We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrödinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate involving the projections onto the positive and negative frequencies.
We extend the method of sub and supersolutions in order to prove existence of -solutions of the equation in , where is a Carathéodory function. The proof is based on Schauder's fixed point theorem.
Over the last 40 years, electrically conductive polymers have become well established as important electrode materials. Polyanilines, polythiophenes and polypyrroles have received particular attention due to their ease of synthesis, chemical stability, mechanical robustness and the ability to tailor their properties. Electrochemical synthesis of these materials as films have proved to be a robust and simple way to realise surface layers with controlled thickness, electrical conductivity and ion transport. In the last decade, the biomedical compatibility of electrodeposited polymers has become recognised; in particular, polypyrroles have been studied extensively and can provide an effective route to pharmaceutical drug release. The factors controlling the electrodeposition of this polymer from practical electrolytes are considered in this review including electrolyte composition and operating conditions such as the temperature and electrode potential. Voltammetry and current-time behaviour are seen to be effective techniques for film characterisation during and after their formation. The degree of take-up and the rate of drug release depend greatly on the structure, composition and oxidation state of the polymer film. Specialised aspects are considered, including galvanic cells with a Mg anode, use of catalytic nanomotors or implantable biofuel cells for a self-powered drug delivery system and nanoporous surfaces and nanostructures. Following a survey of polymer and drug types, progress in this field is summarised and aspects requiring further research are highlighted. 相似文献
This paper presents a feasibility study of a non-aqueous rechargeable battery based on aluminum and poly-(3,4-ethylenedioxythiophene) conductive polymer in a chloroaluminate ionic liquid. The polymer was electrodeposited on a vitreous carbon working electrode in a chloride aqueous solution and the structure was analyzed by scanning electron microscopy. The doping/de-doping mechanism of chloride ions into the polymer structure was studied using a quartz crystal microbalance and cyclic voltammetry. The deposition/dissolution of the aluminum negative electrode were investigated by electrochemical and microscopic methods. Performance data were obtained with a laboratory-scale aluminum-conductive polymer battery at constant current showing an average cell discharge voltage of 1 V and specific energies of at least 84 Wh kg−1 referred to the mass of the polymer and aluminum. The system is novel and the paper outlines further research to improve the cell performance.
A distannylated electron-deficient bithiophene imide (BTI-Tin) monomer was synthesized and polymerized with imide-functionalized co-units to afford homopolymer PBTI and copolymer P(BTI-BTI2), both featuring an acceptor–acceptor backbone with high molecular weight. Both polymers exhibited excellent unipolar n-type character in transistors with electron mobility up to 2.60 cm2 V−1 s−1. When applied as acceptor materials in all-polymer solar cells, PBTI and P(BTI-BTI2) achieved high power-conversion efficiency (PCE) of 6.67 % and 8.61 %, respectively. The PCE (6.67 %) of polymer PBTI, synthesized from the distannylated monomer, is much higher than that (0.14 %) of the same polymer PBTI*, synthesized from typical dibrominated monomer. The 8.61 % PCE of copolymer P(BTI-BTI2) is also higher than those (<1 %) of homopolymers synthesized from dibrominated monomers. The results demonstrate the success of BTI-Tin for accessing n-type polymers with greatly improved device performance. 相似文献
We have obtained and characterized self assembled monolayers (SAMs) of 4-aminothiophenol (4-ATP) and 1-(4-mercaptophenyl)-2,6-diphenyl-4-(4-pyridyl)pyridinium tetrafluoroborate (MDPP) functionalized with iron phthalocyanine (FePc) adsorbed on gold (111) electrodes. The catalytic activity of these SAMs/FePc was examined for the reduction of O2 in aqueous media (pH = 4) and compared with that of bare gold and of gold coated directly with FePc molecules. Scanning tunneling microscopy (STM) studies confirm the functionalization of the 4-ATP by FePc. The electrocatalytic studies carried out with Au/FePc, Au/4-ATP/FePc and Au/MDPP/FePc electrodes show that the O2 reduction takes place by a 4-electron transfer to give water in contrast to a 2-electron-transfer process observed on the bare gold. The activity of the electrodes increases as follows: Au < Au/FePc < Au/4-ATP/FePc < Au/MDPP/FePc. 相似文献
The interesting case of long intramolecular d(10)-d(10) contacts has been studied through [Ag(4)L(2)](2+) and [Au(4)L(2)](2+) (L = 3,5-bis((N-methylimidazolyl)methyl)pyrazole) systems, showing interesting features gained by analysis of the electronic structure and the overall shielding tensor in the molecular domain, in terms of its components. The long intramolecular closed-shell separations are attributed to the population of the bonding, nonbonding, and antibonding combinations of the ns atomic shells in the [M(4)](4+) core, contrasting with that observed in systems with shorter d(10)-d(10) distances. This point allows to concludeb that separations shorter then the sum of the van der Waals radii (3.4 ? for Ag-Ag, and 3.2 ? for Au-Au) of the nucleus involved requires a net bonding population between ns and np atomic shells of the d(10) closed-shell centers. Moreover, [Au(4)L(2)](2+) exhibits an increased covalency observed for the enhanced charge-donation due to the stabilization of the ns and destabilization of the (n - 1)d driven by the relativistic effects. The magnetic response denotes a slight interaction between the closed-shell centers at distances in the range of their sum of van der Waals radii because the observed remote effect (or anisotropic effect) caused by each d(10) nucleus does not influence considerably the neighbor center. The analysis of δ in terms of its components allows to conclude that the [Au(4)L(2)](2+) system exhibits an increased magnetic response due to the increase in the number of the inner-electrons in comparison to [Ag(4)L(2)](2+). 相似文献