This research was designed to fabricate and characterize novel polyhedral phase segregated microstructures of polystyrene (PS)-matrix composites filled with multi-walled carbon nanotubes (MWNT) and indium tin oxide (ITO) nanopowders. PS-composites were compression molded with MWNT and ITO separately first. The resulting composites were conducting, and remained optically transparent. Mixtures of MWNT and ITO were then used to form mixed ITO/MWNT PS-composites in order to optimize their transparency and conductivity. This was achieved by fabricating composites with varying concentrations of fillers. Impedance spectroscopy was used to characterize the electrical properties of the PS-composites. Optical properties were characterized by measuring the transmission of light through the PS-composite in the visible light spectrum using a spectrophotometer. The electrical properties and microstructural attributes of the fillers used were also characterized. The main objective of the project was to understand the relationships between the structural, electrical, and optical properties of the PS-composites. The resistivity of PS-composites filled with MWNT ranged from 105 to 1013 Ω cm for samples with 0.007 to 0.9 vol% MWNT. The resistivity of PS-composites filled with ITO ranged from 107 to 1013 Ω cm for PS-composites with 0.034 to 0.86 vol% ITO. PS/ITO composites had a percolation threshold of 0.15, 0.25, or 0.3 phr ITO, depending on the type of ITO used in the composite. The percolation threshold of PS/MWNT composites was found to be 0.01 phr MWNT. Mixed ITO/MWNT PS-composites were already percolated, the concentrations investigated in xv ii this study were already above the percolation threshold of these composites. A time dependence on impedance was found for PS-composites filled with MWNT. As time increases there is a decrease in impedance, and in some cases also a dependence on voltage. All PS-composites showed a dependence on the microstructure of the PS matrix and the filler material. The resistivity and percolation threshold were lower for PS/MWNT composites than PS/ITO composites due to the difference in filler size and aspect ratio, since MWNT have a smaller size. The orientation of PS grains with respect to neighboring grains was found to affect the resistivity of PS/MWNT. PS/MWNT composites with preferentially oriented PS grains were found to have a lower resistivity. Mixed ITO/MWNT PS-composites with the right filler concentrations were able to maintain transmission while decreasing resistivity. The fracture surface of fractured PS-composites prepared in this work indicated that there was bonding between adjacent PS-grains. From this work, it can be concluded that large grain hybrid ITO/MWNT PS-composites provide insight into the effect of combining nanometer sized filler materials together in a polymer matrix on the resultant structural, electrical, and optical properties of the composite. In the future, it is recommended that this study be used to aid research in flexible transparent conducting electrodes using a polymer matrix and hybrid/mixed nanometer sized conducting fillers.

This paper offers an existence result for finite dimensional stochastic differential inclusions with maximal monotone drift and diffusion terms. Kravets studied only set-valued drifts in [5], whereas Motyl [4] additionally observed set-valued diffusions in an infinite dimensional context. In the proof we make use of the Yosida approximation of maximal monotone operators to achieve stochastic differential equations which are solvable by a theorem of Krylov and Rozovskij [7]. The selection property is verified with certain properties of the considered set-valued maps. Concerning Lipschitz continuous set-valued diffusion terms, uniqueness holds. At last two examples for application are given.

Itô’s Lemma Ausarbeitung im Rahmen des Seminars "Finanzmathematik", SS 2009 Die Arbeiten des japanischen Mathematikers Kiyosi Itô aus den 1940er Jahren bilden heute die Grundlage der Theorie stochastischer Integration und stochastischer Differentialgleichungen. Die Ausarbeitung beschäftigt sich mit Itô's Kalkül, in dem zunächst das Itô-Integral bezüglich diverser Integratoren bereitgestellt wird, um sich anschließend mit Itô's Lemma bzw. der Itô-Formel als grundlegendes Hilfsmittel stochastischer Integration zu widmen. Am Ende wird ein kurzer Ausblick auf das Black-Scholes-Modell für zeitstetige Finanzmärkte vollzogen. Grundlage für die Ausarbeitung ist das Buch "Risk-Neutral Valuation" von Nicholas H. Bingham und Rüdiger Kiesel.

This thesis focuses on the use of surface modifiers to tune the properties of both metals and metal oxides. Particular attention is given to examine the modification of transparent conducting oxides (TCOs) including indium tin oxide and zinc oxide both through the use of phosphonic acids as well as organic and metal-organic dopants. In this thesis a variety of known and new phosphonic acids are synthesized. A subset of these molecules are then used to probe the relationship between the ability of a phosphonic acid to tune the work function of ITO and how that interrelates with the coverage and molecular orientation of the modifier on the surface. Experimental techniques including XPS, UPS, and NEXAFS are coupled with theoretical DFT calculations in order to more closely examine this relationship. Literature surrounding the modification of zinc oxide with phosphonic acids is not as prevalent as that found for the modification of ITO. Thus, effort is placed on attempting to determine optimal modification conditions for phosphonic acids on zinc oxide. As zinc oxide is already a low work function metal oxide, modifiers were synthesized in an attempt to further decrease the work function of this substrate in an effort to minimize the barrier to carrier collection/injection. Etching of the substrate by phosphonic acids is also examined. In a related technique, n- and p-dopants are used to modify the surfaces of ITO, zinc oxide, and gold and it was found that the work function can be drastically altered, to approximately 3.3 – 3.6 eV for all three of the substrates examined. Surface reactions are straightforward to conduct typically taking only 60 s to achieve this change in work function.

Transparent electrodes (TEs) have become important components of displays, touch screens, and solar photovoltaic (PV) energy conversion devices. As electrodes, they must be electrically conductive while being transparent. Transparent materials are normally poor conductors and materials with high electrical conductivity, such as metals, are typically not transparent. From the few candidate materials, indium tin oxide (ITO) is currently the best available, but indium is an expensive material and ITO cost has risen with increasing demand. Therefore, alternative materials or methods are sought to encourage production needs of applications and help in reducing their price. This thesis presents and discusses results of experimental work for a method, field-directed chaining, to produce a TE device which is nanowire-based, with a figure of merit FoM= 2.39 x10E-4 Ohm E-1, comparable to ITO but with potential for far lower cost. Using electric field-directed chaining, multiple parallel long chains of metal nanowires are assembled on inexpensive transparent materials such as glass by field directed nanowire chaining, using methods first demonstrated in our laboratory. In this work, we have improved the fraction of functional chains, by tuning the field/voltage, a key step in increasing the FoM and lowering the cost. The effect of operating parameters on TE optical and electrical properties has been studied and identified as well. From experiments with twenty seven substrates, each with a range of electric field and nanowire concentration, the highest light transmission achieved is 78% and the lowest sheet resistance achieved is 100 Ohm/sq. Among all the operating parameters, the electric field has the most significant influence on the fraction of nanowire chains that are functional. In the operating range of electric field strength available to us, we observed a monotonic increase in the fraction of functional nanowire chains. We found a counter-intuitive change in TE properties in a sub-range of nanowire concentration, associated with a change in the structure of chained patterns. / Graduate

abstract: Gold-silver alloy nanoparticles (NPs) capped with adenosine 5'-triphosphate were synthesized by borohydride reduction of dilute aqueous metal precursors. High-resolution transmission electron microscopy showed the as-synthesized particles to be spherical with average diameters ~4 nm. Optical properties were measured by UV-Visible spectroscopy (UV-Vis), and the formation of alloy NPs was verified across all gold:silver ratios by a linear shift in the plasmon band maxima against alloy composition. The molar absorptivities of the NPs decreased non-linearly with increasing gold content from 2.0 x 108 M-1 cm-1 (fÉmax = 404 nm) for pure silver to 4.1 x 107 M-1 cm-1 (fÉmax = 511 nm) for pure gold. The NPs were immobilized onto transparent indium-tin oxide composite electrodes using layer-by-layer (LbL) deposition with poly(diallyldimethylammonium) acting as a cationic binder. The UV-Vis absorbance of the LbL film was used to calculate the surface coverage of alloy NPs on the electrode. Typical preparations had average NP surface coverages of 2.8 x 10-13 mol NPs/cm2 (~5% of cubic closest packing) with saturated films reaching ~20% of ccp for single-layer preparations (1.0 ~ 10-12 mol NPs/cm2). X-ray photoelectron spectroscopy confirmed the presence of alloy NPs in the LbL film and showed silver enrichment of the NP surfaces by ~9%. Irreversible oxidative dissolution (dealloying) of the less noble silver atoms from the NPs on LbL electrodes was performed by cyclic voltammetry (CV) in sulfuric acid. Alloy NPs with higher gold content required larger overpotentials for silver dealloying. Dealloying of the more-noble gold atoms from the alloy NPs was also achieved by CV in sodium chloride. The silver was oxidized first to cohesive silver chloride, and then gold dealloyed to soluble HAuCl4- at higher potentials. Silver oxidation was inhibited during the first oxidative scan, but subsequent cycles showed typical, reversible silver-to-silver chloride voltammetry. The potentials for both silver oxidation and gold dealloying also shifted to more oxidizing potentials with increasing gold content, and both processes converged for alloy NPs with >60% gold content. Charge-mediated electrochemistry of silver NPs immobilized in LbL films, using Fc(meOH) as the charge carrier, showed that 67% of the NPs were electrochemically inactive. / Dissertation/Thesis / M.S. Chemistry 2014

This thesis deals with the stochastic integral with respect to Gaussian processes, which can be expressed in the form Bt = t 0 K(t, s)dWs. Here W stands for a Brownian motion and K for a square integrable Volterra kernel. Such processes generalize fractional Brownian motion. Since these processes are not semimartin- gales, Itô calculus cannot be used and other methods must be employed to define the stochastic integral with respect to these proceses. Two ways are considered in this thesis. If both the integrand and the process B are regular enough, it is possible to define the integral in the pathwise sense as a generalization of Lebesgue-Stieltjes integral. The other method uses the methods of Malliavin cal- culus and defines the integral as an adjoint operator to the Malliavin derivative. As an application, the stochastic differential equation dSt = µStdt + σStdBt, which is used to model price of a stock, is solved. Implications of such a model are briefly discussed. 1

This doctoral thesis endeavors to extend probability and statistical models using stochastic differential equations. The described models capture essential features from data that are not explained by classical diffusion models driven by Brownian motion. New results obtained by the author are presented in five articles. These are divided into two parts. The first part involves three articles on statistical inference and simulation of a family of processes related to fractional Brownian motion and Ornstein-Uhlenbeck process, the so-called fractional Ornstein-Uhlenbeck process of the second kind (fOU2). In two of the articles, we show how to simulate fOU2 by means of circulant embedding method and memoryless transformations. In the other one, we construct a least squares consistent estimator of the drift parameter and prove the central limit theorem using techniques from Stochastic Calculus for Gaussian processes and Malliavin Calculus. The second phase of my research consists of two articles about jump market models and arbitrage portfolio strategies for an insider trader. One of the articles describes two arbitrage free markets according to their risk neutral valuation formula and an arbitrage strategy by switching the markets. The key aspect is the difference in volatility between the markets. Statistical evidence of this situation is shown from a sequential data set. In the other one, we analyze the arbitrage strategies of an strong insider in a pure jump Markov chain financial market by means of a likelihood process. This is constructed in an enlarged filtration using Itô calculus and general theory of stochastic processes. / Föreliggande doktorsavhandling strävar efter att utöka sannolikhetsbaserade och statistiska modeller med stokastiska differentialekvationer. De beskrivna modellerna fångar väsentliga egenskaper i data som inte förklaras av klassiska diffusionsmodeller för brownsk rörelse.  Nya resultat, som författaren har härlett, presenteras i fem uppsatser. De är ordnade i två delar. Del 1 innehåller tre uppsatser om statistisk inferens och simulering av en familj av stokastiska processer som är relaterade till fraktionell brownsk rörelse och Ornstein-Uhlenbeckprocessen, så kallade andra ordningens fraktionella Ornstein-Uhlenbeckprocesser (fOU2). I två av uppsatserna visar vi hur vi kan simulera fOU2-processer med hjälp av cyklisk inbäddning och minneslös transformering. I den tredje uppsatsen konstruerar vi en minsta-kvadratestimator som ger konsistent skattning av driftparametern och bevisar centrala gränsvärdessatsen med tekniker från statistisk analys för gaussiska processer och malliavinsk analys.  Del 2 av min forskning består av två uppsatser om marknadsmodeller med plötsliga hopp och portföljstrategier med arbitrage för en insiderhandlare. En av uppsatserna beskriver två arbitragefria marknader med riskneutrala värderingsformeln och en arbitragestrategi som består i växla mellan marknaderna. Den väsentliga komponenten är skillnaden mellan marknadernas volatilitet. Statistisk evidens i den här situationen visas utifrån ett sekventiellt datamaterial. I den andra uppsatsen analyserar vi arbitragestrategier hos en insiderhandlare i en finansiell marknad som förändrar sig enligt en Markovkedja där alla förändringar i tillstånd består av plötsliga hopp. Det gör vi med en likelihoodprocess. Vi konstruerar detta med utökad filtrering med hjälp av Itôanalys och allmän teori för stokastiska processer. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Manuscript. Paper 5: Manuscript.</p>

This paper offers an existence result for finite dimensional stochastic differential inclusions with maximal monotone drift and diffusion terms. Kravets studied only set-valued drifts in [5], whereas Motyl [4] additionally observed set-valued diffusions in an infinite dimensional context. In the proof we make use of the Yosida approximation of maximal monotone operators to achieve stochastic differential equations which are solvable by a theorem of Krylov and Rozovskij [7]. The selection property is verified with certain properties of the considered set-valued maps. Concerning Lipschitz continuous set-valued diffusion terms, uniqueness holds. At last two examples for application are given.

Stochastic differential inclusions can be considered as a generalisation of stochastic differential equations. In particular a multivalued mapping describes the set of equations, in which a solution has to be found. This paper presents an existence result for a special parabolic stochastic inclusion. The proof is based on the method of upper and lower solutions. In the deterministic case this method was effectively introduced by S. Carl.