regime, with the aim to explain the temperature dependence of absorption spectra published in [A. Canaguier-Durand et al. Angew. Chem. Int. Ed. 52, 10533 (2013)]. We have found that the latter mechanism, although not impossible, could not result in any observable changes as, for the experimental parameters, it is too weak. The study of absorption spectra in the presence of disorder has revealed that the temperature dependence can be accounted for by the vibrational dressing of electronic transitions.

Over the last several years considerable efforts have been made to develop Bose-Einstein condensate (BEC) based devices for a number of applications including fundamental research, precision measurements, and navgation systems. These devices, capable of complex functionality, can be built from simpler components which is currently done in both optics and microelectronics. These components include cold atom equivalents of beamsplitters, mirrors, waveguides, diodes, and transistors. The operation of the individual components must be fully understood before they can be assembled into a more complex device. The primary goal of this dissertation is to present a theoretical analysis of these components. It begins with a theoretical analysis of several different types of cold-atom beamsplitters in the context of BEC interferometry. Next, the dynamics of an interferometer that uses optical pulses to control the dynamics of the BEC will be presented. Finally, a proposal for a BEC based component that has behavior that is similar to an electronic transistor is introduced.

In this thesis we present a theoretical analysis of the instability in a cold atom interferometer. Interferometers are often used to split a signal (e.g. optical beam, matter wave), where each part of the signal evolves separately, then the interferometer recombines the signal. Interference effects from the recombination can be used to extract information about the different environments the the split signal traversed. The interferometer considered here splits a matter wave, the wave function of a Bose-Einstein Condensate, by using a guiding potential and then recombines the matter wave. The recombination process is shown to be unstable and the nature of the instability is characterized.

DNA condensation is a fundamental process in all living organisms. The highly abundant nucleoid-associated proteins, HU and IHF, present in bacteria, have been shown to play an important role in shaping the nucleoid. However, the exact mechanism is not well understood. In this thesis, we have demonstrated that both HU and IHF guide DNA to condense into linear bundle-like structures in presence of cellular condensing components, but the proteins alone do not condense DNA into densely packed structures. Our results suggest a mechanism by which HU and IHF could act as architectural proteins during in vitro and in vivo DNA condensation. More recently, DNA condensation has attracted much attention for its relevance in optimizing artificial DNA delivery systems for gene therapy. The research presented in this dissertation provides in depth biophysical studies that demonstrate how local modulations in the nucleic acid structure can be used to control both the size and the morphology DNA condensates. We describe a novel strategy for improving the condensation of oligonucleotides that is based on the self-organization of half-sliding complementary oligonucleotides into long duplexes (ca. kb) with flexible sites at regular intervals along the duplex backbones, in the form of single-stranded nicks or single-stranded gaps. Our results also provide new insights into the role of DNA flexibility in condensate formation and suggest the potential for the use of this DNA structure in the design of vectors for oligonucleotide and gene delivery.