Study of solvation of alkali cations with poly(ethylene oxide)

The interaction of sodium, potassium and caesium salts with poly(ethylene oxide) in nitromethane is considered as a model for solvation of alkali counterions with a heterochain polymer during the anionic polymerization of heterocycles. The methods of ²³Na and ¹³³Cs n.m.r. and of conductometry sensitive towards the state of the cation have been used for studying the equilibria. It has been shown that poly(ethylene oxide) binds cations much more strongly than monomeric cyclic ethers, a solvation shell being formed involving several (6–12) oxygen atoms of the same macromolecule. The equilibrium constants of the formation of solvate complexes have been evaluated; they increase with increasing chain length and decreasing cation radius. The mechanism of interactions and their role in the processes of anionic polymerization are discussed.     

Potential in the “Clearance” of torus: Development on spherical functions

The method of solution of the Dirichlet problem for potentials of volume bodies with torus topology when the boundary conditions are set in the form of a series on spherical harmonics on pieces of two spherical surfaces is developed. The problem representation of an exterior potential homogeneous gravitating (or charged by static electric charge) circular torus out of a substance in a special (??intermediate??) spherical zone is presented and solved. The solution is received in the form of a combination of the Laplace series on even positive and odd negative degrees of the radius-vector of a test point. Coefficients of this series are received in a final analytical form. The general member of the series at the limit of big n tends to zero so the series converges fast and the radius of convergence are defined by torus geometry. The specified solution meets a gap in the theory, connecting together earlier discovered by us, two expansions in the Laplace series of a torus potential in ??interior?? and ??exterior?? spherical space zones. Thus, it is proved that it is possible to present the torus potential by power rows in all free space from the substance. For control of results by means of the obtained series, equipotential surfaces of the torus were calculated.     

Mechanism of erythrocyte aggregation enhancement by ultrasonic field

Effect of a standing ultrasonic wave on the spontaneous and induced (specific, immune) processes of erythrocyte aggregation is studied in vitro on the basis of the data obtained from the elastic scattering of light. The effect of the time of ultrasonic action and the concentration of the initial reagents on the enhancement of these processes is analyzed. An approximate theoretical model is developed to describe the mechanism of the enhancement of erythrocyte aggregation by an ultrasonic field and the observation of the process of interest by the turbidimetric optical method. The model provides a good agreement between theory and experiment. The results of the study are used to derive recommendations as to how to increase the resolving power of the turbidimetric method of immunoanalysis with the aid of ultrasound.     

Inverse Problems of Spectral Analysis and Carleson Interpolation

Mathematical Notes -     

Three-dimensional potential of a homogeneous circular torus in terms of equigravitating elements

The complete system of the simplest equigravitating elements presented for a homogeneous circular torus comprises a compound one-dimensional rod consisting of three links with a purely imaginary density, as well as two real point masses located at the ends of the rod. In terms of these elements, the three-dimensional gravitational potential of the torus at an arbitrary point is derived. The surface of the potential is constructed, and the family of equipotential curves is found.     

Effect of the functionality of junctions on the elasticity of polymacromonomer networks: Computer simulation

The elastic properties of polymer networks formed via the radical polymerization of macromonomers with two polymerizable end groups are studied via computer simulation. It is shown that variation in the average functionality of network junctions, f _avg, in a wide range (∼5–55) leads to a significant change in the shear modulus of the network. According to experiments with real networks (gels of poly(ethylene oxide) macromonomers), the shear modulus increases as f _avg increases. This effect is not due only to a decrease in the fluctuations of positions of network junctions. The main cause of the increase in the modulus is that the modulus component due to interaction between polymer chains (entanglements) increases as the functionality of junctions in the investigated networks increases. The conclusion is made that these networks gain entanglements during the formation of network junctions with high functionality rather than inherit them from the solution of macromonomer chains.     

Self-organization in two- and three-dimensional adsorbates with attractive lateral interactions

Self-consistent lattice gas models for the dynamics of monolayer and multilayer adsorbates with attractive lateral interactions are investigated. The existence of spinodal regions with uphill diffusion is shown. For monolayer growth, periodic stationary distributions of adsorbate density are found analytically. Generalized kinetic BET-model for multilayer growth is studied numerically. A possibility for surface transformation into self-organized arrays of quantum dot-like structures is shown.