A Fundamental Model Methodology for the Analysis, Design and Fabrication of a Narrow Transparency Window in a Bulk Meta-Material

abstract: The optical valley of water, where water is transparent only in the visible range, is a fascinating phenomenon and cannot be modeled by conventional dielectric material modeling. While dielectric properties of materials can be modeled as a sum of Lorentz or Debye simple harmonic oscillators, water is the exception. In 1992 Diaz and Alexopoulos published a causal and passive circuit model that predicted the window of water by adding a “zero shunt” circuit in parallel with every Debye and Lorentz circuit branch. Other than the Diaz model, extensive literature survey yielded no universal dielectric material model that included water or offered an explanation for this window phenomenon. A hybrid phenomenological model of water, proposed by Shubitidze and Osterberg, was the only model other than the Diaz-Alexopoulos model that tried to predict and match the optical valley of water. However, we show that when we apply the requirement that the permittivity function must be a complex analytic function, it fails our test of causality and the model terms lack physical meaning, exhibiting various mathematical and physical contradictions. Left with only the Diaz proposed fundamental model as the only casual model, this dissertation explores its physical implications. Specifically, the theoretical prescription of Kyriazidou et al for creating artificial dielectric materials with a narrow band transparency is experimentally demonstrated for the first time at radiofrequencies. It is proposed that the most general component of the model of the frequency dependent permittivity of materials is not the simple harmonic oscillator but rather the harmonic oscillator augmented by the presence of a zero shunt circuit. The experimental demonstration illustrates the synthesis and design of a new generation of window materials based on that model. Physically realizable Lorentz coatings and RF Debye “molecules” for creating the desired windows material are designed using the full physics computational electromagnetic code. The prescribed material is then implemented in printed circuit board technology combined with composite manufacturing to successfully fabricate a lab demonstrator that exhibits a narrow RF window at a preselected frequency of interest. Demonstrator test data shows good agreement with HFSS predictions.Dissertation/ThesisDoctoral Dissertation Materials Science and Engineering 201

Asymptotic analysis of extreme electrochemical transport

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 237-244).In the study of electrochemical transport processes, experimental exploration currently outpaces theoretical understanding of new phenomena. Classical electrochemical transport theory is not equipped to explain the behavior of electrochemical systems in the extreme operating conditions required by modern devices. In this thesis, we extend the classical theory to examine the response of two electrochemical systems that form the basis for novel electrochemical devices. We first examine the DC response of an electrochemical thin film, such as the separator in a micro-battery, driven by current applied through reactive electrodes. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer which mediates Faradaic reactions with Butler-Volmer kinetics. Our analysis differs from previous studies in two significant ways. First, we impose the full nonlinear, reactive boundary conditions appropriate for electrolytic/galvanic cells.(cont.) Since surface effects become important for physically small systems, the use of reactive boundary conditions is critical in order to gain insight into the behavior of actual electrochemical thin films that are sandwiched between reactive electrodes, especially at high current densities. For instance, our analysis shows that reaction rate constants and the Stern-layer capacitance have a strong influence on the response of the thin film. Second, we analyze the system at high current densities (far beyond the classical diffusion-limited current) which may be important for high power-density applications. At high currents, we obtain previously unknown characterizations of two interesting features at the cathode end of the cell: (i) a nested boundary layer structure and (ii) an extended space charge region. Next, we study the response of a metal (i.e., polarizable) colloid sphere in an electrolyte solution over a range of applied electric fields.(cont.) This problem, which underlies novel electrokinetically driven microfluidic devices, has traditionally been analyzed using circuit models which neglect bulk concentration variations that arise due to double layer charging. Our analysis, in contrast, is based on the Nernst-Planck equations which explicitly allow for bulk concentration gradients. A key feature of our analysis is the use of surface conservation laws to provide effective boundary conditions that couple the double layer charging dynamics, surface transport processes, and bulk transport processes. The formulation and derivation of these surface conservation laws via boundary layer analysis is one of the main contributions of this thesis. For steady applied fields, our analysis shows that bulk concentrations gradients become significant at high applied fields and affect both bulk and double layer transport processes. We also find that surface transport becomes important for strong applied fields as a result of enhanced absorption of ions by the double layer.(cont.) Unlike existing theoretical studies which focus on weak applied fields (so that both of these effects remain weak), we explore the response of the system to strong applied fields where both bulk concentration gradients and surface transport contribute at leading order. For the unsteady problem at applied fields that are not too strong, we find that diffusion processes, which are necessary for the system to relax to steady-state, are suppressed at leading-order but appear as higher-order corrections. This result is derived in a novel way using time-dependent matched asymptotic analysis. Unfortunately, the dynamic response of the system to large applied fields seems to introduce several complications that make the analysis (both mathematical and numerical) quite challenging; the resolution of these challenges is left for future work. Both of these problems require the use of novel techniques of asymptotic analysis (e.g., multiple parameter asymptotic expansions, surface conservation laws, and time-dependent asymptotic matching) and advanced numerical methods (e.g., pseudospectral methods, Newton-Kantorovich method, and direct matrix calculation of Jacobians) which may be applicable elsewhere.by Kevin Taylor Chu.Ph.D