Study of radical methyl methacrylate-methacrylic acid copolymerization in isopropyl alcohol by dynamic laser scattering and C-NMR spectroscopy

The copolymerization of methyl methacrylate and methacrylic acid in isopropyl alcohol is studied by kinetic, dynamic laser scattering and ¹³C-NMR methods. Correlations are established between the dependence of the copolymerization rate, the apparent average molecular weight, the diffusion coefficients and the configurational triad composition on the monomer feed. These correlations and the fact that both copolymerization constants are smaller than unity (r_MMA = 0.63 ± 0.03; r_MA = 0.25 ± 0.05) are in good agreement with the assumption that a comonomer complex takes part in the propagation reaction. A new Markov chain method for the estimation of the configurational triad mole fraction which accounts for the complex participation in a macromolecule formation is developed. Qualitative criteria for evidence the participation of the comonomer complex in copolymerization are proposed using experimental and terminal model calculated mole fractions of the compositional triads and diads.     

Cyclic Hypomonotonicity,Cyclic Submonotonicity,and Integration

Rockafellar has shown that the subdifferentials of convex functions are always cyclically monotone operators. Moreover, maximal cyclically monotone operators are necessarily operators of this type, since one can construct explicitly a convex function, which turns out to be unique up to a constant, whose subdifferential gives back the operator. This result is a cornerstone in convex analysis and relates tightly convexity and monotonicity. In this paper, we establish analogous robust results that relate weak convexity notions to corresponding notions of weak monotonicity, provided one deals with locally Lipschitz functions and locally bounded operators. In particular, the subdifferentials of locally Lipschitz functions that are directionally hypomonotone [respectively, directionally submonotone] enjoy also an additional cyclic strengthening of this notion and in fact are maximal under this new property. Moreover, every maximal cyclically hypomonotone [respectively, maximal cyclically submonotone] operator is always the Clarke subdifferential of some directionally weakly convex [respectively, directionally approximately convex] locally Lipschitz function, unique up to a constant, which in finite dimentions is a lower C² function [respectively, a lower C¹ function].     

Residence times in kink sites and Markov chain model of alloy and intermetallic compound deposition

The concept of the residence time τ_ksp of an atom in a kink site has recently been suggested to understand the processes in electrochemical deposition of alloys and intermetallic compounds. Different kink sites with different residence times must be defined for alloys and intermetallic compounds. Based on this model, the finite Markov chain theory is applied to describe the selectivity of the growth process. An analytical relationship between the alloy composition and the metal ion concentrations in the electrolyte is derived. General model parameters are ratios g _i = K _ii/K _ij of equilibrium constants of the reaction of electrolyte ions with different kink sites on the surface (i, j representing different alloy components). These ratios are called selectivity constants. For simple conditions, the equation g _i ≈ τ_ii/τ_ij connects the g _i values with the residence times. The theory is tested in the deposition of alloys Co-Ni (anomalous co-deposition) and Ni-Mo (induced co-deposition). Additionally, Bi₂Te₃, an example of stoichiometric semiconductor deposition, is treated. Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 10, pp. 1216–1223. The text was submitted by the authors in English.     

Second-order subdifferentials of C1,1 functions and optimality conditions

We present second-order subdifferentials of Clarke's type of C ^1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ⁿ , considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C ^1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994.     

CO(2) laser with modulated losses: Theoretical models and experiments in the chaotic regime

We compare two different theoretical models for a CO(2) laser, namely, the two- and four-level model, and show that the second one traces with much better accuracy the experimentally observed chaotic dynamics when the cavity losses are sinusoidally modulated. Even though the two-level model provides a qualitative explanation of the chaotic dynamics, only the four-level one assures a quantitative fitting. We also show that, at the onset of chaos, the chaotic dynamics is low dimensional and can be described in terms of a noninvertible one-dimensional map.     

Gitterschwingungsspektren. LXIII. Be(lO3)2 · 4 H2O,ein Hydrat mit ungewöhnlicher Bindungsstruktur und Gitterdynamik

Lattice Vibration Spectra. LXIII. Be(IO₃)₂ · 4 H₂O, a Hydrate with Unusual Bonding and Lattice Dynamics The IR and Raman spectra (4000–50 cm^?1) of Be(IO₃)₂ · 4 H₂O and of deuterated specimens are recorded at 90 and 300 K and discussed in terms of the unusual relations of the masses of the atoms involved and the large polarization power of the beryllium ions. Thus, the translatory modes of the Be²⁺ ions (BeO₄ skeleton vibrations), the librations of the H₂O molecules, and the internal vibrations of the IO₃^? ions in the spectral regions of 300–400 and 600–1000 cm^?1 couple and coincide producing unusual v_H/v_D isotopic ratios of partly < 1. The H-bond donor strengths of the water molecules is so much increased (due to the very large ionic potential of Be²⁺ ions, viz. 49 e nm^?1) (synergetic effect) that the H-bonds formed are similar in strength as those in hydrates of hydroxides with the very strong H-bond acceptor group OH^? (v_OD of matrix isolated HDO molecules 2 074 and 2 244 (H₂O I) and 2 206 and 2 349 cm^?1 (H₂O II))     

Raman spectroscopic study of the hydration of short-chain poly(oxyethylene)s C <Subscript>1</Subscript>E<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>C <Subscript>1</Subscript> (<Emphasis Type="Italic">n</Emphasis>=1−4)

The hypothesis that the degree of hydration of poly(oxyethylene) (POE) in aqueous solution depends on the mole ratio of water molecules to ether oxygen atoms in the molecule has been verified by studying the isotropic Raman spectra in the O−H stretching region for four short-chain POEs (C ₁E _n C ₁ withn=1−4). Excellent coincidence of the O−H stretching Raman band for all four POEs studied in the range of mole ratio H₂O/O _ether from 25 to 0.6 was observed, thus confirming the assumption stated above. A conclusion that all ether oxygen atoms in the POE molecule participate in hydrogen bonding with water molecules has been made.     

General Method for Evaluation of Alternating Tendency in Copolymerization

A new method for deriving expressions for the mole fractions of alternating n-ads and the average lengths of the alternating sequences of n-component copolymers (n > 2) was developed based on the apparatus of finite Markov chains. These characteristics are considered as indexes of alternating tendency forn-component copolymerization. A specific property of n-component copolymerization (n > 3) compared with binary copolymerization is the fact that alternating n-ads might be constructed by two, three, or more types of monomeric units. In order to express this specific property of three and multi-component copolymers the term, alternating order, is introduced. The method developed in the paper permits the alternating indexes to be determined differentially in dependence of alternating order. Expressions for the average lengths and the compositions of all possible alternating sequences starting with a given monomer unit and ending with unit found only at that position, are derived as well. The alternating indexes for binary radical copolymerization of styrene and methyl methacrylate and for ternary radical copolymerization of styrene, methyl methacrylate, and acrylonitrile were determined.