Organometallic chemistry of diphosphazanes. Rhodium(I) complexes of RN(PX2)2 (R = C6H5; X = OC6H5, OC6H4Br?p, R = CH3; X = OC6H5)

Reactions of [Rh(COD)Cl](2) with the ligand RN(PX(2))(2) (1: R=C6H5; X=OC6H5) give mono- or disubstituted complexes of the type [Rh-2(COD)Cl-2{eta(2)-C6H5N(P(OC6H5)(2))(2)}-] or [RhCl{eta(2)-C6H5N(P(OC6H5)(2))(2)}](2), depending on the reaction conditions. Reaction of 1 with [Rh(CO)(2)Cl](2) gives the symmetric binuclear complex, [Rh(CO)Cl{mu-C6H5N(P(OC6H5)(2))(2)}], whereas the same reaction with 2 (R=CH3; X=OC6H5) leads to the formation of an asymmetric complex of the type [Rh(CO)(mu-CO)Cl{mu-CH3N(P(OC6H5)(2))(2)}] containing both terminal and bridging CO groups. Interestingly the reaction of 3 (R=C6H5, X = OC6H4Br-p) with either [Rh(COD)Cl](2) or [Rh(CO)(2)Cl](2) leads only to the formation of the chlorine bridged binuclear complex, [RhCl{eta(2)-C6H5N(P(OC6H4Br-p)(2))(2)}](2). The structural elucidation of the complexes was carried out by elemental analyses, IR and P-31 NMR spectroscopic data.

Short-bite chiral diphosphazanes derived from (S)-?-methyl benzyl amine and their Pd, Pt and Rh metal complexes

New chiral diphosphazane ligands of the type Ph(2)PN(S-*CHMePh)PYY' {YY'= Ph(2) (2), O2C6H4 (3); Y= Ph, Y'= Cl {4a (SS), 4b (SR)}, N(2)C(3)HMe(2)-3,5 {5a (SR), 5b (SS)} are synthesised starting from a chiral aminophosphine, Ph(2)PNH(S-*CHMePh) (1). The structure of one of the diastereomer 5a has been confirmed by single crystal X-ray diffraction {Orthorhombic system, P2(1)2(1)2(1); a=10.456 (4), b=15.362 (7), c=17.379 (6) Angstrom, Z=4}. Transition metal mononuclear complexes [Rh{eta(2)-(Ph(2)P)(2)N- (S-*CHMePh)}(2)](+)(BF4)(-) (6), [PdCl2{eta(2)-(Ph(2)P)(2)N(S-*CHMePh)}] (7) and [PtCl2{eta(2)-(Ph(2)P)(2)N- (S-*CHMePh)}] (8) have also been synthesised. The structure of the palladium complex 7 is solved by X-ray crystallography {Orthorhombic system, P2(1)2(1)2(1); a=8.746 (2), b=18.086 (2), c=20.811 (3) Angstrom, Z=4}. All these compounds are characterised by micro analyses, IR and NMR spectroscopic data.

Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Dynamics of Fractional Brownian Walks

We investigate the dynamics of polymers whose solution configurations are represented by fractional Brownian walks. The calculation of the two dynamical quantities considered here, the longest relaxation time tau(r) and the intrinsic viscosity [eta], is formulated in terms of Langevin equations and is carried out within the continuum approach developed in an earlier paper. Our results for tau(r) and [eta] reproduce known scaling relations and provide reasonable numerical estimates of scaling amplitudes. The possible relevance of the work to the study of globular proteins and other compact polymeric phases is discussed.

Photolysis of arene chromium tricarbonyl complexes in presence of amine-boranes: Observation of sigma-borane complexes in solution

Activation of the B-H sigma-bond of amine-boranes on the chromium(0) center of arene chromium tricarbonyl complexes (eta(6)-arene) Cr(CO)(3) (arene = fluorobenzene, 1a; benzene, 1b and mesitylene, 1c) has been studied. Photolysis of 1b in presence of ammonia-borane (H3N center dot BH3, AB) and tert-butylamine-borane ((BuH2N)-Bu-t center dot BH3, TBAB) resulted in H-2 evolution and precipitation of a BNHx polymer. On the other hand, photolysis in the presence of trimethylamine-borane (Me3N center dot BH3, TMAB) resulted in the formation of a sigma-borane complex (2) along with Cr(CO)(5)(eta(1)-HBH2 center dot NMe3) (3). The sigma-borane complexes (eta(6)-arene) Cr-( CO)(2)(eta(1)-HBH2 center dot NMe3) (arene = fluorobenzene, 2a; benzene, 2b and mesitylene, 2c) were characterized in solution by H-1, B-11, and C-13 NMR spectroscopy. Electron withdrawing substituents on the arene ring provide the more stable sigma-borane moiety in this series of complexes. (C) 2011 Elsevier B.V. All rights reserved.

Thiophene adsorption studies on clean and hydrogen-preadsorbed MoS2(100) surface

It is known from temperature-programmed desorption studies that the binding energy of thiophene over Mo/gamma-Al2O3 and Co-Mo/gamma-Al2O3, hydrodesulfurization catalysts, is lower in the presence of hydrogen. The adsorption of thiophene on clean and hydrogen-adsorbed MoS2 was modelled using extended Huckel tight binding band structure calculations. In the eta(1) adsorption configuration the calculations show a lower binding energy for adsorption on the hydrogen-preadsorbed surface similar to that observed experimentally. The lowering is due to an increased occupancy of the Mo density of states in the presence of hydrogen.

Universal behaviour in erosive burning of solid propellants

This paper considers the extensive data and correlations on the erosive burning of solid propellants. A relatively simple nondimensional relationship between the ratio of the actual to nonerosive burn rate (eta) and a quantity g, which is the product of g(0)-the ratio of free stream mass flux to the mass flux from the surface for nonerosive condition-and Re-0(m), where Re-0 is the Reynolds number based on the nonerosive mass flux of the propellant and port diameter, is shown to correlate most data within the accuracies of the experiments with m = -0.125. This shows the above relationship to account for the effects of pressure, aluminum, even up to a proportion of 17%, burn rate catalysts, and motor size. It is concluded that the suggested correlation between eta and g may be adopted universally for most practical propellants. (C) 1997 by The Combustion Institute.

Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote-Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant-solvent interaction potential. When the solute-solvent interaction is modeled by a 6-12 Lennard-Jones potential, we find that over a large variation of viscosity (eta), the rate (k) can indeed be fitted very well to a fractional viscosity dependence: (k similar to eta(-alpha)), with the exponent alpha in the range 1 greater than or equal to alpha >0. The calculated values of the exponent appear to be in very good agreement with many experimental results. In particular, the theory, for the first time, explains the experimentally observed high value of alpha even at the barrier frequency, omega(b). similar or equal to 9 X 10(12) s(-1) for the isomerization reaction of 2-(2'-propenyl)anthracene in liquid eta-alkanes. The present study can also explain the reason for the very low value of vb observed in another study for the isomerization reaction of trans-stilbene in liquid n-alkanes. For omega(b) greater than or equal to 2.0 X 10(13) s(-1), we obtain alpha similar or equal to 0, which implies that the barrier crossing rate becomes identical to the transition-state theory predictions. A careful analysis of isomerization reaction dynamics involving large amplitude motion suggests that the barrier crossing dynamics itself may become irrelevant in highly viscous liquids and the rate might again be coupled directly to the viscosity. This crossover is predicted to be strongly temperature dependent and could be studied by changing the solvent viscosity by the application of pressure. (C) 1999 American Institute of Physics. [S0021-9606(9950514-X].

Synthesis and structure of a novel terminal imido complex of titanium

The reaction of eta(5)-Cp*TiCl3 and (LiNHBu)-Bu-t in hexanes yields a novel [eta(5)-Cp*Ti(=(NBu)-Bu-t)((NHBu)-Bu-t)(2)]Li . (NH2Bu)-Bu-t complex with a terminal tert-butylimido moiety. The synthesis and X-ray structural characterization are described. (C) 1999 Elsevier Science S.A. All rights reserved.

Assessment of conditional moment closure models of turbulent autoignition using DNS data

A systematic assessment of the submodels of conditional moment closure (CMC) formalism for the autoignition problem is carried out using direct numerical simulation (DNS) data. An initially non-premixed, n-heptane/air system, subjected to a three-dimensional, homogeneous, isotropic, and decaying turbulence, is considered. Two kinetic schemes, (1) a one-step and (2) a reduced four-step reaction mechanism, are considered for chemistry An alternative formulation is developed for closure of the mean chemical source term , based on the condition that the instantaneous fluctuation of excess temperature is small. With this model, it is shown that the CMC equations describe the autoignition process all the way up to near the equilibrium limit. The effect of second-order terms (namely, conditional variance of temperature excess sigma(2) and conditional correlations of species q(ij)) in modeling is examined. Comparison with DNS data shows that sigma(2) has little effect on the predicted conditional mean temperature evolution, if the average conditional scalar dissipation rate is properly modeled. Using DNS data, a correction factor is introduced in the modeling of nonlinear terms to include the effect of species fluctuations. Computations including such a correction factor show that the species conditional correlations q(ij) have little effect on model predictions with a one-step reaction, but those q(ij) involving intermediate species are found to be crucial when four-step reduced kinetics is considered. The "most reactive mixture fraction" is found to vary with time when a four-step kinetics is considered. First-order CMC results are found to be qualitatively wrong if the conditional mean scalar dissipation rate is not modeled properly. The autoignition delay time predicted by the CMC model compares excellently with DNS results and shows a trend similar to experimental data over a range of initial temperatures.

Chemistry of dihydrogen complexes containing only phosphorus co-ligands

A series of new dicationic dihydrogen complexes of ruthenium of the type cis-[(dppm)(2)Ru(eta(2)-H-2)(L)][BF4](2) (dppm = Ph2PCH2PPh2; L = phosphite) have been prepared by protonating the precursor hydride complexes cis-[(dPPM)(2)Ru(H)(L)][BF4] using HBF4.Et2O. The precursor hydride complexes have been obtained from trans-[(dppm)(2)Ru(H)(L)][BF4][(L = phospfiite) via a rare acid-catalysed isomerization reaction in six coordinate species. The trans-[(dppm)(2)Ru(H)(L)][BF4] complexes (L = phosphine) upon protonation gave the isomerized derivatives, however, further addition of acid resulted in a five-coordinate species, [(dppm)(2)RuCl](+) presumably via an intermediate phosphine dihydrogen complex. The electronic as well as the steric properties of the co-ligands seem to strongly influence the structure-reactivity behaviour of this series of complexes.

Organometallic chemistry of diphosphazanes. Part 15. Half-sandwich cyclopentadienyl ruthenium complexes of achiral and chiral diphosphazanes

Reaction of [CpRu(PPh3)(2)Cl] (1) {Cp = eta(5)-(C5H5)} with X2PN(CHMe2) PYY' {X = Y = Y' = Ph (L-1); X = Y = Ph, Y' = OC6H4Me-4 (L-4); X = Y = Ph, Y' = OC6H3Me2- 3,5 (L-5); X = Y = Ph, Y' = N2C3HMe2 (L-6)} yields the cationic chelate complexes, [CpRu(eta(2)-(X2PN(CHMe2) PYY')) PPh3] Cl. On the other hand, the reaction of 1 with X2PN(CHMe2)PYY' {X = Ph, YY' = O2C6H4(L-3)} gives the complex, [CpRu(eta(1)-L-2)(2)PPh3] Cl. Both types of complexes are formed with X2PN(CHMe2) PYY' {X = Ph, YY' = O2C6H4 (L-3)}. The reaction of 1 with (R),(S)-(H12C20O2) PN(CHMe2) PPh2 (L-7) yields both cationic and neutral complexes, [CpRu{eta(2)-(L-7)} PPh3] Cl and [CpRu{eta(1)-(L-7)}(2)PPh3] Cl and [CpRu{eta(2)-(L-7)}Cl]. The reactions of optically pure diphosphazane, Ph2PN(*CHMePh) PPhY (Y = Ph (L-8); Y = N2C3HMe2-3,5 (L-9)) with 1 give the neutral and cationic ruthenium complexes, [CpRu{eta(2)-(Ph2PN(R) PPhY)} Cl] and [CpRu{eta(2)-(Ph2PN(R)PPhY)} PPh3] Cl. "Chiral-at-metal" ruthenium complexes of diphosphazanes have been synthesized with high diastereoselectivity. The absolute configuration of a novel ruthenium complex, (SCSPRRu)-[(eta(5)-C5H5) Ru*{eta(2)-(Ph2PN(*CHMePh)P*Ph( N2C3HMe2-3,5))} Cl] possessing three chiral centers, is established by X-ray crystallography. The reactions of [CpRu{eta(2)-(L-8)} Cl] with mono or diphosphanes in the presence of NH4PF6 yield the cationic complexes, [CpRu{eta(2)-(L-8)}{eta(1)-(P)}] PF6 {P = P(OMe)(3), PPh3, Ph2P(CH2)(n)PPh2 (n = 1 or 2)}.

Stability of fluid flow past a membrane

The stability of fluid flow past a membrane of infinitesimal thickness is analysed in the limit of zero Reynolds number using linear and weakly nonlinear analyses. The system consists of two Newtonian fluids of thickness R* and H R*, separated by an infinitesimally thick membrane, which is flat in the unperturbed state. The dynamics of the membrane is described by its normal displacement from the flat state, as well as a surface displacement field which provides the displacement of material points from their steady-state positions due to the tangential stress exerted by the fluid flow. The surface stress in the membrane (force per unit length) contains an elastic component proportional to the strain along the surface of the membrane, and a viscous component proportional to the strain rate. The linear analysis reveals that the fluctuations become unstable in the long-wave (alpha --> 0) limit when the non-dimensional strain rate in the fluid exceeds a critical value Lambda(t), and this critical value increases proportional to alpha(2) in this limit. Here, alpha is the dimensionless wavenumber of the perturbations scaled by the inverse of the fluid thickness R*(-1), and the dimensionless strain rate is given by Lambda(t) = ((gamma) over dot* R*eta*/Gamma*), where eta* is the fluid viscosity, Gamma* is the tension of the membrane and (gamma) over dot* is the strain rate in the fluid. The weakly nonlinear stability analysis shows that perturbations are supercritically stable in the alpha --> 0 limit.

Theoretical Studies on the Structure and Bonding of Metallacyclocumulenes, -cyclopentynes, and -cycloallenes

In this paper, we compare the electronic structure of the hafnacycloallene complex Cp(2)HfC(4)Rr'(2)R `' (5Hf), which was previously described by Erker et al., with those of the titanium, zirconium, and hafnium complexes Cp(2)M(eta(4)-RHC(4)HR) (3M; i.e. metallacyclopent-2,3,4-trienes, metallacyclocumulenes) and Cp(2)M(eta(2)-R(2)C(4)R(2)) (4M; i.e. 1-metallacyclopent-3-ynes) using density functional theory (BP86/LANL2DZ) calculations. Moreover, the eta(3)-phenylallenyl zirconocene complex 7Zr, which was synthesized by Wojcicki et al., is included for the comparison. These calculations and extended Huckel calculations show that the bonding in complex 5Hf is remarkably similar to that of complexes 4M and 7Zr. An analysis of the structural parameters and bonding reveals that the unique interaction of the internal carbon atoms along with the terminal carbon atoms with the bent-metallocene moiety is the reason for the unusual stability of these metallacycles. The molecular orbital analysis further suggests that complex 5Hf can react with another metal fragment to give the bimetallic complexes 9 and 10. The electronic structures of complexes 3M, 4M, 5Hf, and 7Zr have been comparatively studied to get a general understanding of the bonding in these metallacycles.