Nonlinear waves in gas-fluidized beds

A mathematical model for gas-fluidized beds is examined which treats both the particles and gas as continua by volume averaging. The system is then considered as two interlocking one-phase fluids. For small perturbations to the uniform state, these equations have been shown by Crighton (1991) to reduce to the Burgers-KdV equation and under certain criteria, we have instability. We consider the unstable situation when the amplification effects are a perturbation to the KdV equation and take an initial condition of a single KdV soliton. The growth of this soliton is followed through several regions in which the unstable Burgers-KdV equation is no longer appropriate, but KdV remains the leading order equation. Eventually, there is a fundamental change in the solution and the new governing equations are fully nonlinear and O(1). These admit a solitary wave solution which matches back onto the KdV soliton. Thus, we can follow the formation of a bubble from a small amplitude perturbation to the uniform state.University of Cambridge, Cambridge, United Kingdom. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 797–800, August, 1993.     

A model for ground-state and excited-state microwave optical double resonance

A model is developed to describe the physical principles of both ground-state and excited-state microwave optical double resonance. This model uses a steady-state kinetic analysis to determine the populations of three quantum levels in the presence of two monochromatic radiation fields. The microwave transition rate and the laser transition rate are obtained from separate analyses using the semiclassical two-state transition probability averaged over the effects of collisions. The Doppler effect of the optical transition rate is explicitly included. The competing effects of laser power, microwave power, and pressure on signal intensity and lineshape are described. Calculated lineshapes and relative signal intensities based on this model are in good agreement with previous measurements on BaO and NO₂.     

The back effect of a wall on a jet

Zusammenfassung Ein ebener Flüssigkeitsstrahl von der Weited wird normal gegen eine Wand geleitet, die von der Quelleh Einheiten entfernt ist. Man nimmt gewöhnlich an, dass, wenn das Verhältnish/d gross ist, die Auswirkung des Hindernisses nicht zur Quelle des Strahles zurückwirkt, so dass im besonderen wichtige Eigenschaften des Strahls, wie sein Impuls und die Massenströmung, dürch den Widerstand unberührt bleiben.An einem einfachen Modell, in dem der Strahl, bestehend aus einer inkompressiblen und reibungslosen Flüssigkeit, von einem Schlitz in der Wand einer unendlichen Kammer ausströmt, zeigen wir, dass, soweit diese Haupteigenschaften betroffen sind, der Strahl durch das Hindernis beinahe ungestört bleibt, selbst für Werte der Verhältniszahlh/d, die nahe an der Einheit liegen.     

Dithiomethylether as a ligand in the hydrogenase h-cluster

An X-ray crystallographic refinement of the H-cluster of [FeFe]-hydrogenase from Clostridium pasteurianum has been carried out to close-to atomic resolution and is the highest resolution [FeFe]-hydrogenase presented to date. The 1.39 A, anisotropically refined [FeFe]-hydrogenase structure provides a basis for examining the outstanding issue of the composition of the unique nonprotein dithiolate ligand of the H-cluster. In addition to influencing the electronic structure of the H-cluster, the composition of the ligand has mechanistic implications due to the potential of the bridge-head gamma-group participating in proton transfer during catalysis. In this work, sequential density functional theory optimizations of the dithiolate ligand embedded in a 3.5-3.9 A protein environment provide an unbiased approach to examining the most likely composition of the ligand. Structural, conformational, and energetic considerations indicate a preference for dithiomethylether as an H-cluster ligand and strongly disfavor the dithiomethylammonium as a catalytic base for hydrogen production.     

Improved functional group compatibility in the palladium-catalyzed synthesis of aryl amines

[reaction: see text] The use of Pd2dba3 with bulky, electron-rich ligands 1 or 2 and LiN(TMS)2 as the base for the coupling of amines with aryl halides containing hydroxyl, amide, or enolizable keto groups is described. This protocol expands the utility of palladium-catalyzed C-N bond formation by allowing for the use of aryl halides containing these functional groups, obviating the need for protecting group manipulations.     

High-resolution solid-state 2H NMR spectroscopy of polymorphs of glycine

High-resolution solid-state (2)H MAS NMR studies of the α and γ polymorphs of fully deuterated glycine (glycine-d(5)) are reported. Analysis of spinning sideband patterns is used to determine the (2)H quadrupole interaction parameters, and is shown to yield good agreement with the corresponding parameters determined from single-crystal (2)H NMR measurements (the maximum deviation in quadrupole coupling constants determined from these two approaches is only 1%). From analysis of simulated (2)H MAS NMR sideband patterns as a function of reorientational jump frequency (κ) for the -N(+)D(3) group in glycine-d(5), the experimentally observed differences in the (2)H MAS NMR spectrum for the -N(+)D(3) deutrons in the α and γ polymorphs is attributed to differences in the rate of reorientation of the -N(+)D(3) group. These simulations show severe broadening of the (2)H MAS NMR signal in the intermediate motion regime, suggesting that deuterons undergoing reorientational motions at rates in the range κ ≈ 10(4)-10(6) s(-1) are likely to be undetectable in (2)H MAS NMR measurements for materials with natural isotopic abundances. The (1)H NMR chemical shifts for the α and γ polymorphs of glycine have been determined from the (2)H MAS NMR results, taking into account the known second-order shift. Further quantum mechanical calculations of (2)H quadrupole interaction parameters and (1)H chemical shifts reveal the structural dependence of these parameters in the two polymorphs and suggest that the existence of two short intermolecular C-H···O contacts for one of the H atoms of the >CH(2) group in the α polymorph have a significant influence on the (2)H quadrupole coupling and (1)H chemical shift for this site.     

Spin crossover in a four-coordinate iron(II) complex

The four-coordinate iron(II) phosphoraniminato complex PhB(MesIm)(3)Fe-N═PPh(3) undergoes an S = 0 to S = 2 spin transition with T(C) = 81 K, as determined by variable-temperature magnetic measurements and Mo?ssbauer spectroscopy. Variable-temperature single-crystal X-ray diffraction revealed that the S = 0 to S = 2 transition is associated with an increase in the Fe-C and Fe-N bond distances and a decrease in the N-P bond distance. These structural changes have been interpreted in terms of electronic structure theory.     

Ultrafast observation of a solvent dependent spin state equilibrium in CpCo(CO)

We report the observation of a solvent-dependent spin state equilibrium in the 16-electron photoproduct CpCo(CO). Time-resolved infrared spectroscopy has been used to observe the concurrent formation of two distinct solvated monocarbonyl photoproducts, both of which arise from the same triplet CpCo(CO) precursor. Experiments in different solvent environments, combined with electronic structure theory calculations, allow us to assign the two solvated photoproducts to singlet and triplet CpCo(CO)(solvent) complexes. These results add to our previous picture of triplet reactivity for 16-electron organometallic photoproducts, in which triplets were not believed to interact strongly with solvent molecules. In the case of this photoproduct, it appears that spin crossover does not present a significant barrier to reactivity, and relative thermodynamic stabilities determine the spin state of the CpCo(CO) photoproduct in solution on the picosecond time scale. While the existence of transition metal complexes with two thermally accessible spin states is well-known, this is, to our knowledge, the first observation of a transient photoproduct that exhibits an equilibrium between two stable spin states, and also the first observed case in which a solvent has been able to coordinate as a token ligand to two spin states of the same photoproduct.