Existence of an Angular Density of Roots of Entire Functions of Order Zero

We obtain sufficient conditions for the set of roots of an entire function of order zero of strongly regular growth to possess an angular density.     

Nonlocal excitonic–mechanical interaction in a nanosystem

The dynamics of a nanoparticle during its dipole interaction with an excitonic excitation in an extended quasi-one-dimensional polarizable medium is investigated. Bundles of J-aggregates of dye molecules are considered as an example of the latter. The nonlocal excitonic–mechanical interaction between the field of an amplifying or absorbing nanoparticle and excitons in a bundle has been simulated numerically. It has been found that the interaction between the field of the induced nanoparticle dipole and the fields of the molecular dipoles in an aggregate can lead to a change in the particle trajectory and excitonic pulse shape. The possibility of controlling the nanoparticle by excitonic pulses and the reverse effect of the nanoparticle field on the dynamics of excitons due to the nonlocal excitonic–mechanical interaction has been demonstrated.     

Correction of pH of diluted solutions of electrolytes by electrodialysis with bipolar membranes

The current efficiencies of the water dissociation water and the voltage-current characteristics of the bipolar (asymmetric bipolar) membranes were measured in a two-chamber electrochemical cell. The cell was formed of an MB-3 bipolar membrane or an asymmetric bipolar membrane, which is an MA-40 heterogeneous membrane with a thin surface layer in the form of a cation-selective homogeneous film and MA-40 and MA-41 heterogeneous monopolar membranes. The dissociation of water on MA-40 in 0.01 M sodium chloride decreased the current efficiency of the acid and alkali both in the channel with a bipolar membrane and in the channel with an asymmetric bipolar membrane. The effective ion transport numbers across MA-40 and MA-41 at different pH values were determined. The water dissociation rate on MA-40 decreased at pH > 9.5. A kinetic model of the electrodialysis of a dilute solution of sodium chloride in a two-chamber unit cell with a bipolar and anionite membranes was suggested.     

Transfer of electrolyte ions and water dissociation in anion-exchange membranes under intense current conditions

Polarization characteristics of electromembrane systems (EMS) based on the Russian commercial heterogeneous membranes MA-40 and MA-41, the anion-exchange heterogeneous membrane AMH (Mega, Czech Republic), and the modified membrane MA-40M are studied by the method of rotating membrane disk in dilute sodium chloride solutions. The effective transport numbers of ions are found; the partial voltammetric characteristics (VAC) with respect to chloride and hydroxyl ions are measured; the limiting current densities are calculated as a function of the membrane disk rotation rate. In terms of the theory of the overlimiting state of EMS, based on experimental VAC and the dependences of the effective transport numbers on the current density, the following internal parameters of systems under study are calculated: the space charge and electric field strength distribution over the diffusion layer and the membrane. It is shown that water dissociation can be virtually completely eliminated by substituting chemically stable quaternary ammonium groups inert with respect to water dissociation in the surface layer of a heterogeneous anion-exchange membrane MA-40 for the active ternary and secondary functional amino groups. The maximum electric field strength values at the membrane/solution interface, which were found in the framework of the theory of over-limiting state, turned out to be close for all anion-exchange membranes studied, namely, (7?C9) × 10⁶ V/cm. This suggests that it is the nature of ionogenic groups in the surface layer rather than the field effect that plays the decisive role in the membrane ability to accelerate the water dissociation reaction. It is proved experimentally that in highly intense current modes of the electrodialysis process, the thermal hydrolysis of quaternary ammonium bases occurs in strongly basic MA-41 and AMH membranes by the Hofmann reaction to form ternary amino groups catalytically active in water dissociation reaction. Based on the concept on the catalytic mechanism of water dissociation, the fraction of ternary amino groups formed by thermal hydrolysis in the surface layer (the space charge region) of monopolar anion-exchange membranes MA-41 and AMH is assessed quantitatively as 0.7 and 6.5%, respectively.     

Steady-state Ion Transport through a Three-Layered Membrane System: A Mathematical Model Allowing for Violation of the Electroneutrality Condition

A relatively simple mathematical model based on the Poisson equation is considered. The model is intended for modeling transport through multilayered ion-exchange membranes operating at overlimiting currents. The boundary-value problem is solved by a numerical method of parallel shooting and by an approximate method based on the assumption that the charge density is distributed quasi-uniformly. Concentration profiles in diffusion layers and membranes, current–voltage curves, and dependences of effective transport numbers on the current density are examined.     

Sodium chloride concentration by electrodialysis with hybrid organic-inorganic ion-exchange membranes: An investigation of the process

This study examines how conditions for modifying homogeneous MF-4SK and heterogeneous MK-40 membranes with tetraethoxysilane affect membrane properties. The microstructure of the bulk membrane and its surface, both before and after exposure to the modifying agent, is examined by scanning electron microscopy, spark spectrophotometry, and standard contact porosimetry. The process of sodium chloride concentration by electrodialysis with hybrid organic-inorganic membranes in cells with noncirculating concentration compartments is investigated, and a mathematical model of the concentration process by electrodialysis is used to determine transport properties: current efficiency, diffusion and osmotic permeabilities, and the salt hydration number. For highly hydrophilic membranes, it is shown that water transport occurs both in ion hydration shells and also as free water. It is established that after modified membranes undergo additional heat treatment, the transport of free water ceases, and the water transport number decreases. This is in accord with an increase in the salt content of the concentrate during concentration by electrodialysis.     

Influence of the nature of membrane ionogenic groups on water dissociation and electrolyte ion transport: A rotating membrane disk study

Polarization properties of electromembrane systems (EMS) consisting of a heterogeneous membrane, either the MK-41 phosphonic acid membrane or the MK-40 sulfonic acid membrane, and dilute sodium chloride solutions are investigated with the rotating membrane disk method. For the MK-41/0.01 M NaCl and MK-41/0.001 M NaCl EMS, effective ion transport numbers and partial current-voltage curves (CVC) are measured for sodium and hydrogen ions, and limiting-current densities and the diffusion-layer thickness are calculated as functions of the rotation rate of the membrane disk. With the theory of the overlimiting state of EMS, internal parameters of the systems under investigation—the diffusion-layer thickness, the space-charge distribution, and electric-field strengths in the diffusion layer and in the membrane—are calculated from experimentally obtained CVC and the dependence of effective transport numbers on current density. The catalytic influence of ionogenic groups on the dissociation rate of water is analyzed quantitatively. Partial CVC for H⁺ ions are calculated for the space-charge region in MK-40 and MK-41 membranes. Analogous CVC for bipolar membranes containing sulfonic acid and phosphonic acid groups are compared. The dissociation mechanism of water is the same in all EMS and is independent of the membrane type and the nature of the functional groups.     

Dissipative soliton-like plasmon-polariton pulses in extended medium

The propagation of the coupled state of the electron density perturbation in an extended metallic medium and the excitation of a two-level resonant medium are analyzed. The one- and two-photon transitions in the resonant medium are considered. The electron density perturbation is described using the hydrodynamic approximation. The formation of plasmon-polariton pulses is analyzed in the case when losses in the extended medium are compensated for by the pumping of the two-level dielectric medium. Numerical analysis carried out for the two models revealed that the losses in a soliton-like pulse in a thin metallic medium can be compensated for due to the energy transfer from the amplifying medium to electron density waves. It is shown that the dispersion of a medium containing a two-level component may considerably affect the characteristics of the pulses. The possibility of effectively controlling the evolution of soliton-like pulses by varying an external electromagnetic field and the characteristics of the matrix is demonstrated.     

Joint Effect of the Dipole–Dipole Interaction and Constant Dipole Moment on the Shape of the Field Pulse without an Envelope

Journal of Experimental and Theoretical Physics - An integrable model is proposed for a two-level medium with a constant dipole moment, which describes the evolution of electromagnetic field pulses...