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Diffusion is an omnipresent, most fundamental phenomenon in nature and thus critical for the performance of numerous technologies. This is in particular true for nanoporous materials with manifold applications for matter upgrading by separation, purification and conversion. The path lengths of molecular transportation within the industrial plants range from the elementary steps of diffusion within the micropores of the individual particles up to the matter flow over macroscopic distances. Each of them might be decisive in determining overall performance so that detailed knowledge of all modes of mass transfer is crucial for a knowledge-based optimization of the devices with reference to their transport properties. The rate of mass transfer is particularly complicated to be assessed within the individual (adsorbent) particles/crystallites with pore sizes of the order of molecular dimensions. We are going to present two powerful techniques exactly for this application, operating under both equilibrium (Pulsed Field Gradient (PFG) NMR) and non-equilibrium (Microimaging by interference microscopy and IR microscopy) conditions. The potentials of these techniques are demonstrated in a few showcases, notably including the options of transport enhancement in pore hierarchies. The contribution concludes with a survey on present activities within an IUPAC initiative aiming at the elaboration of “guidelines for measurements and reporting of diffusion properties of chemical compounds in nanoporous materials”.

The inverse problem in finance consists of determining the unknown parameters of the pricing equation from the values quoted from the market. We formulate the inverse problem as a minimization problem for an appropriate cost function to minimize the difference between the solution of the model and the market observations. Efficient gradient based optimization requires accurate gradient estimation of the cost function. In this thesis we highlight the adjoint method for computing gradients of the cost function in the context of gradient based optimization and show its importance. We derive the continuous adjoint equations with appropriate boundary conditions for three main option pricing models: the Black-Scholes model, the Heston's model and the jump diffusion model, for European type options. These adjoint equations can be used to compute the gradient of the cost function accurately for parameter estimation problems. The adjoint method allows efficient evaluation of the gradient of a cost function F(σ) with respect to parameters σ where F depends on σ indirectly, via an intermediate variable. Compared to the finite difference method and the sensitivity equation method, the adjoint equation method is very efficient in computing the gradient of the cost function. The sensitivity equations method requires solving a PDE corresponding to each parameter in the model to estimate the gradient of the cost function. The adjoint method requires solving a single adjoint equation once. Hence, for a large number of parameters in the model, the adjoint equation method is very efficient. Due to its nature, the adjoint equation has to be solved backward in time. The adjoint equation derived from the jump diffusion model is harder to solve due to its non local integral term. But algorithms that can be used to solve the Partial Integro-Differential Equation (PIDE) derived from jump diffusion model can be modified to solve the adjoint equation derived from the PIDE. / Ph. D.

In this thesis, the interface between the electron donor polymer and the electron acceptor fullerene in organic photovoltaic devices is studied. Starting from a bilayer system of donor and acceptor materials, the proximity of polymer and fullerene throughout the bulk of the devices is improved by inducing an interdiffusion of the two materials by heating the devices in the vicinity of the glass transition temperature of the polymer. In this manner, a concentration gradient of polymer and fullerene throughout the bulk is created. The proximity of a fullerene within 10 nm of any photoexcitation in the polymer ensures that the efficient charge separation occurs. Measurements of the absorption, photoluminescence, and photocurrent spectra as well as I-V characteristics are used to study the interdiffusion and its influence on the efficiency of the photovoltaic devices. In addition, the film morphology is studied on a microscopic level with transmission electron microscopy and with Auger spectroscopy combined with ion beam milling to create a depth profile of the polymer concentration in the film. Initial studies to induce an interdiffusion were done on poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene) (MEH-PPV) as the electron donor polymer and the buckminsterfullerene C60 as the electron acceptor. Interdiffused devices show an order of magnitude photoluminescence quenching with concomitant increase in the photocurrents by an order of magnitude. Variation of the polymer layer thickness shows that the photocurrents increase with decreasing thickness down to 70 nm due to charge transport limitation. The choice of layer thickness in organic photovoltaic devices is critical for optimization of the efficiency. The interdiffusion process is also monitored in situ and a permanent increase in photocurrents is observed during the heat treatment. Transmission electron microscopy (TEM) studies on cross sections of the film reveal that C60 interdiffuses into the MEH-PPV bulk in the form of >10 nm clusters. This clustering of C60 is a result of its tendency to crystallize and the low miscibility of C60 in MEH-PPV, leading to strong phase separation. To improve the interdiffusion process, the donor polymer is replaced by poly(3-octylthiophene-2,5-diyl) (P3OT), which has a better miscibility with C60. Again, the photocurrents of the interdiffused devices are improved significantly. A monochromatic power conversion efficiency of 1.5 % is obtained for illumination of 3.8 mW/cm2 at 470 nm. The polymer concentration in unheated and interdiffused films is studied with Auger spectroscopy in combination with ion beam milling. The concentration profile shows a distinct interface between P3OT and C60 in unheated films and a slow rise of the P3OT concentration throughout a large cross-section of the interdiffused film. TEM studies on P3OT/C60 films show that C60 still has some tendency to form clusters. The results of this thesis demonstrate that thermally-controlled interdiffusion is a viable approach for fabrication of efficient photovoltaic devices through nanoscale control of composition and morphology. These results are also used to draw conclusions about the influence of film morphology on the photovoltaic device efficiency and to identify important issues related to materials choice for the interdiffusion process. Prospective variations in materials choice are suggested to achieve better film morphologies. / Ph. D.

An in-depth study of concentration gradients in thermally-interdiffused polymer – fullerene photovoltaic devices, with a focus on thickness and heat treatments, is presented in this thesis. Device performance is improved from the bilayer by the creation of a concentration gradient of the donor and acceptor materials throughout the active layer of the device. Concentration gradients are expected to improve device performance by optimizing the charge transfer, transport and collection processes. This is achieved through heat-induced interdiffusion of the two materials at temperatures above the glass transition temperature of the polymer. Investigation of the poly(3-octylthiophene) (P3OT) – C₆₀ system show a three-fold improvement in the external quantum efficiencies (EQE) as compared with bilayer devices. Auger spectroscopy, combined with argon-ion beam milling, serves to record the concentration depth profile and identify concentration gradients in the device through detection of the sulfur in the P3OT backbone. Concentration gradients are optimized to yield the best devices through a thickness variation study conducted on the P3OT – C₆₀ system for fixed thermal interdiffusion conditions at 118 °C for 5 minutes. An optimum thickness of 40 to 60 nm is obtained for the two materials that yields the ideal morphology of a concentration gradient as recorded by Auger spectroscopy. For such devices, the concentration gradient is seen to extend through the device, ending in a thin layer of pure material at each electrode. A monochromatic power conversion efficiency of 2.05% is obtained for 5.3 mW/cm²⁺ illumination at 470 nm. A brief study is also presented to optimize the concentration gradient profile through variations of the thermal parameters. The dependence of the concentration gradient on the interdiffusion time and temperature is investigated. The merits of heat treatment on the crystallinity of P3OT and the overall device performance are also discussed. It is shown in some case that devices with annealed P3OT layers show almost twice the EQE as non-annealed P3OT layer devices. Potential alternatives for C₆₀ in interdiffused devices with P3OT have been presented. [6,6]-phenyl C₆₁-butyric acid methyl ester (PCBM), a well-investigated acceptor for blend devices, is studied as an acceptor in concentration gradient devices. A method for spin-coating uniform bilayers of P3OT and PCBM, without solution damage to either layer, is presented. A thermal variation study of the interdiffusion conditions on this system indicated higher interdiffusion temperatures and times are preferred for P3OT – PCBM systems. For interdiffusion at 150 °C for ten minutes, EQE values approaching 35 % at 500 nm are obtained. Auger spectroscopy studies on this system yielded the same conclusions about the concentration gradient device morphology that gives optimum device output. 1:1 and 1:2 blends of P3OT – PCBM are also studied. The influence of various thermal treatments on these devices is described. The endohedral fullerene Sc₃N@C₈₀ is introduced as a new acceptor material. The endohedral fullerene consists of Sc₃N cluster enclosed in a C₈₀ cage. An order of magnitude increase is seen in device performance upon sublimation of these molecules on a P3OT layer confirming its effectiveness as an acceptor. Preliminary studies done on this system indicated the need for greater thermal treatment to produce optimum concentration gradients. An in depth study for varying temperatures and times is presented. The best device performance was seen for interdiffusion at 160 °C for 25 minutes. The endohedral fullerene devices also show a long-term deterioration and so best result are presented from a set of devices fabricated within the same time period. The study of these three donor-acceptor systems confirms that the conclusions on the thickness dependence and device performance study conducted for the P3OT – C₆₀ system extend to other acceptors. A model of EQE for varying thicknesses based on absorption in the interdiffused concentration gradient regions is also presented. This model effectively highlights the influence of P3OT layer thickness on the trends observed in the EQE. It did not, however, reproduce the experimental thickness variation results for varying C₆₀ thicknesses. Incorporation of the effects of the electric field intensity distribution is expected to correct for this. Suggestions have been given on how this might be achieved. / Ph. D.

A low-speed, axisymmetric turbulent boundary layer under a strong adverse pressure gradient is experimentally studied for its relevance to marine applications, urban air-transportation and turbulence ingestion noise. The combined effect of lateral curvature and streamwise pressure gradient are examined on the mean flow, turbulence structure, velocity correlations and wall pressure fluctuations. Additionally, the upstream influence of a rotor operating in this flow is examined to improve the understanding of the turbulence necessary to develop advanced noise prediction tools. Measurements were made in Virginia Tech Stability tunnel documenting the flow over a 0.432-m diameter body-of-revolution comprised of a forward nose-cone, a constant diameter mid-body and a 20 degree tail-cone, at a length based Reynolds number of 1.2 million. The principal finding of this work is the resemblance of the boundary layer to a free-shear layer where the turbulence far from the wall plays a dominant role, unlike in the canonical case of the flat-plate boundary layer. The mean flow along the tail developed inflection points in the outer regions and the associated velocity and turbulence stress profiles were self-similar with a recently proposed embedded shear layer scaling. As the mean flow decelerates downstream, the large-scale motions energize and grow along with the boundary layer thickness; However, the structure is roughly self-similar with the shear-layer scaling, emphasizing the role of the shear-layer in the large-scale structure. Additionally, the correlation structure is discussed to provide information towards the development of turbulence models and aeroacoustic predictions. The associated wall pressure fluctuations, measured with a longitudinal array of microphones, evolved significantly downstream with the dimensional wall pressure spectra weakening by over 20-dB per Hz. However, the spectra collapsed to within 2-dB with the wall-wake scaling, where the pressure-scale is the wall shear stress, and the time-scale is derived from the boundary layer thickness and edge velocity. The success of this scaling, even in the viscous roll-off regions, suggests the increasing importance of the outer region on the near-wall turbulence and wall-pressure. Investigation of the space-time structure revealed the presence of a quasi-periodic feature with the conditional signature of a roller-eddy. The structure appeared to scale with the wall-wake scaling, and was found to convect downstream at speeds matching those at the inflection points (and outer turbulence peak). It is hypothesized that the outer region turbulence in strong adverse pressure gradient flow strongly drive the near-wall turbulence and therefore both the wall pressure and shear stress. Subsequent measurements made with the rotor operating at the tail, using high-speed particle image velocimetry, provided the space-time structure of the inflow turbulence as a function of the rotor thrust. The impact of the rotor on the mean flow, turbulence and correlation structure in the vicinity of the rotor is discussed to supply information towards validating numerical simulations and developing turbulence models that account for the distortion due to the rotor. This work was sponsored by the Office of Naval Research, in particular Drs. Ki-Han Kim and John Muench under grants N00014-17-1-2698 and N00014-20-1-2650. / Doctor of Philosophy / Understanding turbulent flows adjacent to surfaces placed in fluid flows is necessary to develop efficient technologies to mitigate undesirable drag, vibrations and noise. Particularly, this is of an increased interest with the imminent abundance of urban short-haul air transportation. While several fundamental aspects of these flows have been clarified, certain specific areas still remain to be addressed, including the impact of curved surfaces, like those of submarine hulls and aircraft fuselage, and the impact of mean pressure gradients. This study seeks to fill some of these gaps by studying the flow over a body-of-revolution through wind tunnel experiments. The nature of the velocity and wall-pressure fluctuations are examined in detail. It was found that the boundary layer was significantly different from the canonical case of a flat-plate flow, with the mean velocity and turbulence structure developing the characteristics of a free-shear layer (flows unbounded by surfaces). Specifically, the velocity and turbulence intensity appeared self-similar with a recently proposed embedded shear layer scaling, which is based on the parameters at the inflection point in the mean velocity profile. The large-scale motions in the outer regions, despite energizing and growing as the flow decelerated downstream, appeared self-similar with the shear layer parameters, emphasizing the role of shear layer motions within in the boundary layer. This is important since the turbulence relatively further from the wall are now the important sources of pressure fluctuations and therefore drag, vibrations and noise. The associated wall-pressure fluctuation were studied with a focus on the wall-pressure spectrum and the space-time structure. A quasi-periodic feature was detected in the instantaneous fluctuations, which had a conditional structure reminiscent of a conditional roller, and appeared to convect downstream at speeds matching those at the inflection points in the velocity profile. Therefore it is hypothesized that the large-scale motions in the embedded shear layer play a dominant role on the near-wall turbulence and therefore on the wall pressure and shear-stress. This is different from the behavior of the wall-studied flow past a flat-plate. It is therefore important to factor this into technologies aiming to increase the efficiency and quieten the vehicles

A generalized Conjugate Gradient like method is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. Preconditioning techniques are employed with the Conjugate Gradient like method to enhance the stability and convergence rate of the overall iterative method. The superiority of the new solver is established by comparisons with a conventional Line GaussSeidel Relaxation (LGSR) solver. Comparisons are based on 'number of iterations required to converge to a steady-state solution' and 'total CPU time required for convergence'. Three test cases representing widely varying flow physics are chosen to investigate the performance of the solvers. Computational test results for very low speed (incompressible flow over a backward facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (shockon- shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the 1vfach 0.1 case, speed-up factors of 30 (in terms of iterations) and 20 (in terms of CPU time) are found in favor of the new solver when compared with the LGSR solver. The corresponding speed-up factors for the transonic flow case are 20 and 18, respectively. The hypersonic case shows relatively lower speed-up factors of 5 and 4, respectively. This study reveals that preconditioning can greatly enhance the range of applicability and improve the performance of Conjugate Gradient like methods. / Ph. D.

Water and ion transport critically determine the performance of many functional materials and devices, from fuel cells to lithium ion batteries to soft mechanical actuators. This dissertation aims to address some fundamental issues regarding transport and anisotropy, structural heterogeneity and molecular interactions inside ionic polymers. I first discuss a main deficiency of a standard protocol for calibrating high pulsed-field-gradient NMR. I show that high gradient calibration using low γ nuclei is not amenable to measurements on slow diffusing high γ nuclei. Then I employ NMR diffusometry to investigate transport and anisotropy for a series of ionic polymers, from poly(arylene ether sulfone) hydrophilic-hydrophobic multi-block copolymers to polymer blends to perfluorosulfonate random copolymers. For the multi-block copolymers, NMR diffusion measurements yield diffusion anisotropy as a function of water uptake and block lengths. ²H NMR spectroscopy on absorbed D₂O probes membrane alignment modes. These measurements also provide insights into average defect distributions. For the blend membranes, we examine the impact of compatibilizer on their transport properties. An increase in compatibilizer significantly improves the membrane phase homogeneity confirmed by SEM and transport studies. Theories of diffusion in porous media yield changes in domain size and tortuosity that correspond to drastic changes in local restrictions to water diffusion among different blend membranes. NMR relaxometry studies yield multi-component T₁ values, which further probe structural heterogeneities on smaller scales than diffusion experiments. For the random copolymer, the exploration of ion transport reveals inter-ionic associations of ionic liquids (ILs) modulated by hydration level and ionic medium. When ILs diffuse inside ionic polymers, isolated anions diffuse faster (≥ 4X) than cations at high hydration whereas ion associations result in substantially faster cation diffusion (≤ 3X) at low hydration inside membranes, revealing prevalent anionic aggregates. Finally, I present the strategy and analytical protocol for studying ionomer membranes using ILs. The normal cation diffusion contrasts to the anomalous anion diffusion caused by local confinement structures inside the membranes, which vary drastically with temperature and hydration level. These structures correspond to a density variation of SO₃⁻ groups, which define a distribution of local electrical potentials that fluctuate with temperature and nature of ionic media. / Ph. D.

A full solar eclipse is going to be visible from a range of states in the contiguous United States on August 21, 2017. Since the atmosphere of the Earth is charged by the sun, the blocking of the sunlight by the moon may cause short term changes to the atmosphere, such as density and temperature alterations. There are many ways to measure these changes, one of these being ionospheric scintillation. Ionospheric scintillation is rapid amplitude and phase fluctuations of signals passing through the ionosphere caused by electron density irregularities in the ionosphere. At mid-latitudes, scintillation is not as common of an occurrence as it is in equatorial or high-altitude regions. One of the theories that this paper looks into is the possibility of the solar eclipse producing an instability in the ionosphere that will cause the mid-latitude region to experience scintillations that would not normally be present. Instabilities that could produce scintillation are reviewed and altered further to model similar conditions to those that might occur during the solar eclipse. From this, the satellites that are being used are discuses, as is hardware and software tools were developed to record the scintillation measurements. Although this work was accomplished before the eclipse occurred, measurement tools were developed and verified along with generating a model that predicted if the solar eclipse will produce an instability large enough to cause scintillation for high frequency satellite downlinks. / Master of Science