Synthesis and crystal structures of heterobimetallic Fe-Cd,Fe-Zn,and Fe-In complexes containing hemilabile phosphorus/oxygen and silicon/oxygen bridging ligands

The reactions of K[Fe{Si(OMe)₃}(CO)₃(PY)][PY=Ph₂PCH₂C(O)Ph, Ph₂PCH₂C(O)[(-C₅H₄)FeCp] (Cp=⁵-C₅H₅), Ph₂P(CH₂)₂CN] with CdCl₂·2.5H₂O, ZnX ₂ (X=Cl, I) or InCl₃ afforded Fe-Cd-Fe or Fe-M(-X)₂ M-Fe (M=Cd, Zn, In;X=Cl, I) and Fe-InCl₂ complexes. Some of them contain an unusual and labile -²-SiO alkoxysilyl bridge which may be associated with a bridging mode for the ketophosphine ligand (first such example structurally established), thus providing original results in bimetallic chemistry on the intramolecular coordination of oxygendonor functions ofchemically different hemilabile ligands firmly attached to a neighboring metal center. The structures of the trinuclear complex (3), of the chlorobenzene solvate of the tetranuclear complex (4a·C₆H₅Cl) and of [mer-(OC)₃{(EtO)₃Si} (4e) have been determined by X-ray diffraction. Crystals of 3 are orthorhombic, space groupPbcn, witha=19.010(4),b=11.766(5),c=26.998(7)Å, andZ=4. Crystals of4a·C₆H₅Cl are monoclinic, space groupC2/c witha=22.455(3),b=17.680(2),c=16.627(4)Å, =90.80(4)°, andZ=4. Crystals of4e are monoclinic, space groupC2/c witha=25.392(5),b=18.554(6),c=16.28(1)Å, =120.73(3)°, andZ=4. The structures were solved using direct methods and Fourier difference techniques and refined by blocked full-matrix least squares toR=0.035 (R _w =0.049) for 2719 observed reflections, toR=0.042 (R _w =0.056) for 3082 observed reflections, and toR=0.057 (R _w =0.075) for 1850 observed reflections for3, 4a·C₆H₅Cl and4e, respectively. The Fe-Zn complexes (9a), (9b) and (9c) were prepared and characterized by spectroscopic methods.Part 21 in the Series: Complexes with Functional Phosphines. Part 20: P. Braunstein, S. Coco Cea, A. DeCian, and J. Fischer (1992).Inorg. Chem. 31, 4203.     

Borel fibrations and G-spaces

Considering discrete groups G only, we present an elementary proof of the familiar equivalence of the category of G-spaces (with maps equivariant up to homotopy) and the category of Borel fibrations over BG.     

Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

Symbolic dynamics for the renormalization map of a quasiperiodic Schrödinger equation

A rigorous analysis is given of the dynamics of the renormalization map associated to a discrete Schrödinger operatorH onl ²(), defined byH(n)=(n+1)+(n–1)+Vf(n)(n), whereV is a real parameter,f is a certain discontinuous period-1 function, and is the golden mean. The renormalization map forH is a diffeomorphism,T, of ³, preserving a cubic surfaceS _V . ForV8 we prove that the non-wandering set of the restriction ofT toS _v is a hyperbolic set, on whichT is conjugate to a subshift on six symbols. It follows from results in dynamical systems theory that the optimally approximating periodic operators toH have spectra which obey a global scaling law. We also define a set which we call the pseudospectrum of the operatorH. We prove it to be a Cantor set of measure zero, and obtain bounds on its Hausdorff dimension. It is an open question whether the pseudospectrum coincides with the spectrum ofH.     

Joint production of ϕ mesons andπ ±,π 0,p,\bar p,K s 0 andK ± in hadronic interactions

The joint production of ? mesons andπ ^±,π ⁰,p, \(\bar p\) ,K _s ⁰ andK ^± is investigated using a sample of 600,000 inclusive ? meson events obtained in hadron Be interactions with incidentπ ^±,p, \(\bar p\) andK ^± beams. Evidence is presented for the joint production of ? mesons and strange particles produced with non-strange incident beams. With incidentK ^± beam the number of additional strange particles is suppressed. The results are found to be in agreement with the qualitative predictions of a parton fusion model. The comparison with the Lund model for lowp _T processes is fair.     

Effect of time on the interfacial and foaming properties of beta-lactoglobulin/acacia gum electrostatic complexes and coacervates at pH 4.2

The electrostatic complexation between beta-lactoglobulin and acacia gum was investigated at pH 4.2 and 25 degrees C. The binding isotherm revealed a spontaneous exothermic reaction, leading to a DeltaHobs = -2108 kJ mol(-1) and a saturation protein to polysaccharide weight mixing ratio of 2:1. Soluble electrostatic complexes formed in these conditions were characterized by a hydrodynamic diameter of 119 +/- 0.6 nm and a polydispersity index of 0.097. The effect of time on the interfacial and foaming properties of these soluble complexes was investigated at a concentration of 0.1 wt % at two different times after mixing (4 min, referred as t approximately 0 h and t = 24 h). At t approximately 0 h, the mixture is mainly made of aggregating soluble electrostatic complexes, whereas after 24 h these complexes have already insolubilize to form liquid coacervates. The surface elasticity, viscosity and phase angle obtained at low frequency (0.01 Hz) using oscillating bubble tensiometry revealed higher fluidity and less rigidity in the film formed at t approximately 0 h. This observation was confirmed by diminishing bubble experiments coupled with microscopy of the thin film. It was thicker, more homogeneous and contained more water at t approximately 0 h as compared to t = 24 h (thinner film, less water). This led to very different gas permeability's of Kt approximately 0 h = 0.021 cm s(-1) and Kt=24 h) = 0.449 cm s(-1), respectively. Aqueous foams produced with the beta-lactoglobulin/acacia gum electrostatic complexes or coacervates exhibited very different stability. The former (t approximately 0 h) had a stable volume, combining low drainage rate and mainly air bubble disproportionation as the destabilization mechanism. By contrast, using coacervates aged for 24 h, the foam was significantly less stable, combining fast liquid drainage and air bubble destabilization though fast gas diffusion followed by film rupture and bubble coalescence. The strong effect of time on the air/water interfacial properties of the beta-lactoglobulin/acacia gum electrostatic complexes can be understood by their reorganization at the interface to form a coacervate phase that is more fluid/viscous at t approximately 0 h vs rigid/elastic at t = 24 h.