Complexation thermodynamics of free and graft oligomers with complementary polymers

The dilute solution complexation equilibrium between linear macromolecules and smaller complementary oligomers is considered when: (1) the oligomers are free in solution; and (2) the oligomers are covalently attached at one end to the polymer. A general statistical mechanical framework is developed and is illustrated using a simple random walk model for polymer conformation. The statistical mechanical partition functions are formulated using a generating function technique, allowing thermodynamic averages in the complexed state to be calculated. Loops, trains, and tails of all possible length are allowed in the conformation of a complexed oligomer. Simulation results for the free oligomer case are compared with those obtained for oligomers covalently attached to the polymeric molecular. The model provides a theoretical explanation for the experimentally observed enhancement of complexation of oligomers grafted to the complementary polymers.     

Preparations and spectroscopic studies of organotin complexes of diclofenac

The reactions of the potent and widely used anti-inflammatory drug diclofenac, HL, with diorganotin(IV) oxides were studied. The dimeric tetraorganodistannoxane complexes [Me(2)LSnOSnLMe(2)](2), [Bu(2)LSnOSnLBu(2)](2), [Ph(2)LSnOSnLPh(2)](2) and the dibutyltin complex [Bu(2)SnL(2)], have been prepared and structurally characterized in the solid state by means of vibrational and 119Sn M?ssbauer spectroscopy. Determination of lattice dynamics by temperature-dependent 119Sn M?ssbauer spectroscopy. From the variable-temperature M?ssbauer effect, the Debye temperature was determined. The complexes have been characterized in solution by NMR (1H and 13C) spectroscopy. Vibrational, M?ssbauer, and NMR data are discussed in terms of the proposed structures.     

Polycondensation of mono- and difunctional derivatives of p-xylene

A new method for the production of polydimethylbenzylenes,$ \rlap{--} [{\rm C}_6 {\rm H}_4 ({\rm CH})_2 {\rm CH}_{\rm 2} \rlap{--} ]_n $, involves the polycondensation of the mono- and dichloromethyl and mono- and diacetoxymethyl derivatives of p-xylene via an acid-catalyzed reaction in anhydrous acetic acid. The reaction of the difunctional derivatives is slower than the reaction of the monofunctional ones, leading to linear, predominantly crystalline, high-melting polymers with molecular weights of 2000–3000. Polycondensation of both monomers under different feed ratios leads to polymers with the same structure, and the monofunctional monomers condense with themselves more favorably than with the difunctional ones. Thus a head-to-head structure is preferred, and crystalline polymers of high structural purity are obtained.     

NIEDERKOORDINIERTE PHOSPHORVERBINDUNGEN, 701 1-METALLA-2,5-DIPHOSPHA PENTA-1,3-DIENE DURCH 1,4-ADDITION VON METALLCARBONYLCYCLOPENTADIENYLHYDRIDEN AN 1,4-DIPHOSPHABUTA-1,3-DIEN

Abstract

Reactions of carbonyl cyclopentadienyl hydrides from molybdenum and tungsten with 1,4-diphosphabuta-1,3-diene yield metalla-diphospha-pentadiene with a metal-phosphorus-double bond.

Metalla-diphosphapentadiene mit einer Metall-Phosphor-Doppelbindung werden durch Umsetzung von Carbonylcyclopentadienylhydriden des Molybdäns und Wolframs mit einem 1,4-Diphospha-buta-1,3-dien erhalten.     

A numerical investigation of the influence of the aspect ratio in three‐dimensional separated flows

The influence of aspect ratio in three‐dimensional, numerical experiments of separated flows is studied in the case of the backward‐facing step at Reynolds numbers 600, 800, and 950. The computational domain is designed as an actual laboratory experiment. The governing equations are the steady state, isothermal, and incompressible Navier–Stokes equations. The expansion ratio of the computational domain is 1:2. The aspect ratio varies from 1:10 to 1:40. The results of the computations focus on the spanwise variations of the length and the strength of the two eddies along the lower and upper wall. It is concluded that both numerical and laboratory experiments should be designed with an aspect ratio of at least 1:20, if only the accuracy of the position of the detachment and the re‐attachment points matters. If the accuracy of the shear‐stress distributions is also taken into account, then an aspect ratio of at least 1:30 should be chosen. Finally, if the magnitudes of the vortex centers are also considered, then only the aspect ratio of 1:40 qualifies for a realization of two‐dimensional flow conditions in the plane of symmetry. This is contrary to the common practice in the field, at least from the side of laboratory experiments, where an aspect ratio of 1:10 is still considered adequate for this purpose. Copyright © 2011 John Wiley & Sons, Ltd.     

The 19F and 31P magnetic resonance spectra of phosphorus trifluoride in nematic solution

The phosphorus and fluorine N.M.R. spectra of PF₃ in a nematic solvent (EBBA) are discussed. The molecular geometry is found to agree with structures obtained from microwave and electron diffraction studies. The sign of the ordering parameter is assumed negative, the signs of the phosphorus fluorine coupling constant and of the chemical shift anisotropies follow from this assumption, and are found to be in agreement with theoretical predictions. The effect of temperature on the isotropic chemical shift of fluorine is discussed.     

Optimal control and admissible relaxation for subdifferential evolution inclusions

In this paper we study the relaxation of optimal control problems monitored by subdifferential evolution inclusions. First under appropriate convexity conditions, we establish an existence result. Then we introduce the relaxed problem and show that it always has a solution under fairly general hypotheses on the data. Subsequently we examine when the relaxation is admissible. So we show that every relaxed trajectory can be approximated by extremal original ones (i.e. original trajectories generated by bang-bang controls) and that the values of the original and relaxed problems are equal. Some examples are also presented.     

Embeddings of 2-spheres in 4-manifolds

We prove that the action of the orthogonal group of an integral, unimodular lattice whose rank and signature satisfy a certain indefiniteness condition acts transitively on pairs of mutually orthogonal elements with the same isometric invariants.