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The coordination and local geometry of Cu+ cations in Cu(I)-ZSM-5 and the adsorption of CO to such cations were explored using density functional theory. A thorough examination was made of the effects of placing Cu+ in each of the cation-exchange sites available in the MFI lattice, the location of the Al atom in the site, and the number of Al atoms in the site. Cu+ cations in I2 exchange sites, located at the edge of the main and sinusoidal channels, are coordinated to two framework O atoms before and after CO adsorption. The calculated adsorption energy for CO adsorbed on such cations lies between 30 and 33 kcal/mol, and the C−O vibrational frequency lies between 2150 and 2158 cm-1. Cu+ associated with five- or six-membered rings, i.e., M5, M6, Z5, and Z6 exchange sites, located in the main and sinusoidal channels of the zeolite, are 3-fold coordinated to framework O atoms, but the coordination number can decrease to 2 upon CO adsorption. The calculated CO adsorption energy of Cu+ in such sites is in the range of 25−28 kcal/mol. Cu+ cations located in the basket structures formed by two fused five-membered rings, in M7 sites, bind CO with a calculated adsorption energy of 21 kcal/mol. The results of this study indicate that the presence of Cu+ cations in different exchange sites cannot be identified on the basis of infrared spectra of adsorbed CO and would be difficult to identify by temperature-programmed desorption of adsorbed CO. Evidence for two types of Cu+ coordination can be obtained, though, from Cu K-edge extended X-ray absorption fine structure data. It is also shown that changes in Cu+ coordination occurring upon CO adsorption can be observed by Cu K-edge X-ray absorption near-edge structure data.
An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
Abstract This paper presents an application of the theory of the degree of a map to the study of the existence of solutions and some related problems for resistive nonlinear networks. Many well‐known results in this area have been generalized to allow coupling among the nonlinear resistors. The usual hypothesis requiring the nonlinear resistors to be eventually increasing has been weakened considerably by only requiring the resistors to be eventually passive . Instead of investigating special cases by special techniques, we study the network equations from a geometrical point of view. The concept of homotopy of odd fields provides a unified yet simple approach for analyzing a large class of practical nonlinear networks. Many known results belong to this category and are derived as special cases of our generalized theorems. This approach leads to a much better understanding of the geometric structure of the vector fields associated with the network equations. As a result, in so far as the existence of solutions is concerned, the concept of eventual passivity is shown to be far more basic than that of eventual increasingness. The emphasis of the concept of eventual passivity also leads naturally to the inclusion of coupling among the nonlinear resistors. The homotopy of odd fields also provides some useful techniques for locating the solutions. Along this line, we also study the bounding region of solutions and discuss the operating range of nonlinear resistors.
Coronavirus Pandemic: Europe Is Once Again Forged in a CrisisTo an American, the debate around how the European Union should respond to the COVID-19 crisis has a familiar ring.Europe has been debating debt mutualization, transfer union and fi scal federalism for years.The pandemic is just another opportunity for sounding familiar themes.But the crisis is also a reminder that there is nothing distinctively European about this rhetoric.Closer to home (my home, anyway, where I am spending considerable time at the moment), we see southern state politicians like Florida Senator Rick Scott impugning northern states like New York for their profl igacy.Or, as President Trump put it on Twitter, "Why should the people and taxpayers of America be bailing out poorly run states (like Illinois, as [sic] example) and cities, in all cases Democrat run and managed, when most of the other states are not looking for bailout help?"Northern Europeans have no monopoly on such sentiments.Crises, wherever they occur, have a way of bringing out sectional divisions and reinforcing cultural stereotypes.
This tutorial clarifies the axiomatic definition of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$( \color{#FF0000}v^{\color{#000000}(\color{#FF0000}\alpha\color{#000000})}\color{#000000},\color{#FF0000}i^{ \color{#000000}(\color{#FF0000}\beta\color{#000000})}\color{#000000})$</tex></formula> circuit elements via a lookup table dubbed an A-pad, of admissible <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(\color{#FF0000}v\color{#000000},\color{#FF0000}i\color{#000000})$</tex></formula> signals measured via Gedanken probing circuits. The <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(\color{#FF0000}v^{ \color{#000000}(\color{#FF00FF}\alpha\color{#000000})}\color{#000000},\color{#FF0000}i^{\color{#000000}( \color{#FF00FF}\beta\color{#000000})}\color{#000000})$</tex></formula> elements are ordered via a complexity metric. Under this metric, the memristor emerges naturally as the fourth element, characterized by a state-dependent Ohm's law. A logical generalization to memristive devices reveals a common fingerprint consisting of a dense continuum of pinched hysteresis loops whose area decreases with the frequency <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$ \omega$</tex></formula> and tends to a straight line as <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\omega \rightarrow\infty$</tex></formula> , for all bipolar periodic signals and for all initial conditions. This common fingerprint suggests that the term memristor be used henceforth as a moniker for memristive devices.