Two-phase channel structures based on alpha-cyclodextrin-polyethylene glycol inclusion complexes

Wide-angle X-ray scattering observations of alpha-cyclodextrin (CD)-poly(ethylene glycol) (PEG) inclusion complexes (ICs) have shown for the first time that two crystalline columnar modifications (forms I and II) are produced in the process of their formation. This was made possible by precise azimuthal X-ray diffraction scanning of oriented IC samples. Form I is characterized by CDs threaded onto PEG chains and arranged along channels in the order head-to-head/tail-to-tail, while form II is formed by unbound CDs also arranged into columns in a head-to-tail and also possibly a head-to-head/tail-to-tail manner, probably as a result of template crystallization on the form I IC crystals. It was shown that similar structural peculiarities are inherent for channel structures based on ICs obtained with PEG with a wide range of molecular weights (MWs). The characteristic feature of ICs based on PEG, especially with MW > 8000, is the presence of unbound polymer in the composition of the complex. The amount of unbound PEG was shown to rise with increasing MW of PEG, resulting in greater imperfections in the IC crystalline structure. The polyblock structure of ICs based on alpha-CD and PEG was therefore proposed.     

Supermolecular structures and flow birefringence in polymer solutions

Experimental studies of supermolecular structures and localized flow birefringence in solutions of high-molecular weight polymer are described. Advantage is taken of poly(ethylene oxide) and polyisobutylene. Supermolecular structures are examined with the aid of optical microscopy using freeze-dried samples of the polymer solutions. Birefringence is investigated that arises in planar elongational flow in a cross-slot cell. Flow velocities at which the onset of the localized birefringence occurs are determined. Then these velocities are correlated with viscoelastic characteristics of the solutions. The presence of a liquid-crystalline fibrillar network in the polymer solutions exhibiting flow birefringence is ascertained. The fibrils are birefringent objects. The fibrils are birefringent objects. The localized birefringence phenomenon is explained in term of the orientation of the fibrils in elongational flow. It has been shown that the onset of localized birefringence occurs at a critical Weissenberg number, the value of which is close to unity.     

Determination of the adsorption volume and surface of carbon adsorbents with developed mesoporosity

The isotherms of excess adsorption of CH₄ (atP=0.001–160 MPa), SF₆ (atP=0.001–2.4 MPa), and C₆H₆ (atP=0.0001–0.1 MPa) on carbon adsorbents—microporous carbons CMS and FAS with developed mesoporosity and graphitized soot—were measured in the 298–408 K temperature region. Calculation of the isotherms of absolute adsorption of the total content of these substances requires knowledge of the adsorption volume, which was determined by different methods: by the Dubinin—Radushkevich equation; by the experimental isotherm of excess adsorption and the equation of absolute adsorption; by the method using the intersection of nonlinear isosteres of excess adsorption and isosteres of absolute adsorption; by the comparative plot of values of the excess C₆H₆ adsorption Γ_FAS—Γ_soor; by the method using the difference of molecular radii of adsorptives and the surface of the specific adsorbent; and by the calculation of the adsorption layer thickness using the FHH equation for mesoporous systems. The results of determination of the adsorption volume for microporous systems of these carbons agree well with each other and with the passport data for the adsorbents. Analysis of the results revealed the peculiarity of the sulfur hexafluoride adsorption related to the formation of associates on the surface of the carbon adsorbents. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 4, pp. 688–696, April, 2000.     

Synthesis of polyrotaxanes based on α-cyclodextrin and poly(ethylene oxide)

Inclusion complexes of poly(ethylene oxide) with α-cyclodextrin are the key compounds in the synthesis of polyrotaxanes. These complexes prepared in aqueous solutions contain free cyclodextrin, which cocrystallizes with the major reaction product. These complexes dissociate upon dissolution in DMF and DMSO to form cyclodextrin and pseudopolyrotaxanes with a low cyclodextrin content. Polyrotaxane was synthesized with the use of poly(ethylene oxide)-α,ω-bis-amine as a linear component. The end-groups of the polymer in the inclusion complex were modified by the reaction with 2,4-dinitrofluorobenzene. A procedure was developed for purification of a polyrotaxane with high cyclodextrin content. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1914–1918, August, 2005.     

On some nonlinear problems in mathematical physics with exponents close to critical ones

The paper deals with several problems having the following common feature. The differential equation under consideration contains a power function of the solution or of its gradient, with the exponent depending on a small parameter. This dependence is such that a certain property of the solutions corresponding to the positive values of the parameter may disappear as the latter tends to zero. This phenomenon is shown to be lacking in the case where not only the said exponent, but also the coefficients of the equation depend on the small parameter in a suitable way. Several theorems are proved on sharp conditions, ensuring such uniformity of various properties exhibited by the solutions. Bibliography: 44 titles. Dedicated to Olga Arsenievna Oleinik This paper has been supported in part by the Russian Foundation for Basic Research (Project 93-013-1744) and by the International Science Foundation (Grant MIE000). Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000.     

Spatial No-Waiting Stations with Moving Customers

We analyze spatial MAP/G/∞-, spatial MAP/G/c/0¹ and spatial Cox/G/∞-stations with group arrivals over some Polish space X (with Borel σ-algebra X), including the aspect of customer motion in space. For models with MAP-input, characteristic differential equations are set up that describe the dynamics of phase dependent random functions Q _r;ij (u,t;S′), where Q _r;ij (u,t;S′) is the probability to observe, at time u≤t, the number r of those customers in some source set S′∈X, who will be in a destination set S∈X at time t. For Cox/G/∞-stations, i.e., infinite server stations with doubly stochastic input, the arrival intensities as well as service times may depend on some general stochastic process (J′ _t ) _t≥0 with countable state space. For that case we obtain explicit expressions for space–time distributions as well as stationary and non-stationary characteristics.     

Dynamical gain saturation in Kerr-lens mode-locked CW solid- state lasers

It is shown that dynamical gain saturation, usually neglected for solid-state lasers, can contribute significantly to the pulse-shaping mechanism in Kerr-lens mode-locked lasers. In particular, in combination with self-phase modulation it can cause red shifts and blue shifts of the laser spectrum. A control of the reciprocal gain and loss saturation rates using these shifts leads to improved mode- locking stability.     

Regenerative queueing processes and their qualitative and quantitative analysis

Recently developed methods of qualitative analysis for regenerative processes arising in queueing are presented. These methods are essentially qualitative and use notions such as coupling, probability metrics, etc. They are developed for studying various properties of regenerative models, including convergence rate to a stationary regime, continuity of their characteristics with respect to some parameters and first-occurrence time of an event such as queue overflowing. In spite of their qualitative nature they lead to good quantitative estimates of underlying properties with computer methods available to calculate them.     

Solving two-Level variational inequality

An approach to solving a mathematical program with variational inequality or nonlinear complementarity constraints is presented. It consists in a variational re-formulation of the optimization criterion and looking for a solution of thus obtained variational inequality among the points satisfying the initial variational constraints.This research was supported by the Russian Fundamental Research Foundation, Grant No. 93-012-842