Hydrolysis and Condensation of Transition Metal Alkoxide: Experiments and Simulations

We present here an experimental and numerical study of the chemical and aggregative mechanisms for titanium alkoxide in a reverse micellar medium. NMR experiments were done to study the first step of the sol-gel process: hydrolysis of titanium isopropoxide. Light and X-ray scattering experiments were then conducted to characterize the clustering of aggregates and aggregation kinetics. Fractal dimension, measured by U.S.A.X.S., varies with the hydrolysis ratio and the hydration of the surfactant. This evolution was explained by polydispersity of the hydrolysis which depends on the surfactant concentration. This hypothesis was tested through a numerical simulation of irreversible aggregation using a chemically limited aggregation model. The hydrolyzed sites are distributed among the monomers by a random procedure governed by a polydispersity parameterp, varying from 0 to 1. The total number of hydrolyzed sites is governed by a parameterq belonging to the interval [0, 1]. Thep-q evolution of the fractal dimension coincides rather well with the experimental data in all the region of the two dimensional phase space.     

Applications of laser for ceramic alloying on metallic surfaces

Summary Ceramic and metallic materials were alloyed and cladded on a C40 steel by means of a CO₂ laser heat source. The main objectives of the research were to obtain a surface modification of the C40 steel in order to increase its wear resistance and to develop a repeatable coating process of potential industrial application. In the following sections, the laser coating process (including experimental equipment and working parameters) and the most important metallurgical results are described.     

Gelfand type problem for singular quadratic quasilinear equations

In this paper, we study the existence of positive solutions for the quasilinear elliptic singular problem

$$\left\{\begin{array}{ll}-\Delta u + c\,\frac{|\nabla u|^2}{u^\gamma} = \lambda\,f(u), \quad \quad \mbox{in $\Omega$},\\ u=0, \quad \qquad \qquad \qquad \quad \, \, \, \, \, \mbox{on $\partial$$\Omega$},\end{array}\right.$$

where \({c,\lambda >0}\), \({\gamma \in (0,1)}\), f is strictly increasing and derivable in \({[0,\infty)}\) with \({f(0)>0}\). We show that there exists \({\lambda^*>0}\) such that \({(0,\lambda^*]}\) is the maximal set of values such there exists solution. In addition, we prove that for \({\lambda<\lambda^*}\) there exists minimal and bounded solutions. Moreover, we give sufficient conditions for existence and regularity of solutions for \({\lambda=\lambda^*}\).

     

Crystalline BP‐Doped Phenanthryne via Photolysis of The Elusive Boraphosphaketene

The synthesis and reactivity study of the first isolable boraphosphaketene, cyclic(alkyl)(amino) carbene (CAAC)‐borafluorene‐P=C=O ( 2 ), is described. Photolysis of compound 2 results in the formation of CAAC‐stabilized BP‐doped phenanthryne ( 3 ) through tandem decarbonylation, monoatomic phosphide insertion, and ring‐expansion. Notably, while BN‐doped phenanthryne was previously discussed as a reactive intermediate which could not be isolated, the heavier BP‐doped analogue exhibits remarkable solution and solid‐state stability. The reactivity of 2 with stable carbenes was also explored. Addition of CAAC to 2 led to migration of the original CAAC ligand from boron to phosphorus and coordination of the added CAAC to carbon, affording compound 4 . Reaction of 1,3‐diisopropyl‐4,5‐dimethylimidazol‐2‐ylidene (NHC) with 2 resulted in N?C bond activation to give the unusual spiro‐heterocyclic compound ( 5 ).     

Identification of flow mechanisms for a soft crystal

We study the behavior under flow of soft spherical micelles forming a fcc phase at high volume fraction. Due to the size (300 ?) of the elementary objects, the structure can be investigated through X-rays and neutron scattering, at rest and under flow in a Couette cell. Using scattering in two perpendicular directions, different mechanisms of flow are identified. At intermediate shear (around 100 s^-1) the system exhibits the so called layer sliding mechanism where two dimensional hexagonal compact planes of spheres align themselves with the Couette cell walls. At lower shear rate, the fcc structure is locally preserved, and the flow is mediated by defects between crystallites. At high shear rate, we observe the melting of the structure and a liquid-like structure factor. Moreover, we were able to use the existence of the layer sliding regime to generate a fcc monocrystal by annealing the satcking faults between the decorrelated planes created by the layer sliding. Received: 7 July 1997 / Received in final form: 16 January 1998 / Accepted: 5 March 1998     

Pyranosidic homologation: Part I: Extending the carbohydrate template C6 and C4

The aldehyde ( ) reacts with ylid ( ) to give ( ) as 4:1 Z/E mixture which, upon methanolysis under catalysis by pyridinium -toluenesulfonate (PPTS), affords the bispyranoside ( ) as single anomer.     

A comment on SCF energy partitioning schemes

Starting from the symmetry groupG × SU(2) for the special case of negligible spin-orbit coupling, a general character formula is derived for them-tuplet representation, which is realized in the space of state functions ofn-electron systems in fields with symmetryG. Apart from the characters of the initial representation for the single electron space function, the formula only contains the number of particlesn and the multiplicitym.

Herrn Professor Dr. Hermann Hartmann zu seinem 60. Geburtstag gewidmet.