Principal Component Analysis of Results Obtained from Finite-Difference Time-Domain Algorithms

Finite-Differences Time-Domain (FDTD) algorithms are well established tools of computational electromagnetism. Because of their practical implementation as computer codes, they are affected by many numerical artefact and noise. In order to obtain better results we propose using Principal Component Analysis (PCA) based on multivariate statistical techniques. The PCA has been successfully used for the analysis of noise and spatial temporal structure in a sequence of images. It allows a straightforward discrimination between the numerical noise and the actual electromagnetic variables, and the quantitative estimation of their respective contributions. Besides, The GDTD results can be filtered to clean the effect of the noise. In this contribution we will show how the method can be applied to several FDTD simulations: the propagation of a pulse in vacuum, the analysis of two-dimensional photonic crystals. In this last case, PCA has revealed hidden electromagnetic structures related to actual modes of the photonic crystal.

Pitting and porous layer formation on n-InP anodes

Surface pitting occurs when InP electrodes are anodized in KOH electrolytes at concentrations in the range 2 - 5 mol dm-3. The process has been investigated using atomic force microscopy (AFM) and the results correlated with cross-sectional transmission electron microscopy (TEM) and electroanalytical measurements. AFM measurements show that pitting of the surface occurs and the density of pits is observed to increase with time under both potentiodynamic and potentiostatic conditions. This indicates a progressive pit nucleation process and implies that the development of porous domains beneath the surface is also progressive in nature. Evidence for this is seen in plan view TEM images in which individual domains are seen to be at different stages of development. Analysis of the cyclic voltammograms of InP electrodes in 5 mol dm-3 KOH indicates that, above a critical potential for pit formation, the anodic current is predominantly time dependent and there is little differential dependence of the current on potential. Thus, pores continue to grow with time when the potential is high enough to maintain depletion layer breakdown conditions.

Interference lithography for optical devices and coatings

Interference lithography can create large-area, defect-free nanostructures with unique optical properties. In this thesis, interference lithography will be utilized to create photonic crystals for functional devices or coatings. For instance, typical lithographic processing techniques were used to create 1, 2 and 3 dimensional photonic crystals in SU8 photoresist. These structures were in-filled with birefringent liquid crystal to make active devices, and the orientation of the liquid crystal directors within the SU8 matrix was studied. Most of this thesis will be focused on utilizing polymerization induced phase separation as a single-step method for fabrication by interference lithography. For example, layered polymer/nanoparticle composites have been created through the one-step two-beam interference lithographic exposure of a dispersion of 25 and 50 nm silica particles within a photopolymerizable mixture at a wavelength of 532 nm. In the areas of constructive interference, the monomer begins to polymerize via a free-radical process and concurrently the nanoparticles move into the regions of destructive interference. The holographic exposure of the particles within the monomer resin offers a single-step method to anisotropically structure the nanoconstituents within a composite. A one-step holographic exposure was also used to fabricate self- healing coatings that use water from the environment to catalyze polymerization. Polymerization induced phase separation was used to sequester an isocyanate monomer within an acrylate matrix. Due to the periodic modulation of the index of refraction between the monomer and polymer, the coating can reflect a desired wavelength, allowing for tunable coloration. When the coating is scratched, polymerization of the liquid isocyanate is catalyzed by moisture in air; if the indices of the two polymers are matched, the coatings turn transparent after healing. Interference lithography offers a method of creating multifunctional self-healing coatings that readout when damage has occurred.

Mesoscale Optoelectronic Design of Wire-Based Photovoltaic and Photoelectrochemical Devices

The overarching theme of this thesis is mesoscale optical and optoelectronic design of photovoltaic and photoelectrochemical devices. In a photovoltaic device, light absorption and charge carrier transport are coupled together on the mesoscale, and in a photoelectrochemical device, light absorption, charge carrier transport, catalysis, and solution species transport are all coupled together on the mesoscale. The work discussed herein demonstrates that simulation-based mesoscale optical and optoelectronic modeling can lead to detailed understanding of the operation and performance of these complex mesostructured devices, serve as a powerful tool for device optimization, and efficiently guide device design and experimental fabrication efforts. In-depth studies of two mesoscale wire-based device designs illustrate these principles—(i) an optoelectronic study of a tandem Si|WO3 microwire photoelectrochemical device, and (ii) an optical study of III-V nanowire arrays.

The study of the monolithic, tandem, Si|WO3 microwire photoelectrochemical device begins with development and validation of an optoelectronic model with experiment. This study capitalizes on synergy between experiment and simulation to demonstrate the model’s predictive power for extractable device voltage and light-limited current density. The developed model is then used to understand the limiting factors of the device and optimize its optoelectronic performance. The results of this work reveal that high fidelity modeling can facilitate unequivocal identification of limiting phenomena, such as parasitic absorption via excitation of a surface plasmon-polariton mode, and quick design optimization, achieving over a 300% enhancement in optoelectronic performance over a nominal design for this device architecture, which would be time-consuming and challenging to do via experiment.

The work on III-V nanowire arrays also starts as a collaboration of experiment and simulation aimed at gaining understanding of unprecedented, experimentally observed absorption enhancements in sparse arrays of vertically-oriented GaAs nanowires. To explain this resonant absorption in periodic arrays of high index semiconductor nanowires, a unified framework that combines a leaky waveguide theory perspective and that of photonic crystals supporting Bloch modes is developed in the context of silicon, using both analytic theory and electromagnetic simulations. This detailed theoretical understanding is then applied to a simulation-based optimization of light absorption in sparse arrays of GaAs nanowires. Near-unity absorption in sparse, 5% fill fraction arrays is demonstrated via tapering of nanowires and multiple wire radii in a single array. Finally, experimental efforts are presented towards fabrication of the optimized array geometries. A hybrid self-catalyzed and selective area MOCVD growth method is used to establish morphology control of GaP nanowire arrays. Similarly, morphology and pattern control of nanowires is demonstrated with ICP-RIE of InP. Optical characterization of the InP nanowire arrays gives proof of principle that tapering and multiple wire radii can lead to near-unity absorption in sparse arrays of InP nanowires.

Photonic characteristics of Langmuir-Blodgett self-assembled monolayers of colloidal silica particles

Monodispersed colloidal crystals based on silica sub-micrometric particles were synthesized using the Stöber-Fink-Bohn process. The control of nucleation and coalescence result in improved characteristics such as high sphericity and very low size dispersion. The resulting silica particles show characteristics suitable for self-assembling across large areas of closely-packed 2D crystal monolayers by an accurate Langmuir-Blodgett deposition process on glass, fused silica and silicon substrates. Due to their special optical properties, colloidal films have potential applications in fields including photonics, electronics, electro-optics, medicine (detectors and sensors), membrane filters and surface devices. The deposited monolayers of silica particles were characterized by means of FESEM, AFM and optical transmittance measurements in order to analyze their specific properties and characteristics. We propose a theoretical calculation for the photonic band gaps in 2D systems using an extrapolation of the photonic behavior of the crystal from 3D to 2D. In this work we show that the methodology used and the conditions in self-assembly processes are decisive for producing high-quality two-dimensional colloidal crystals by the Langmuir-Blodgett technique.

Influence of the molecular weight in mechanical properties and degradation kinetics of chitosan inverted colloidal crystals

Tissue engineering arises from the need to regenerate organs and tissues, requiring the development of scaffolds, which can provide an optimum environment for tissue growth. In this work, chitosan with different molecular weights was used to develop biodegradable 3D inverted colloidal crystals (ICC) structures for bone regeneration, exhibiting uniform pore size and interconnected network. Moreover, in vitro tests were conducted by studying the influence of the molecular weight in the degradation kinetics and mechanical properties. The production of ICC included four major stages: fabrication of microspheres; assembly into a cohesive structure, polymeric solution infiltration and microsphere removal. Chitosan’s degree of deacetylation was determined by infrared spectroscopy and molecular weight was obtained via capillary viscometry. In order to understand the effect of the molecular weight in ICC structures, the mass loss and mechanical properties were analyzed after degradation with lysozyme. Structure morphology observation before and after degradation was performed by scanning electron microscopy. Cellular adhesion and proliferation tests were carried out to evaluate ICC in vitro response. Overall, medium molecular weight ICC revealed the best balance in terms of mechanical properties, degradation rate, morphology and biological behaviour.

Temperature Sensing Using Colloidal-Core Photonic Crystal Fiber

We report on a temperature sensor based on the monitoring of the luminescence spectrum of CdSe/ZnS nanocrystals, dispersed in mineral oil and inserted into the core of a photonic crystal fiber. The high overlap between the pump light and the nanocrystals as well as the luminescence guiding provided by the fiber geometry resulted in relatively high luminescence powers and improved optical signal-to-noise ratio (OSNR). Also, both core end interfaces were sealed so as to generate a more stable and robust waveguide structure. Temperature sensitivity experiments indicated a 70 pm/degrees C spectral shift over the 5 degrees C to 90 degrees C range.

Defects in thermosensitive colloidal crystals

Poly-N-Isopropylacrylamide (PNIPAM) colloidal particles form crystal phases that show a thermosensitive behaviour and can be used as atomic model systems. This polymer has both hydrophilic and hydrophobic character and has interesting stimuli-responsive properties in aqueous solution, of which the most important is the temperature response. Above a certain temperature, called Lower Critical Solution Temperature (LCST), the system undergoes a volume phase transition (VPT). Above the LCST, the water is expelled from the polymer network and the swollen state at low temperature transforms into a shrunken state at high temperature. The thermoresponsive behaviour of PNIPAM can be influenced by pH and ionic strength, as well as by the presence of copolymers, such as acrylic acid. In a system formed both by particles of PNIPAM and PNIPAM doped with acrylic acid, one can control the size ratio of the two components by changing the temperature of the mixture, while keeping particle interactions relatively the same. It is therefore possible to obtain thermoresponsive colloidal crystal in which temperature changes induce defects whose formation processes and dynamics can be analysed in an optical microscope at a convenient spatial and temporal scale. The goal of this thesis project was to find the conditions in which such a system could be formed, by using characterization techniques such as Static Light Scattering, Dynamic Light Scattering and Confocal Laser Scanning Microscopy. Two PNIPAM-AAc systems were available, and after characterization it was possible to select a suitable one, on the basis of its low polydispersity and the lack of a VPT, regardless of the external conditions (system JPN_7). The synthesis of a PNIPAM system was attempted, with particles of dimensions matching the JPN_7 system and, unlike JPN_7, displaying a VPT, and one suitable candidate for the mixed system was finally found (system CB_5). The best conditions to obtain thermoresponsive crystal were selected, and the formation and healing of defects were investigated with CLSM temperature scans. The obtained results show that the approach is the correct one and that the present report could represent a useful start for future developments in defect analysis and defect dynamics studies.

Computer simulations of two-dimensional colloidal crystals in confinement

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two ``walls'' providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-) long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y-direction along the walls then crosses over from the logarithmic increase (characteristic for $d=2$) to a linear increase (characteristic for d=1). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising- and XY-models is made

Computer simulations of two-dimensional colloidal crystals under confinement and shear

In this thesis we are presenting a broadly based computer simulation study of two-dimensional colloidal crystals under different external conditions. In order to fully understand the phenomena which occur when the system is being compressed or when the walls are being sheared, it proved necessary to study also the basic motion of the particles and the diffusion processes which occur in the case without these external forces. In the first part of this thesis we investigate the structural transition in the number of rows which occurs when the crystal is being compressed by placing the structured walls closer together. Previous attempts to locate this transition were impeded by huge hysteresis effects. We were able to determine the transition point with higher precision by applying both the Schmid-Schilling thermodynamic integration method and the phase switch Monte Carlo method in order to determine the free energies. These simulations showed not only that the phase switch method can successfully be applied to systems with a few thousand particles and a soft crystalline structure with a superimposed pattern of defects, but also that this method is way more efficient than a thermodynamic integration when free energy differences are to be calculated. Additionally, the phase switch method enabled us to distinguish between several energetically very similar structures and to determine which one of them was actually stable. Another aspect considered in the first result chapter of this thesis is the ensemble inequivalence which can be observed when the structural transition is studied in the NpT and in the NVT ensemble. The second part of this work deals with the basic motion occurring in colloidal crystals confined by structured walls. Several cases are compared where the walls are placed in different positions, thereby introducing an incommensurability into the crystalline structure. Also the movement of the solitons, which are created in the course of the structural transition, is investigated. Furthermore, we will present results showing that not only the well-known mechanism of vacancies and interstitial particles leads to diffusion in our model system, but that also cooperative ring rotation phenomena occur. In this part and the following we applied Langevin dynamics simulations. In the last chapter of this work we will present results on the effect of shear on the colloidal crystal. The shear was implemented by moving the walls with constant velocity. We have observed shear banding and, depending on the shear velocity, that the inner part of the crystal breaks into several domains with different orientations. At very high shear velocities holes are created in the structure, which originate close to the walls, but also diffuse into the inner part of the crystal.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

Monte Carlo simulations of nucleation of colloidal crystals

A crystal nucleus in a finite volume may exhibit phase coexistence with a surrounding fluid. The thermodynamic properties of the coexisting fluid (pressure and chemical potential) are enhanced relative to their coexistence values. This enhancement is uniquely related to the surface excess free energy. rnA model for weakly attractive soft colloidal particles is investigated, the so called Asakura-Oosawa model. In simulations, this model allows for the calculation of the pressure in the liquid using the virial formula directly. The phase coexistence pressure in the thermodynamic limit is obtained from the interface velocity method. We introduce a method by which the chemical potential in dense liquids can be measured. There is neither a need to locate the interface nor to compute the anisotropic interfacial tension to obtain nucleation barriers. Therefore, our analysis is appropriate for nuclei of arbitrary shape. Monte Carlo simulations over a wide range of nucleus volumes yield to nucleation barriers independent from the total system volume. The interfacial tension is determined via the ensemble-switch method, hence a detailed test of classical nucleation theory is possible. The anisotropy of the interfacial tension and the resulting non-spherical shape has only a minor effect on the barrier for the Asakura-Oosawa model.

Photonic Logic Based on Molecular Reorientation of Nematic Liquid Crystals

A new type of photonic logic, based on the use of nematic liquid crystals is proposed. The system takes advantage of the refractive-index changes induced by laser beams. Examples of AND, OR and NOR functions are presented.

Properties of patchy colloidal particles close to a surface: a Monte Carlo and density functional study

We investigate the behavior of a patchy particle model close to a hard-wall via Monte Carlo simulation and density functional theory (DFT). Two DFT approaches, based on the homogeneous and inhomogeneous versions of Wertheim's first order perturbation theory for the association free energy are used. We evaluate, by simulation and theory, the equilibrium bulk phase diagram of the fluid and analyze the surface properties for two isochores, one of which is close to the liquid side of the gas-liquid coexistence curve. We find that the density profile near the wall crosses over from a typical high-temperature adsorption profile to a low-temperature desorption one, for the isochore close to coexistence. We relate this behavior to the properties of the bulk network liquid and find that the theoretical descriptions are reasonably accurate in this regime. At very low temperatures, however, an almost fully bonded network is formed, and the simulations reveal a second adsorption regime which is not captured by DFT. We trace this failure to the neglect of orientational correlations of the particles, which are found to exhibit surface induced orientational order in this regime.