Perfectly matched layer termination for finite-element meshes: Implementation and application

Perfectly matched layer (PML) absorbers deteriorate the condition of the resulting finite-element sparse systems. Therefore, poor convergence scenarios are observed when an iterative solver is employed. In this work, we show that, by choosing the PML parameters in an optimal manner, substantial speedup in the solution convergence is achieved without affecting PML absorption. A robust preconditioned solver with nearly no breakdown possibilities is suggested, implemented, and tested for two microwave circuit applications. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 166–172, 1999.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/35043/1/11_ftp.pd

Oligorotaxane radicals under orders

A strategy for creating foldameric oligorotaxanes composed of only positively charged components is reported. Threadlike components-namely oligoviologens-in which different numbers of 4,4'-bipyridinium (BIPY(2+)) subunits are linked by p-xylylene bridges, are shown to be capable of being threaded by cyclobis(paraquat-p-phenylene) (CBPQT(4+)) rings following the introduction of radical-pairing interactions under reducing conditions. UV/vis/NIR spectroscopic and electrochemical investigations suggest that the reduced oligopseudorotaxanes fold into highly ordered secondary structures as a result of the formation of BIPY(\u2022+) radical cation pairs. Furthermore, by installing bulky stoppers at each end of the oligopseudorotaxanes by means of Cu-free alkyne-azide cycloadditions, their analogous oligorotaxanes, which retain the same stoichiometries as their progenitors, can be prepared. Solution-state studies of the oligorotaxanes indicate that their mechanically interlocked structures lead to the enforced interactions between the dumbbell and ring components, allowing them to fold (contract) in their reduced states and unfold (expand) in their fully oxidized states as a result of Coulombic repulsions. This electrochemically controlled reversible folding and unfolding process, during which the oligorotaxanes experience length contractions and expansions, is reminiscent of the mechanisms of actuation associated with muscle fibers

Ex^2Box: Interdependent Modes of Binding in a Two-Nanometer-Long Synthetic Receptor

Incorporation of two biphenylene-bridged 4,4′-bipyridinium extended viologen units into a para-phenylene-based cyclophane results in a synthetic receptor that is 2 nm long and adopts a box-like geometry. This cyclophane, Ex^2Box^4+, possesses the ability to form binary and ternary complexes with a myriad of guest molecules ranging from long π-electron-rich polycyclic aromatic hydrocarbons, such as tetracene, tetraphene, and chrysene, to π-electron-poor 2,6-dinitrotoluene, 1,2,4-trichlorobenzene, and both the 9,10- and 1,4-anthraquinone molecules. Moreover, Ex^2Box^4+ is capable of forming one-to-one complexes with polyether macrocycles that consist of two π-electron-rich dioxynaphthalene units, namely, 1,5-dinaphtho[38]crown-10. This type of broad molecular recognition is possible because the electronic constitution of Ex^2Box^4+ is such that the pyridinium rings located at the “ends” of the cyclophane are electron-poor and prefer to enter into donor–acceptor interactions with π-electron-rich guests, while the “middle” of the cyclophane, consisting of the biphenylene spacer, is more electron-rich and can interact with π-electron-poor guests. In some cases, these different modes of binding can act in concert to generate one-to-one complexes which possess high stability constants in organic media. The binding affinity of Ex^2Box^4+ was investigated in the solid state by way of single-crystal X-ray diffraction and in solution by using UV–vis and NMR spectroscopy for 12 inclusion complexes consisting of the tetracationic cyclophane and the corresponding guests of different sizes, shapes, and electronic compositions. Additionally, density functional theory was carried out to elucidate the relative energetic differences between the different modes of binding of Ex^2Box^4+ with anthracene, 9,10-anthraquinone, and 1,4-anthraquinone in order to understand the degree with which each mode of binding contributes to the overall encapsulation of each guest

Radically Enhanced Molecular Switches

The mechanism governing the redox-stimulated switching behavior of a tristable [2]rotaxane consisting of a cyclobis(paraquat-p-phenylene) (CBPQT^4+) ring encircling a dumbbell, containing tetrathiafulvalene (TTF) and 1,5-dioxynaphthalene (DNP) recognition units which are separated from each other along a polyether chain carrying 2,6-diisopropylphenyl stoppers by a 4,4′-bipyridinium (BIPY^2+) unit, is described. The BIPY^2+ unit acts to increase the lifetime of the metastable state coconformation (MSCC) significantly by restricting the shuttling motion of the CBPQTT^4+ ring to such an extent that the MSCC can be isolated in the solid state and is stable for weeks on end. As controls, the redox-induced mechanism of switching of two bistable [2]rotaxanes and one bistable [2]catenane composed of CBPQT^4+ rings encircling dumbbells or macrocyclic polyethers, respectively, that contain a BIPY2+ unit with either a TTF or DNP unit, is investigated. Variable scan-rate cyclic voltammetry and digital simulations of the tristable and bistable [2]rotaxanes and [2]catenane reveal a mechanism which involves a bisradical state coconformation (BRCC) in which only one of the BIPY^•+ units in the CBPQT^2(•+) ring is oxidized to the BIPY2+ dication. This observation of the BRCC was further confirmed by theoretical calculations as well as by X-ray crystallography of the [2]catenane in its bisradical tetracationic redox state. It is evident that the incorporation of a kinetic barrier between the donor recognition units in the tristable [2]rotaxane can prolong the lifetime and stability of the MSCC, an observation which augurs well for the development of nonvolatile molecular flash memory devices

A Radically Configurable Six-State Compound

Most organic radicals possess short lifetimes and quickly undergo dimerization or oxidation. Here, we report on the synthesis by radical templation of a class of air- and water-stable organic radicals, trapped within a homo[2]catenane composed of two rigid and fixed cyclobis (paraquat-p-phenylene) rings. The highly energetic octacationic homo[2]catenane, which is capable of accepting up to eight electrons, can be configured reversibly, both chemically and electrochemically, between each one of six experimentally accessible redox states (0, 2+, 4+, 6+, 7+, and 8+) from within the total of nine states evaluated by quantum mechanical methods. All six of the observable redox states have been identified by electrochemical techniques, three (4+, 6+, and 7+) have been characterized by x-ray crystallography, four (4+, 6+, 7+, and 8+) by electron paramagnetic resonance spectroscopy, one (7+) by superconducting quantum interference device magnetometry, and one (8+) by nuclear magnetic resonance spectroscopy