Yttrium Complexes of Arsine,Arsenide, and Arsinidene Ligands

Deprotonation of the yttrium–arsine complex [Cp′₃Y{As(H)₂Mes}] ( 1 ) (Cp′=η⁵‐C₅H₄Me, Mes=mesityl) by nBuLi produces the μ‐arsenide complex [{Cp′₂Y[μ‐As(H)Mes]}₃] ( 2 ). Deprotonation of the As? H bonds in 2 by nBuLi produces [Li(thf)₄]₂[{Cp′₂Y(μ₃‐AsMes)}₃Li], [Li(thf)₄]₂[ 3 ], in which the dianion 3 contains the first example of an arsinidene ligand in rare‐earth metal chemistry. The molecular structures of the arsine, arsenide, and arsinidene complexes are described, and the yttrium–arsenic bonding is analyzed by density functional theory.     

Surface rheology and foaming properties of sodium oleate and C12(EO)6 aqueous solutions

The dynamic surface tension (DST) and the surface viscoelastic modulus of sodium oleate aqueous solutions at different concentrations were measured using an image analysis tensiometer based on the oscillating bubble technique. The diffusion coefficient of oleate moieties was calculated from DST measurements and the surface viscoelastic modulus using the Langmuir-Szyszkowski and the diffusion-controlled adsorption models. The viscoelastic moduli obtained from model calculations were compared with the corresponding experimental values. The diffusion coefficient of C(12)(EO)(6) in water and the parameters of the Langmuir-Szyszkowski adsorption isotherm were taken from the literature and used to calculate the surface viscoelastic modulus of its aqueous solutions at different concentrations. The foaming properties of both C(12)(EO)(6) and sodium oleate solutions, viz., the foam conductance and the water volume fraction in the foam, were measured using a commercial Foamscan device. Foaming experiments with C(12)(EO)(6) and sodium oleate solutions were carried out either under static conditions; i.e., the foam conductance and the water volume fraction were measured as a function of time after the generation of a fixed volume of foam, or under dynamic conditions; i.e., the foam conductance and the water volume fraction were measured during foam formation. The variations in the foam permeability as a function of surfactant concentration were related to the viscoelastic properties of the air/water interface and to the presence of micelles in the foam films. With foams in which the water volume fraction was higher than 0.05, the foam electrical conduction could be described using a simple parallel resistor model and their conductance measurements were related to the foam water volume fraction. The results related to water drainage under static conditions were used to interpret water drainage under dynamic conditions. Preliminary conjectures on the influence of foam permeability and water volume fraction on the yield of the flotation deinking process were drawn from these results.     

An atomic force microscopy study of asphaltenes on mica surfaces. Influence of added resins and demulsifiers

 Monolayers of asphaltene and resins on the water surface have been transferred at a surface pressure of 10 mN/m onto mica substrates using the Langmuir–Blodgett technique. Atomic force microscopy (AFM) has been used to examine the topography of these layers. Monolayers consisting of pure asphaltene fractions provide a rigid film with a close-packed structure, while the resins build up a continuous open network. Mixed films of these two fractions show that a gradual increase in resin concentration leads to an opening of the rigid asphaltene structure towards a more resin like configuration. Increased aggregation when the two heavy functions are present in one film is seen as larger individual units in the AFM pictures. Addition of high-molecular-weight demulsifiers/inhibitors results in the same kind of influence on the asphaltene film as seen with the resins. Received: 30 April 1999 Accepted: 29 November 1999     

Long-wave instabilities and saturation in thin film equations

Hocherman and Rosenau conjectured that long-wave unstable Cahn-Hilliard-type interface models develop finite-time singularities when the nonlinearity in the destabilizing term grows faster at large amplitudes than the nonlinearity in the stabilizing term (Phys.˜ D 67, 1993, pp. 113–125). We consider this conjecture for a class of equations, often used to model thin films in a lubrication context, by showing that if the solutions are uniformly bounded above or below (e.g., are nonnegative), then the destabilizing term can be stronger than previously conjectured yet the solution still remains globally bounded. For example, they conjecture that for the long-wave unstable equation m > n leads to blowup. Using a conservation-of-volume constraint for the case m > n > 0, we conjecture a different critical exponent for possible singularities of nonnegative solutions. We prove that nonlinearities with exponents below the conjectured critical exponent yield globally bounded solutions. Specifically, for the above equation, solutions are bounded if m < n + 2. The bound is proved using energy methods and is then used to prove the existence of nonnegative weak solutions in the sense of distributions. We present preliminary numerical evidence suggesting that m ≥ n + 2 can allow blowup. © 1998 John Wiley & Sons, Inc.     

The energetics of NH3 adsorption at the MgO(001) surface

Ab initio quantum-mechanical calculations based on density-functional theory and the pseudopotential method have been used to study the adsorption of the NH₃ molecule at the MgO(001) surface. The calculations employ slab geometry and periodic boundary conditions, with the occupied orbitals expanded in plane waves. The reliability of the theoretical methods has been verified by calculations on the bare surface and the isolated molecule. Four different adsorption geometries have been studied, and in each case the equilibrium configuration has been determined by full relaxation of the system. The two most stable configurations have about the same adsorption energy, and this energy agrees well with the results of recent thermal desorption measurements. Intermolecular repulsion is found to be a dominant effect at monolayer coverage, but becomes small at coverages below 25%. It is shown that chemical effects are not significant, and that the adsorption mechanism is predominantly physisorption.     

Nuclear stopping power in αα anddd collisions

Inelasticαα anddd collisions were studied at a centre-of-mass energy √S _NN=31.2 GeV per nucleon-nucleon collision, using the Split-Field Magnet (SFM) detector at the CERN ISR. In this paper we show the inclusive and semi-inclusive rapidity distributions of protons, compare them with predictions of the Lund model, and calculate the average rapidity loss for participant protons. From the negative particles we calculate the inelasticity of the interaction, the average energy per particle, and the degree of isotropy of the produced hadrons.     

A comparison of the He(p, 2p)d and He(p, pd)p reactions

The ³He(p, 2p)d and ³He(p, pd)p reactions have been compared at three bombarding energies from 65 to 100 MeV. A comparison of plane wave impulse approximation calculations to the experimental data indicates that multiple scattering effects are large and energy dependent but that they primarily produce a uniform reduction in cross section. Although multiple scattering effects are large the ratio of the cross sections for the two reactions is in agreement with that predicted by the impulse approximation.     

Partial Differentiability of Invariant Splittings

A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial derivatives of the splitting exist and the splitting depends smoothly on the dynamical system itself.