Numerical algorithm for the Mayer problem for nonlinear dynamic systems

An algorithm is proposed for numerical construction of optimal programmed controls in the Mayer problem for a nonlinear dynamic system. In each step of the optimization process, the algorithm uses the method of successive linearization with subsequent projection of the objective functional gradient on the constraints and recovery of violated boundary conditions and constraints. Solutions of some test problems are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 107–114, 1985.     

Redox-induced η5 ⇔ η3 haptotropy of the fluorenyl ligand in 9-substituted η5-fluorenylmanganesetricarbonyl complexes

It has been shown by cyclic voltammetry in THF within the –90 to 40 °C temperature range that fluorenyl (⁵-9-R-C₁₃H₈)Mn(CO)₃ complexes (R=Bu^t (3) and Ph (4)) undergo two-electron reduction to form allyl type [(³-9-R-C₁₃H₈)Mn(CO)₃]^2– dianions as final products. At low temperatures complexes3 and4 are reduced in two one-electron steps according to the EEC-scheme. The first step is reversible and corresponds to the formation of 19-radical anions 3^–. and 4^–.. TheE ⁰ values for redox pairs3 ^0/–. and4 ^0/–. are –1.88 and –1.73 V, respectively. The further reduction of radical anions3 ^–. and4 ^–. at more negative potentials is accompanied by fast ^{5 3} haptocoordination of the fluorenyl ligand to form 18-dianions [(³-9-R-C₁₃H₈)Mn(CO)₃]^2–. These dianions obtained by the reduction of complexes3 and4 by the radical anion of pyrene are stable at –80 °C and are characterized by their IR spectra. At room temperature the ^{5 3} hapticity change is a fast and reversible process occurring at the step of 19-radical anions3 ^–. and4 ^–. and leading to the electron deficient 17-species [(³-9-R-C₁₃H₈)Mn(CO)₃]^–., which are reduced easier than the initial complexes. As a result, complexes3 and4 are reduced to the corresponding dianions [(³-9-R-C₁₃H₈)Mn(CO)₃]^2– at room temperature in one reversible two-electron step according to the ECE-scheme. Reactivities of 19e^–-species of the isomeric ⁵- and ⁶-fluorenylmanganesetricarbonyl complexes are compared.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1347–1353, July, 1995.The work was financially supported by the Russian Foundation for Basic Research (Project No. 93-03-05209) and the International Science Foundation (Grant No. REV 000).     

Empirical formula for the concentration dependence of the conductivity of organic electrolytes for lithium power sources in the vicinity of a maximum

To optimize the compositions of liquid organic electrolytes for lithium power sources, it is useful to have the dependence of the conductivity on the lithium salt concentration in a convenient analytical form. An empirical formula was suggested on the basis of the modified Kohlrausch equation for the concentration dependence of the conductivity of organic electrolytes in the vicinity of a maximum. The accuracy of this equation was checked on solutions of LiBF₄ in propylene carbonate; LiClO₄ in ethylene carbonate; and LiPF₆ in ethylene carbonate/diethyl carbonate (1: 1), ethylene carbonate/ethylmethyl carbonate (1: 1), and ethylene carbonate/methyl acetate (1: 1) at different temperatures. The calculated data are in good agreement with experiment for all the systems. The new empirical formula allows the determination of the maximum conductivity of organic electrolytes based on a few points with good accuracy, which is very important in choosing the electrolyte salt concentration in practice.     

Specific features of the synthesis and the physicochemical properties of nanocomposite polymer electrolytes based on poly(ethylene glycol) diacrylate with the introduction of SiO<Subscript>2</Subscript>

The specific features of the synthesis and the physicochemical properties of new nanocomposite polymer electrolytes (NPE) based on poly(ethylene glycol) diacrylate, a liquid electrolyte, and silicon dioxide were studied. The kinetics of polymerization of the system in question were studied by isothermal calorimetry and the optimal conditions for the hardening of the NPE were selected. The dependence of the conductivity of the electrolyte samples on the amount of SiO₂ nanopowder introduced, the presence of preliminary ultrasonic treatment of the nanocomposite mixture before the synthesis, and the storage duration of the samples was studied using the electrochemical impedance method. The maximum conductivity (4.3?10^–3 S cm^–1 at 20 °C) was observed for samples without preliminary treatment with the introduction of 6 wt.% of SiO₂ and for the samples after ultrasonic treatment with 8 wt.% of SiO₂. The electrolyte films with the optimal SiO₂ content of 4 wt.% maintained their properties for 24 months.     

Self-diffusion of lithium cations and ionic conductivity in polymer electrolytes based on polyesterdiacrylate

The processes of ionic conductivity are studied in a polymer gel electrolyte synthesized based on polyesterdiacrylate and a low-molecular solvent ethylene carbonate. The self-diffusion coefficients of solvent molecules and Li⁺ cations are measured by the NMR with the pulsed magnetic field gradient. The Li⁺ self-diffusion coefficients increase with the increase in the solvent content and are independent of the diffusion time in the interval from 10 to 1600 ms. The latter values imply the absence of limitations for the translational mobility of lithium ions in the spatial range from 10⁻⁷ to 10⁻⁵ m. Based on the Nernst-Einstein equation, the ionic conductivities are calculated and compared with the experimental conductivities measured by the impedance method. These values coincide for high contents of solvent; for low ethylene carbonate concentrations, the calculated conductivities much exceed the experimental values.     

Formation of Hydrophobic and Superhydrophobic Coatings on Track-Etched Membrane Surfaces to Create Composite Membranes for Water Desalination

Colloid Journal - Different methods have been considered for the formation of coatings on the surface of a hydrophilic poly(ethylene terephthalate) track-etched membrane with the help of...     

Causes of the double maximum conductivity of nanocomposite polymer electrolytes for lithium power sources

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Nanocomposite Polymer Electrolytes for the Lithium Power Sources (a Review)

Nanocomposite polymer electrolytes represent a perspective class of polymer electrolytes for electrochemical devices in which nanodisperse filler is introduced to the “solvating matrix + lithium salt” base composition. This three-section paper reviews studies devoted to the preparing and investigating of different types of novel nanocomposite polymer electrolytes for lithium power sources carried out for the last 15 years. Its first section is devoted to the solid nanocomposite polymer electrolyte consisting of polyethylene oxide, lithium salt, and nanodisperse filler (Al₂O₃, TiO₂, SiO₂, etc.); the second section, to nanocomposite polymer membranes based on the polyvinylidene fluoride-co-hexafluoropropylene that can be used as a substitute for inert polyolefine separator of polypropylene, polyethylene, or their alternating layers. It is this type of the nanocomposite polymer electrolytes that is the most perspective one; the great majority of publications are dedicated to this electrolyte. The third section of the review covers the studies of the nanocomposite polymer electrolytes based on different polymers, oligomers, and co-polymers prepared by different methods. Nanoparticles of Al₂O₃, TiO₂, SiO₂, ZnO, MgO, Fe₃O₄, Ca₃(PO₄)2, ZrO₂, clay, ferroelectric ceramics SrBi₄Ti₄O₁₅, a compound SO₄^2-–ZrO₂, molecular sieves, nanochitin, etc., are discussed as possible additives to the nanocomposite polymer electrolytes. The reference list contains 101 items.     

Structure of LiBF4 Solvate Complexes in Ethylene Carbonate,Based on High-Resolution NMR and Quantum-Chemical Data

Russian Journal of Physical Chemistry A - The ion solvation of LiBF4 in ethylene carbonate is studied via high resolution NMR, conductometry, and quantum-chemical simulation. 7Li, 11B, 19F, 13C,...