Polyphosphate chains by addition of oxiranes to phosphoric acid

Addition of diepoxides to the acids of phosphorus provides a new, attractive route to polyphosphates. In order to understand better the mechanism of this reaction and the structure of the products, the model reactions, namely additions of simple oxiranes to the acids of phosphorus, have been studied. It was shown that this reaction is catalysed by the P-OH groups of the acids. Activation of the oxirane molecule occurs predominantly by formation of the hydrogen bonded species while ionized form of acid plays only a minor role at the studied conditions (1,4-dioxane solution, 25°C). Reactivity of subsequent P-OH groups in phosphoric acid increases with increasing degree of substitution by -OCH₂CH₂OH groups. The ratio of the rate constants of formation of mono-, di-, and triesters of phosphoric acid is equal to 1/2/4. This has been attributed to the formation of internal hydrogen bonds, involving substituents and the P-OH groups. The observed order of the rate constants shows that reaction can not be stopped at the diester stage (linear units) and triester species (branched units) are formed fast. However, due to the large difference in the rate of hydrolysis, especially pronounced at basic conditions, triesters of phosphoric acid can easily be converted into the corresponding diesters by simple hydrolysis. Thus, the addition of diepoxides to phosphoric acid, followed by hydrolysis, leads to essentially linear polyphosphate chains.     

Thermodynamic properties of a diluted Heisenberg ferromagnet with interaction anisotropy—Magnetocaloric point of view

The thermodynamics of a site-diluted ferromagnetic Heisenberg model for spin S=1/2 with interaction anisotropy in spin space is investigated. The study is aimed at presenting the magnetocaloric properties of such a model, including the entropy and temperature changes in magnetization/demagnetization processes, generalized Grüneisen ratio as well as the quantities characterizing the efficiency of magnetic cooling cycles. The results are obtained using pair approximation (PA) method and extensively compared with the molecular field approximation (MFA) calculations. The importance of interaction anisotropy and site-dilution is discussed. The inadequacy of the MFA approach (even on the qualitative level) is found for selected quantities, while PA provides the results which are consistent with the experimentally observed behavior.     

Nonlinear Cauchy-Riemann operators in

This paper has arisen from an effort to provide a comprehensive and unifying development of the -theory of quasiconformal mappings in . The governing equations for these mappings form nonlinear differential systems of the first order, analogous in many respects to the Cauchy-Riemann equations in the complex plane. This approach demands that one must work out certain variational integrals involving the Jacobian determinant. Guided by such integrals, we introduce two nonlinear differential operators, denoted by and , which act on weakly differentiable deformations of a domain .

Solutions to the so-called Cauchy-Riemann equations and are simply conformal deformations preserving and reversing orientation, respectively. These operators, though genuinely nonlinear, possess the important feature of being rank-one convex. Among the many desirable properties, we give the fundamental -estimate

In quest of the best constant , we are faced with fascinating problems regarding quasiconvexity of some related variational functionals. Applications to quasiconformal mappings are indicated.

     

Functional differential equations

The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.     

Copper(II) and nickel(II) complexes of a neutral pentadentate Schiff base

A new pentadentate Schiff base 2,6,10-triaza-1,11-bis(2′-aminophenyl)-undeca-1,10-diene, abaDPT, and its complexes of general formula M(abaDPT)X₂ where M = Cu(II), Ni(II), X = Cl, Br, I, NO₃ and ClO₄, have been prepared. The complexes have been characterized by electronic and IR spectra, EPR, magnetic moments, molar conductances, and elemental analysis. IR data show an interaction between halide anion of the outer coordination sphere and the complexed amino group. EPR and spectrophotometric data of most of the copper compounds are consistent with a distorted square pyramidal geometry. Single crystal EPR studies of Cu(abaDPT)(NO₃)₂ and Cu(abaDPT)Br₂ revealed that copper atoms in the former compound occupy two magnetically inequivalent places in the lattice while copper atoms in the latter compound take identical sites. Principal g tensor axes of the two compounds have been determined.     

Critical behavior in vacuum gravitational collapse in 4 + 1 dimensions

We show that the (4 + 1)-dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere orthogonal to the (t,r) plane. Gravitational collapse of such waves is studied numerically and shown to exhibit discretely self-similar type II critical behavior at the threshold of black hole formation.     

Polymeric complexes of cornstarch and waxy cornstarch phosphates with milk casein and their performance as biodegradable materials

Complexes of phosphated cornstarch and waxy cornstarch with casein were prepared and characterised. They were prepared from casein in defatted milk and corn and waxy corn starches phosphated to degree of substitution values (DS) of 0.0637 and 0.0968, respectively. The components were blended in starch to casein ratios of 2:1, 1:1, and 1:2, then precipitated with hydrochloric acid. Aqueous solubility, water binding capacity, IR spectra, and thermal analysis (thermogravimetry, TG, and differential thermogravimetry, DTG) of the precipitates revealed that they were not simple physical mixtures of the components. The components interact with one another electrostatically with involvement of the starch phosphate groups and the peptide bonds of casein as documented by the IR spectra. Because of their insolubility in 7 M aqueous urea solution they might also be considered as complexes in which the components were chemically bound. Enzymatic studies showed that they are biodegradable materials.     

Exceptionally long-range self-assembly of hexa-peri-hexabenzocoronene with dove-tailed alkyl substituents

The substitution of a hexa-peri-hexabenzocoronene by bulky, space-demanding, 2-decyltetradecyl side chains proved to be an effective procedure to influence the thermal and self-aggregation behavior. The extremely large steric requirement of the introduced side chains modulated the aggregation and resulted in a dramatic lowering of the isotropization temperature and a higher solubility. As an additional consequence of the exceptional, long-range self-aggregation of the discotic molecule, spherulite formation was observed during crystallization by polarized light microscopy. Macroscopic self-assembly was induced by zone crystallization of the material, leading to aligned columnar superstructures as revealed by 2D-WAXS experiments. These extraordinary properties have not yet been reported for a discotic columnar material, making this compound very promising for application in electronic devices.