Polymeric liquids in extension: fluid mechanics or rheometry?

We use a transient 3D free surface finite element method to simulate flow of entangled polymer fluids in the dual cylinder wind-up extensional rheometer. The constitutive equations are K-BKZ integral representations of the Doi–Edwards models with and without the independent alignment approximation (IA). It is demonstrated that the actual kinematics in this rheometer is a mixture of planar and uniaxial extension. Moreover, the ratio of planar to uniaxial deformation is highly dependent upon whether IA is invoked. Without IA, the flow has a tendency toward planar extension, while it tends to be more uniaxial with IA invoked. As a second illustration of the techniques, we simulate the phenomenon of delayed rupture after rapid extension of entangled polymer systems. It is demonstrated that this phenomenon can be explained on the basis of the Doi–Edwards model in terms of a Considere-type instability after chain stretch relaxation.     

Effects of Fuel Lewis Number on Localised Forced Ignition of Turbulent Mixing Layers

The influences of fuel Lewis number Le _F on localised forced ignition of inhomogeneous mixtures are analysed using three-dimensional compressible Direct Numerical Simulations (DNS) of turbulent mixing layers for Le _F  = 0.8, 1.0 and 1.2 and a range of different root-mean-square turbulent velocity fluctuation u′ values. For all Le _F cases a tribrachial flame has been observed in case of successful ignition. However, the lean premixed branch tends to merge with the diffusion flame on the stoichiometric mixture fraction isosurface at later stages of the flame evolution. It has been observed that the maximum values of temperature and reaction rate increase with decreasing Le _F during the period of external energy addition. Moreover, Le _F is found to have a significant effect on the behaviours of mean temperature and fuel reaction rate magnitude conditional on mixture fraction values. It is also found that reaction rate and mixture fraction gradient magnitude \(\vert \nabla \xi \vert \) are negatively correlated at the most reactive region for all values of Le _F explored. The probability of finding high values of \(\vert \nabla \xi \vert \) increases with increasing Le _F . For a given value of u′, the extent of burning decreases with increasing Le _F . A moderate increase in u′ gives rise to an increase in the extent of burning for Le _F  = 0.8 and 1.0, which starts to decrease with further increases in u′. For Le _F  = 1.2, the extent of burning decreases monotonically with increasing u′. The extent of edge flame propagation on the stoichiometric mixture fraction ξ = ξ _st isosurface is characterised by the probability of finding burned gas on this isosurface, which decreases with increasing u′ and Le _F . It has been found that it is easier to obtain self-sustained combustion following localised forced ignition in case of inhomogeneous mixtures than that in the case of homogeneous mixtures with the same energy input, energy deposition duration when the ignition centre is placed at the stoichiometric mixture. The difficultly to sustain combustion unaided by external energy addition in homogeneous mixture is particularly prevalent in the case of Le _F  = 1.2.     

Testing of Model Equations for the Mean Dissipation using Kolmogorov Flows

Direct Numerical Simulations (DNS) of Kolmogorov flows are performed at three different Reynolds numbers Re _λ between 110 and 190 by imposing a mean velocity profile in y-direction of the form U(y) = F sin(y) in a periodic box of volume (2π)³. After a few integral times the turbulent flow turns out to be statistically steady. Profiles of mean quantities are then obtained by averaging over planes at constant y. Based on these profiles two different model equations for the mean dissipation ε in the context of two-equation RANS (Reynolds Averaged Navier–Stokes) modelling of turbulence are compared to each other. The high Reynolds number version of the k-ε-model (Jones and Launder, Int J Heat Mass Transfer 15:301–314, 1972), to be called the standard model and a new model by Menter et al. (2006), to be called the Menter–Egorov model, are tested against the DNS results. Both models are solved numerically and it is found that the standard model does not provide a steady solution for the present case, while the Menter–Egorov model does. In addition a fairly good quantitative agreement of the model solution and the DNS data is found for the averaged profiles of the kinetic energy k and the dissipation ε. Furthermore, an analysis based on flow-inherent geometries, called dissipation elements (Wang and Peters, J Fluid Mech 608:113–138, 2008), is used to examine the Menter–Egorov ε model equation. An expression for the evolution of ε is derived by taking appropriate moments of the equation for the evolution of the probability density function (pdf) of the length of dissipation elements. A term-by-term comparison with the model equation allows a prediction of the constants, which with increasing Reynolds number approach the empirical values.     

Synthese und Charakterisierung von Trimethyl(sulfato)platin(IV)Komplexen

Syntheses and Characterization of Trimethyl(sufato)platinum(IV) Complexes [(PtMe₃I)₄] ( 1 ) reacts in benzene/acetone (1 : 1) with excess of freshly precipitated silver sulfate (Pt : Ag = 1 : 2) to give [{[PtMe₃(H₂O)]₂SO₄}_∞] ( 2 ) at working up from acetone (not dried) and water to [{PtMe₃(H₂O)₂}₂SO₄] ( 3 ), respectively. [(PtMe₃I)₄] ( 1 ) reacts with AgBF₄ in the corresponding solvent L to give complexes of the type [PtMe₃L₃]BF₄ (L = Me₂CO 4 , MeOH 5 , MeCN 6 , THF 7 ). The triaqua complex 8 (L = H₂O) has been obtained by reaction of 4 with water. All complexes are characterized by microanalysis and NMR spectroscopy (¹H, ¹³C, ¹⁹⁵Pt). X-ray diffraction analysis of 2 (monoclinic, P2₁) exhibits dinuclear units [Me₃Pt(μ-H₂O)PtMe₃(H₂O)]²⁺ at which oxo ligands of sulfate ions are coordinated in such a way that the crystal is threaded by double chains. The Pt–O bonds to μ-aqua ligand are considerably longer than that to terminal aqua ligand (2.322(9)/2.363(8) vs. 2.234(9) Å). The structural characterization of 3 (triclinic, P 1) reveals [PtMe₃(H₂O)₂]⁺ cations that are bridged by a sulfate ion yielding a dinuclear entity [(H₂O)₂Me₃Pt(μ-SO₄)PtMe₃ · (H₂O)₂]. These entities are linked in the crystal by a network of hydrogen bridges.     

General stereoretentive preparation of chiral secondary mixed alkylmagnesium reagents and their use for enantioselective electrophilic aminations

A general preparation of enantiomerically and diastereomerically enriched secondary alkylmagnesium reagents was reported as well as their use for performing highly stereoselective transition-metal free electrophilic aminations leading to α-chiral amines in up to 97% ee. Thus, the reaction of t-BuLi (2.2 equiv.) with a mixture of chiral secondary alkyl iodides and the commercially available magnesium reagent Me₃SiCH₂MgCl in a 2 : 1 mixture of pentane and diethyl ether at up to −50 °C provided optically enriched secondary mixed alkylmagnesium species of the type alkyl(Me)CHMgCH₂SiMe₃ with high retention of configuration (up to 99% ee). The resulting enantiomerically enriched dialkylmagnesium reagents were trapped with electrophiles such as non-enolizable ketones, aldehydes, acid chlorides, isocyanates, chlorophosphines and O-benzoyl hydroxylamines providing α-chiral tertiary alcohols, ketones, amides, phosphines and tertiary amines in up to 89% yield (over three reaction steps) and up to 99% ee.

We report a general method for the preparation of enantiomerically enriched secondary alkylmagnesium reagents, which undergo highly stereoselective transition-metal free electrophilic aminations, leading to α-chiral amines in up to 97% ee.     

Chemistry at High Dilution: Dinuclear 99 mTc Complexes

The formation of di- or polynuclear complexes at nanomolar concentrations is generally too slow to be observed with ^99mTc. It is reported in this communication that an appropriate choice of potentially bridging ligands, herein thiols HS-R, accelerates the dimerization reaction to an extent that dinuclear complexes are formed at very high dilution. The dinuclear nature of [^99mTc₂(μ₂-SR)₃(CO)₆]⁻ is shown by chromatographic comparison, not only with its rhenium homologue as commonly done, but also with the true ⁹⁹Tc analogue.     

Perturbed Divisible Sandpiles and Quadrature Surfaces

Potential Analysis - The main purpose of the present paper is to establish a link between quadrature surfaces (potential theoretic concept) and sandpile dynamics (Laplacian growth models). For this...     

[(C C)Au(N N)]+ Complexes as a New Family of Anticancer Candidates: Synthesis,Characterization and Exploration of the Antiproliferative Properties

A library of eleven cationic gold(III) complexes of the general formula [(C C)Au(N N)]⁺ when C C is either biphenyl or 4,4’-ditertbutyldiphenyl and N N is a bipyridine, phenanthroline or dipyridylamine derivative have been synthesized and characterized. Contrasting effects on the viability of the triple negative breast cancer cells MDA-MB-231 was observed from a preliminary screening. The antiproliferative activity of the seven most active complexes were further assayed on a larger panel of human cancer cells as well as on non-cancerous cells for comparison. Two complexes stood out for being either highly active or highly selective. Eventually, reactivity studies with biologically meaningful amino acids, glutathione, higher order DNA structures and thioredoxin reductase (TrxR) revealed a markedly different behavior from that of the well-known coordinatively isomeric [(C N C)Au(NHC)]⁺ structure. This makes the [(C C)Au(N N)]⁺ complexes a new class of organogold compounds with an original mode of action.