Decoupling of the nernst-planck and poisson equations. Application to a membrane system at overlimiting currents

This paper deals with one-dimensional stationary Nernst-Planck and Poisson (NPP) equations describing ion electrodiffusion in multicomponent solution/electrode or ion-conductive membrane systems. A general method for resolving ordinary and singularly perturbed problems with these equations is developed. This method is based on the decoupling of NPP equations that results in deduction of an equation containing only the terms with different powers of the electrical field and its derivatives. Then, the solution of this equation, analytical in several cases or numerical, is substituted into the Nernst-Planck equations for calculating the concentration profile for each ion present in the system. Different ionic species are grouped in valency classes that allows one to reduce the dimension of the original set of equations and leads to a relatively easy treatment of multi-ion systems. When applying the method developed, the main attention is paid to ion transfer at limiting and overlimiting currents, where a significant deviation from local electroneutrality occurs. The boundary conditions and different approximations are examined: the local electroneutrality (LEN) assumption and the original assumption of quasi-uniform distribution of the space charge density (QCD). The relations between the ion fluxes at limiting and overlimiting currents are discussed. In particular, attention is paid to the "exaltation" of counterion transfer toward an ion-exchange membrane by co-ion flux leaking through the membrane or generated at the membrane/solution interface. The structure of the multi-ion concentration field in a depleted diffusion boundary layer (DBL) near an ion-exchange membrane at overlimiting currents is analyzed. The presence of salt ions and hydrogen and hydroxyl ions generated in the course of the water "splitting" reaction is considered. The thickness of the DBL and its different zones, as functions of applied current density, are found by fitting experimental current-voltage curves.     

The use of mixtures of ligands in the Ir-catalyzed asymmetric reductive amination of 6-methyl-2,3,4,9-tetrahydro-1<Emphasis Type="Italic">H</Emphasis>-carbazol-1-one

A comparative testing of complex catalysts with homo and hetero combinations of chiral and achiral monodentate phosphite- and phosphine-type ligands in the Ir-catalyzed asymmetric direct reductive amination of 2,3,4,9-tetrahydro-1H-сarbozol-1-ones was carried out. A positive effect of the use in the reaction of a mixture of chiral and achiral ligands was demonstrated. This approach makes feasible a one-pot synthesis of valuable biologically active compounds of (tetrahydro-1H-carbazol-1-yl)amine series.     

Matching of light fluxes in the analysis of measurement data with different space resolutions

We investigate the effect of the dimensions of instantaneous visual fields and the time of accumulation of a signal on the magnitude of light fluxes, recorded by means of charge-coupled device (CCD)-receivers, in scanning different kinds of surfaces. We show that, to compare light fluxes, it is necessary to introduce weight coefficients that take into account the time during which an area measured with a high space resolution is in the visual field of instrumentation with a low space resolution. Errors in the determination of light fluxes, when data obtained with a high space resolution are summed up with equal weight coefficients, have been evaluated. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 123–126, January–February, 2000.     

Theoretical Analysis of the Effect of Ion Concentration in Solution Bulk and at Membrane Surface on the Mass Transfer at Overlimiting Currents

Overlimiting current modes are of considerable interest for the practice of electrodialysis (ED). However, the economical expedience of such ED modes is evident only for desalination of dilute solutions. Here, we show the theoretical analysis of the effect of concentration on the behavior of an ED cell with homogeneous ion-exchange membranes. The study is based on numerical solution of the two-dimensional system of coupled equations of Nernst–Planck–Poisson–Navier–Stokes. It is shown that as the electrolyte concentration in solution that enters the ED desalination chamber increases, the intensity of electroconvection decreases, which induces a decrease in the relative mass-transfer rate (the decrease in the ratio of current density to its limiting value). This effect is stronger in the region of high potential differences where the electroconvective instability of Rubinstein–Zaltzman is realized under the conditions of a nonuniform concentration field caused by solution desalination. In contrast, the increase in the counterion concentration at the membrane surface (associated with the increase in the surface charge) intensifies the electroconvection.     

Effect of ion implantation on the fine structure of NiAl-based coatings formed by magnetron deposition

The phase composition and fine structure of intermetallic coatings are investigated by electron microscopy and X-ray analysis. It is shown that intermetallic Ni₃Al is the main phase of the coating for all samples under study. Ion implantation of coatings with aluminum and boron ions leads to changes in the lattice parameter and the parameters of long-range order, internal elastic stress, grain size, and dislocation structure.     

Effect of alloying and temperature of deformation on the grain structure and phase composition of Ni3Al intermetallic

The structure of Ni₃Al intermetallic alloyed with boron and hafnium is studied at various temperatures of deformation by means of diffraction and scan electron microscopy. The alloy was produced through self-propagating synthesis. The phase composition of the alloy is determined. The effect of doping with boron and hafnium on the alloy structure morphology is revealed.     

Ion Transport in a Three-Layered Ion-Exchange Membrane: A Mathematical Model

An ion transport model is considered. The model is based on the Nernst–Planck equations, the elements of nonequilibrium thermodynamics, the principle of local equilibrium, and the concept of a virtual solution. The model is applied to an ion-exchange membrane with two diffusion layers for the cases of electrotransport of two and three types of ions. To determine transfer coefficients L ^* _j in the Nernst–Planck equations, two approaches are used. In the phenomenological approach, L ^* _j are found from experimental data on the electroconductivity and transport numbers. In the modeling approach, values of L ^* _j are sought for from a model of a microheterogeneous membrane. The obtained boundary-value problem is solved using a numerical method of parallel shooting developed earlier, which perfectly fits specific features of the problem formulation (utilizing the Nernst–Planck equations in all the three layers and the concept of a virtual solution).     

Synthesis of some esters of α-acetoxy-Β,Β,Β-trichloroethylphosphonic acid

Summary By the reaction of dialkyl esters of -hydroxy, ,-trichloroethylphosphonic acid and acetic anhydride in the presence of a few drops of sulfuric acid, the dialkyl esters of -acetoxy-,,-trichloroethylphosphonic acid were obtained in high yields.     

Measurement of the thickness of thin polymer layers by infrared frustrated total internal reflection spectroscopy

A method is proposed for determining the thickness of thin (0.1–5.0 μm) polymer layers and coatings by means of infrared frustrated total internal reflection (FTIR) spectroscopy. This method is based on an analytic expression derived for the dependence of the intensities of absorption bands in IR FTIR spectra on the thickness of a polymer layer. The method is tested on model samples consisting of a thick film of polyethylene terephthalate with a layer of different thicknesses of polystyrene deposited on it. The advantage of this method is the ability to determine the thickness of thin polymer layers deposited on bulk or opaque polymer substrates. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 881–885, November–December, 2008.