Neue Kupferkomplexe mit Phosphaalkenliganden. Molekülstruktur von [Cu{P(Mes*)C(NMe2)2}2]BF4 (Mes* = 2,4,6‐tBu3C6H2)

New Copper Complexes Containing Phosphaalkene Ligands. Molecular Structure of [Cu{P(Mes*)C(NMe₂)₂}₂]BF₄ (Mes* = 2,4,6‐tBu₃C₆H₂) Reaction of equimolar amounts of the inversely polarized phosphaalkene tBuP=C(NMe₂)₂ ( 1a ) and copper(I) bromide or copper(I) iodide, respectively, affords complexes [Cu₃X₃{μ‐P(tBu)C(NMe₂)₂}₃] ( 2 ) (X =Br) and ( 3 ) (X = I) as the formal result of the cyclotrimerization of a 1:1‐adduct. Treatment of 1a with [Cu(L)Cl] (L = PiPr₃; SbiPr₃) leads to the formation of compounds [CuCl(L){P(tBu)C(NMe₂)₂}] ( 4a ) (L = PiPr₃) and ( 4b ) (L = SbiPr₃), respectively. Reaction of [(MeCN)₄Cu]BF₄ with two equivalents of PhP=C(NMe₂)₂ ( 1b ) yields complex [Cu{P(Ph)C(NMe₂)₂}₂]BF₄ ( 5b ). Similarly, compounds [Cu{P(Aryl)C(NMe₂)₂}₂]BF₄ ( 5c (Aryl = Mes and 5d (Aryl = Mes*)) are obtained from ArylP=C(NMe₂)₂ ( 1c : Aryl = Mes; 1d : Mes*) and [(MeCN)₄Cu]BF₄ in the presence of SbiPr₃. Complexes 2 , 3 , 4a , 4b , and 5b‐5d are characterized by means of elemental analyses and spectroscopy (¹H‐, ¹³C{¹H}‐, ³¹P{¹H}‐NMR). The molecular structure of 5d is determined by X‐ray diffraction analysis.     

Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

Study of modified silicas by inverse gas chromatography. Part I: Influence of chain length on grafting ratio

Summary Silica has been modified by an esterification reaction using either n-alcohols or - diols. The grafting ratios were evaluated by elemental analysis of carbon or by the weight loss of the grafted silica heated to 700°C. The grafting ratio can be easily fixed by changing the silica to reactant impregnation ratios. In the case of n-alcohols, the grafting ratios do not vary monotonously with the number of carbon atoms of the grafts and the density of the grafted layer is 25% higher for - diols than for n-alcohols. This observation needs further investigation.     

Inverse relaxation-model and relation to recovery internal friction

Inverse relaxation is studied for hard elastic polypropylene (HEPP), rubber and non-elastic polypropylene. The results show that contractive stress, stress, and internal friction are three essential factors related to the phenomenon. A three-element model in which each element has a definite meaning is proposed to describe this phenomenon. The results also show that, in the first cyclic deformation, relaxation time increases with the increase of recovery for all the materials, which indicates that recovery viscosity increases with the increase of recovery, but the stress rising amplitude (SRA) of inverse relaxation has a maximum in the recovery range. Analysis indicates that SRA equals recovery internal friction (RIF) for ideal material in which stress is solely a function of strain, independent of paths, and approximately equals RIF for non-ideal material at a given strain. From this principle it is found that the order of the work counteracted by RIF for the four materials is the same as that of their second hysteresis loop, and the RIF of HEPP has a sudden increase at the later recovery range.     

Non-ionic amphiphilic block copolymers by RAFT-polymerization and their self-organization

Water-soluble, amphiphilic diblock copolymers were synthesized by reversible addition fragmentation chain transfer polymerization. They consist of poly(butyl acrylate) as hydrophobic block with a low glass transition temperature and three different nonionic water-soluble blocks, namely, the classical hydrophilic block poly(dimethylacrylamide), the strongly hydrophilic poly(acryloyloxyethyl methylsulfoxide), and the thermally sensitive poly(N-acryloylpyrrolidine). Aqueous micellar solutions of the block copolymers were prepared and characterized by static and dynamic light scattering analysis (DLS and SLS). No critical micelle concentration could be detected. The micellization was thermodynamically favored, although kinetically slow, exhibiting a marked dependence on the preparation conditions. The polymers formed micelles with a hydrodynamic diameter from 20 to 100 nm, which were stable upon dilution. The micellar size was correlated with the composition of the block copolymers and their overall molar mass. The micelles formed with the two most hydrophilic blocks were particularly stable upon temperature cycles, whereas the thermally sensitive poly(N-acryloylpyrrolidine) block showed a temperature-induced precipitation. According to combined SLS and DLS analysis, the micelles exhibited an elongated shape such as rods or worms. It should be noted that the block copolymers with the most hydrophilic poly(sulfoxide) block formed inverse micelles in certain organic solvents.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

The use of inverse gas chromatography to study surface thermal oxidation of polypropylene

Thermo-oxidative effects on the surface energy of polypropylene were measured by inverse gas chromatography as a function of exposure time and temperature. Unaltered polypropylene had a surface energy of 33 mJ/m². Oxidized polypropylene, after exposure to air at temperatures of 100 °C and 110 °C, had a range of maximum surface energies from 38 to 41 mJ/m². Comparisons between FTIR carbonyl peak growth and the surface energy showed that both methods detect oxidation, though the increase in surface energy is detected before the carbonyl peak growth is noticeable. The work of adhesion predicted by the surface free energies obtained in this work between a coated calcium carbonate and polypropylene changes by 10% due to the oxidation of the polymer at 110 °C.     

Equilibrium analysis for a mass-conserving model in presence of cavitation

We study the existence of equilibrium positions for the load problem in Lubrication Theory. The problem consists of two surfaces in relative motion separated by a small distance filled by a lubricant. The system is described by the modified Reynolds equation (Elrod–Adams model) which describes the behavior of the lubricant and an extra integral equation given the balance of forces. The balance of forces allows to obtain the unknown position of the surfaces, defined with one degree of freedom.