First-principles methods based on Density functional theory (DFT) are now adopted routinely to calculate the properties of materials. However, one of the biggest challenges of DFT is to describe the electronic behaviors of random alloys. One of the aims of this thesis is to study binary alloys, e.g. Ti-Al, Cu-Au, and multi-component alloys by using two models for chemically random structures: the special quasi-random structure (SQS) and coherent potential approximation (CPA). I investigate these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. Within the SQS approach, the LLD effect can be modeled in a straightforward manner by relaxing the positions of atoms in the supercell. However, within this approach, it is difficult to model the random multi-components alloys due to the large size of the supercells. On the other hand, the CPA approach uses single-site approximation and thus it is not limited by the number of alloy components. But CPA suffers from the neglect of the local lattice relaxation effect, which in some systems and for some properties could be of significant importance. In my studies, the SQS and CPA approaches are combined with the pseudopotential method as implemented in the Vienna Ab-initio Simulation Package (VASP) and the Exact Muffin-Tin Orbitals (EMTO) methods, respectively. The mixing energies or formation enthalpies and elastic parameters of fcc Ti1-xAlx and Cu1-xAux (0 =&lt; x =&lt; 1) random solid solutions and high-entropy multicomponent TiZrVNb, TiZrNbMo and TiZrVNbMo alloys are calculated as a function of concentration. By comparing the results with and without local lattice relaxations, we find that the LLD effect is negligible for the elastic constants C11, C12, and C44. In general, the uncertainties in the elastic parameters associated with the symmetry lowering in supercell studies turn out to be superior to the differences between the two alloy techniques including the effect of LLD. However, the LLD effect on the mixing energies or formation enthalpies is significant and depends on the degree of size mismatch between alloy constituents. In the cases of random Cu-Au and high-entropy alloys, the formation enthalpies and mixing energies are significantly decreased when the LLD effect is considered. This finding sets the limitations of CPA for the mixing energies or formation enthalpies of alloys with large atomic size differences. The other goal of the thesis is to study the effect of exchange-correlation functionals on the formation energies of ordered alloys. For this investigation, we select the Cu-Au binary system which has for many years been in the focus of DFT and beyond DFT schemes. The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation term in DFT is a mature approach and have been adopted routinely to investigate the properties of metallic alloys. In most cases, PBE provides theoretical results in good agreement with experiments. However, the ordered Cu-Au system turned out to be a special case where large deviations between the PBE predictions and observations occur. In this work, we make use of a recently developed exchange-correlation functional, the so-called quasi-nonuniform exchange-correlation approximation (QNA), to calculate the lattice constants and formation energies for ordered Cu-Au alloys as a function of composition. The calculations are performed using the EMTO method and verified by a full-potential method. We find that the QNA functional leads to an excellent agreement between theory and experiment. The PBE strongly overestimates the lattice constants for ordered Cu3Au, CuAu, CuAu3 compounds and also for the pure metals which are nicely corrected by the QNA approach. The errors in the formation energies of Cu3Au, CuAu, CuAu3 relative to the experimental data decrease from 38-45% obtained with PBE to 5-9% calculated for QNA. This excellent result demonstrates that one can reach superior accuracy within DFT for the formation energies and there is no need to go beyond DFT. Furthermore, it shows that error cancellation can be very effective for the formation energies as well and that the main DFT errors obtained at PBE or LDA levels originate from the core-valence overlap region, which is correctly captured by QNA due to its particular construction. Our findings are now extended to disordered alloys, which is briefly discussed already in one of my published papers. / <p>Qc 20170630</p>

With the discovery of the quantum Hall effect more than thirty years ago, a whole new field emerged—that of topological quantum matter. This field is now a very mature one, and many different aspects are covered in the literature. The main text of this thesis introduces the field and gives a background to topological quantum matter, as well as topological aspects of superconductivity and the Abelian fractional quantum Hall (FQH) states.  Together with the main text there are five articles that address five different questions, all connected to topological quantum matter. In the first article, representative wave functions for the Abelian FQH states are calculated using conformal field theory methods. Before this paper was published, similar constructions had been restricted to flat geometries, but in this paper we generalize the analysis to the simplest curved geometry, namely the sphere. On top of being of interest for numerical studies (which usually are performed on a sphere), the response of the FQH liquids to curvature can be used to detect a topological quantity, the shift, which is the average orbital spin of the constituent electrons. In the second article, we construct an effective field theory for the two-dimensional spinless, chiral p-wave superconductor that faithfully describes the topological properties of the bulk state, and also provides a model for the subgap states at vortex cores and edges. In particular, it captures the topologically protected zero-modes and has the correct ground state degeneracy on the torus. In the third paper, tools for a hydrodynamic theory for insulators in three dimensions are derived. Specifically, we use functional bosonization to write insulators as a condensation phase of the U(1) gauge theory obtained in the functional bosonization language. In the fourth paper, we investigate the edge Majorana modes in the two-dimensional chiral p-wave superconductor. We define the model on surfaces with different geometries—the annulus, the cylinder, the Möbius band, and a cone—and with different configurations of magnetic flux threading holes in these surfaces. In particular, we address the following question: Given that, in the absence of magnetic flux, the ground state on the annulus does not support Majorana modes, while the one on the cylinder does, how is it possible that the conical geometry can interpolate smoothly between the two? In the fifth and last article, we demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. We propose this geo-Meissner effect as an unequivocal signature of chiral superconductivity that could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of Majorana modes. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 5: Manuscript.</p>

This work focuses on understanding deformation mechanisms and responsiveness associated with the wrinkling, folding, and snapping of thin polymer films. We demonstrated the use of elastic instabilities in confined regimes, such as the crumpling and snapping of surface attached sheets. We gained fundatmental insight into a thin film's ability to localize strain. By taking advantage of geometric strain localization we were able to develop new strategies for responsive surfaces that will have a broad impact on adhesive, optical, and patterning applications. Using the rapid closure of the Venus flytrap's leaflets as dictated by the onset of a snap instability as motivation, we created surfaces with patterned structures to transition through a snap instability at a prescribed stress state. This mechanism causes surface topography to change over large lateral length scales and very short timescales. Changes in the stress state can be related to triggers such as chemical swelling, light-induced architecture transitions, mechanical pressure, or voltage. The primary advantages of the snap transition are that the magnitude of change, the rate of change, and the sensitivity to change can be dictated by a balance of materials properties and geometry. The patterned structures that exhibit these dynamics are elastomeric shells that geometrically localize strain and can snap between concave and convex curvatures. We have demonstrated the control of the microlens shell geometry and that the transition time follows scaling relationships presented for the Venus flytrap. Furthermore, the microlens arrays have been demonstrated as surfaces that can alter wettability. Using a similar novel processing technique, microarrays of freestanding elastomeric plates were placed in equibiaxial compression to fabricate crumpled morphologies with strain localized regions that are difficult to attain through traditional patterning techniques. The microstructures that form can be initially described using classical plate buckling theory for circular plates under an applied compressive strain. Upon the application of increasing compressive strain, axisymmetric microstructures undergo a secondary bifurcation into highly curved, nonaxisymmetric structures. The inherent interplay between geometry and strain in these systems provides a mechanism for generating responsiveness in the structures. By swelling the elastomeric plates with a compatible solvent, we demonstrated the microstructures ability to reversibly switch between axisymmetric and nonaxisymmetric geometries. To further explore the localization of strain in materials, we have fabricated sharply folded films of glassy, homogenous polymers directly on rigid substrates. The films were uniaxially compressed and buckle after delaminating from the substrate. As the applied strain is increased, we observed strain localization at the center of the delaminated features. We found that normally brittle, polystyrene films can accommodate excessive compressive strains without fracture by undergoing these strain localizing fold events. This technique provided a unique way to examine the curvature and stability of folded features, but was not adequate for understanding the onset of folding. By taking thin films, either glassy or elastomeric, and simply lifting them from the surface of water, we observed and quantified the wrinkle-to-fold transition in an axisymmetric geometry. The films initially wrinkle as they are lifted with a wavelength that is determined by the film thickness and material properties. The wrinkle-to-fold transition is analogous to the transition observed in uniaxially compressed films, but the axisymmetric geometry caused the fold to act as a disclination that increased the radial stress in the film, thereby decreasing the wavelength of the remaining wrinkles. Further straining the films caused the remaining wrinkles to collapse into a discrete number of folds that is independent of film thickness and material properties.

Free-standing ultra-thin films and micro to nanoscale fibers offer a unique geometry in which to study the dynamics of thin film stability and polymer chain dynamics. By melting these films and investigating the subsequent processes of hole formation and growth, and fiber thinning and breakup, many interesting phenomena can be explored, including the nucleation of holes, shear-thinning during hole formation, finite-extensibility of capillary thinning viscoelastic fibers, and confinement effects on entanglement of polymer chains. Free-standing films in the melt are unstable and rupture due to instabilities. The mechanism of membrane failure and hole nucleation is modeled using an energy barrier approach which is shown to capture the dependence of hole nucleation on thickness. The formed holes grow exponentially and are found to grow under a shear thinning, nonlinear viscoelastic, high shear strain regime. These holes impinge upon each other to form suspended fibers. The fibers thin according to a model for the elasto-capillary thinning of the suspended viscoelastic fluid filaments. Monitoring fiber thinning allows for the acquisition of rheological properties as well as the transient, apparent extensional viscosity giving insight into strain hardening and eventual steady-state extensional viscosity. The decay and breakup of these fibers and their interconnected branched structure indicates the effects of confinement on chain entanglement in ultra-thin films. A transition below a critical film thickness, comparable to the dimensions of a polymer chain, shows drastically reduced interchain entanglements and a remarkably faster breakup of suspended fibers. The processes of fiber formation from the melting of ultra-thin films are explored in high detail and produce a new technique for the investigation of rheological and material properties, confinement effects, and the dynamics of thin films and polymer chains.

We have studied the wetting and self-assembly behavior of block copolymer thin films on chemical patterns in various geometries. Carboxylic-terminated, mesh-like patterns were generated on OTS modified silicon wafers by AFM electro-oxidation lithography. The films were pinned on the carboxylic regions due to the strong interaction of the minor component block with the surface which was also found to suppress film dewetting over the unpatterned methyl regions. We have found that the cylindrical microdomains orient normal to the methyl-terminated patterns and remain laterally confined within them. Defect-free, hexagonally packed cylindrical microdomains could be obtained thanks to the "corralling" action of the patterns. Domain deformation or point defects arose when the dimensions or shapes of the patterns were not commensurate with the natural packing of the copolymers. Tetragonal packing of microdomains was observed when a square-shaped confinement geometry, with dimension comparable to 2L 0 (natural period), was used. The stretching or compression of polymer chains was found to accomendate the incommensurable confinement imposed by chemical patterns, and a free energy model was applied for interpretation. Solvent annealing was conbined with chemical dot patterns to direct the self-assembly of block copolymers in thin films, and silicon oxide nanodots were fabricated through a tone-reversal process.

Wrinkles represent a pathway towards the spontaneous generation of ordered surface microstructure for applications in numerous fields. Examples of highly complex ordered wrinkle structures abound in Nature, but the ability to harness this potential for advanced material applications remains limited. This work focuses on understanding the relationship between the patterns on a wrinkled surface and the experimental conditions under which they form. Because wrinkles form in response to applied stresses, particular attention is given to the nature of the stresses in a wrinkling surface. The fundamental insight gained was then utilized to account for observed wrinkle formation phenomena within more complex geometric and kinetic settings. In order to carefully control and measure the applied stresses on a wrinkling film, a swelling-based system was developed using poly(dimethylsiloxane) (PDMS), surface-oxidized with a UV-ozone treatment. The swelling of the oxidized surface upon exposure to an ethanol vapor atmosphere was characterized using beam-bending experiments, allowing quantitative measurements of the applied stress. The wrinkle morphologies were characterized as a function of the overstress, defined as the ratio of the applied swelling stress to the critical buckling stress of the material. A transition in the dominant morphology of the wrinkled surfaces from dimple patterns to ridge patterns was observed at an overstress value of ∼2. The pattern dependence of wrinkles on the ratio of the principal stresses was examined by fabricating samples with a gradient prestress. When swollen, these samples exhibited a smooth morphological transition from non-equibiaxial to equibiaxial patterns, with prestrains as low as 2.5% exhibiting non-equibiaxial characteristics. This transition was seen both in samples with low and high overstresses. To explore the impact of these stress states in more complex geometries, wrinkling hemispherical surfaces with radii of curvature ranging from 50–1000 &mgr;m were fabricated using the same material system. Upon wrinkling, the hemispheres formed complex hierarchical assemblies reminiscent of naturally occurring structures. The curvature of a surface exhibited a correlation with its critical buckling stress, independent of other factors. This enables the surface curvature to be used as an independent control over the dimple-to-ridge transition which occurs as a function of overstress. As in the flat buckling surfaces, this transition was shown to occur at an overstress value of ∼2. Surface curvature was also shown to improve the observed hexagonal ordering of the dimple arrays, resulting in the formation of regular "golf ball" structures. Geometric effects in finite flat plates were also examined. Using circular masks during the oxidation process, plates with radii ranging from 0.4–8.6 mm were created. Upon wrinkling, a dimple-to-ridge transition was observed with increasing plate size, with the morphological switch occurring at a radius of ∼2 mm. This observed transition was not found to be due to the inherent mechanics of plates of different sizes, but instead to a reduction in the oxide conversion due to shadowing or stagnation caused by the masking process, which lowered the applied overstress. The shape of the finite plate was found to have little impact on the resulting wrinkle morphologies. Kinetic aspects of wrinkling were qualitatively characterized by observing the wrinkling process over the course of swelling. Wrinkling was observed to frontally propagate across the surface, and the ordering of the patterns which developed showed a qualitative correlation with the degree of uniformity in the advancing wrinkle front. Swelling with different solvents was found to lead to the formation of different patterns, based on the swelling kinetics of the UVO-treated PDMS upon exposure to each solvent.

We work with two different mechanisms to generate geometric frustration on thin elastic sheets; isotropic differential growth and folding. We describe how controlled growth and prescribing folding patterns are useful tools for designing three-dimensional objects from information printed in two dimensions. The first mechanism is inspired by the possibility to control shapes by swelling polymer films, where we propose a solution for the problem of shape formation by asking the question, “what 2D metric should be prescribed to achieve a given 3D shape?”', namely the reverse problem. We choose two different types of initial configurations of sheets, disk-like with one boundary and annular with two boundaries. We demonstrate our technique by choosing four examples of 3D axisymmetric shapes and finding the respective swelling factors to achieve the desired shape. Second, we present a mechanical model for a single curved fold that explains both the buckled shape of a closed fold and its mechanical stiffness. The buckling arises from the geometrical frustration between the prescribed crease angle and the bending energy of the sheet away from the crease. This frustration increases as the sheet's area increases. Stiff folds result in creases with constant space curvature while softer folds inherit the broken symmetry of the buckled shape. We extend the application of our numerical model to show the potential to study multiple fold structures.

Mesoporous materials are being widely used in the chemical industry in various environmentally friendly separation processes and as catalysts. Our research can be broadly described as an effort to understand the behavior of fluids confined in such materials. More specifically we try to understand the influence of state variables like temperature and pore variables like size, shape, connectivity and structural heterogeneity on both the dynamic and equilibrium behavior of confined fluids. The dynamic processes associated with the approach to equilibrium are largely unexplored. It is important to look into the dynamic behavior for two reasons. First, confined fluids experience enhanced metastabilities and large equilibration times in certain classes of mesoporous materials, and the approach to the metastable/stable equilibrium is of tremendous interest. Secondly, understanding the transport resistances in a microscopic scale will help better engineer heterogeneous catalysts and separation processes. Here we present some of our preliminary studies on dynamics of fluids in ideal pore geometries. The tool that we have used extensively to investigate the relaxation dynamics of fluids in pores is the dynamic mean field theory (DMFT) as developed by Monson [P. A. Monson, J. Chem. Phys., 128, 084701 (2008)]. The theory is based on a lattice gas model of the system and can be viewed as a highly computationally efficient approximation to the dynamics averaged over an ensemble of Kawasaki dynamics Monte Carlo trajectories of the system. It provides a theory of the dynamics of the system consistent with the thermodynamics in mean field theory. The nucleation mechanisms associated with confined fluid phase transitions are emergent features in the calculations. We begin by describing the details of the theory and then present several applications of DMFT. First we present applications to three model pore networks (a) a network of slit pores with a single pore width; (b) a network of slit pores with two pore widths arranged in intersecting channels with a single pore width in each channel; (c) a network of slit pores with two pore widths forming an array of ink-bottles. The results illustrate the effects of pore connectivity upon the dynamics of vapor liquid phase transformations as well as on the mass transfer resistances to equilibration. We then present an application to a case where the solid-fluid interactions lead to partial wetting on a planar surface. The pore filling process in such systems features an asymmetric density distribution where a liquid droplet appears on one of the walls. We also present studies on systems where there is partial drying or drying associated with weakly attractive or repulsive interactions between the fluid and the pore walls. We describe the symmetries exhibited by the lattice model between pore filling for wetting states and pore emptying for drying states, for both the thermodynamics and dynamics. We then present an extension of DMFT to mixtures and present some examples that illustrate the utility of the approach. Finally we present an assessment the accuracy of the DMFT through comparisons with a higher order approximation based on the path probability method as well as Kawasaki dynamics.

The development of a high-throughput impedance spectroscopy instrumentation platform for conductivity characterization of ion transport materials is outlined. Collaborative studies using this system are summarized. Charge conduction mechanisms and conductivity data for small molecule proton conducting liquids, pyrazole, imidazole, 1,2,3-triazole, 1,2,4-triazole, and select mixtures of these compounds are documented. Furthermore, proton diffusivity measurements using a Pulse Field Gradient Nuclear Magnetic Resonance (PFG NMR) technique for imidazole and 1,2,3-triazole binary mixtures are compared. Studies of azole functionalized discotic and linear mesogens with conductivity, structural, and thermal characterizations are detailed.

A wide variety of applications from drug delivery and artificial tissues to sensors and actuators require responsive, "smart" materials. Polyelectrolyte hydrogels show a great sensitivity to stimuli in that small changes in electric potential, salt concentration, or solvent composition can induce dramatic volume changes. These materials have been shown to mimic the response of nerve and muscle tissue to identical stimuli. The goal of this research is to use dynamic light scattering to catalog the effects of molecular architecture and chemical environment on the properties of polymer hydrogels. This will reveal the underlying physics of these systems, so that future materials can be designed to exhibit desired, tunable responses.