Gold-Catalyzed Cycloisomerization of Sulfur Ylides to Dihydrobenzothiepines

The metal-promoted nucleophilic addition of sulfur ylides to π-systems is a well-established reactivity. However, the driving force of such transformations, elimination of a sulfide moiety, entails stoichiometric byproducts making them unfavorable in terms of atom economy. In this work, a new take on sulfur ylide chemistry is reported, an atom-economical gold(I)-catalyzed synthesis of dihydrobenzo[b]thiepines. The reaction proceeds under mild conditions at room temperature.     

A generalized expression for the ratio of the critical temperature to the critical pressure with the van der Waals surface area

Using an extensive database of experimental critical properties for heavy compounds, which have been compiled mostly from recent literature sources, it is shown that the ratio T_c: P_c (critical temperature over critical pressure) can be expressed in terms of the van der Waals surface area (Q_w), which is readily available for any compound from the group contributions of Bondi (given also in UNIFAC tables). The proposed correlation is based on the hole theory of Kurata and Isida for n-paraffin liquids, which is mathematically equivalent to Flory's theory of polymer solutions. The method is suitable for medium to high molecular weight compounds with unknown critical constants. For example, if only one of the two critical constants is available, then the proposed generalized equation offers a useful rapid procedure for the estimation of the other critical property for use in corresponding states, and other relevant applications where knowledge of the critical properties is required. Furthermore, the T_c: P_c method can be used in many cases for identifying the most suitable among the existing group contribution methods for estimating the critical properties of heavy and complex compounds for which experimental values are, very often, not available.     

Smoothness of holonomy covers for singular foliations and essential isotropy

Given a singular foliation, we attach an “essential isotropy” group to each of its leaves, and show that its discreteness is the integrability obstruction of a natural Lie algebroid over the leaf. We show that a condition ensuring discreteness is the local surjectivity of a transversal exponential map associated with the maximal ideal of vector fields prescribed to be tangent to the foliation. The essential isotropy group is also shown to control the smoothness of the holonomy cover of the leaf (the associated fiber of the holonomy groupoid), as well as the smoothness of the associated isotropy group. Namely, the (topological) closeness of the essential isotropy group is a necessary and sufficient condition for the holonomy cover to be a smooth (finite-dimensional) manifold and the isotropy group to be a Lie group. These results are useful towards understanding the normal form of a singular foliation around a compact leaf. At the end of this article we briefly outline work of ours on this normal form, to be presented in a subsequent paper.     

Detection and quantification of industrial polyethylene branching topologies via Fourier-transform rheology,NMR and simulation using the Pom-pom model

The significance of sparse long-chain branching in polyolefines towards mechanical properties is well-known. Topology is a very important structural property of polyethylene, as is molecular weight distribution. The method of Fourier-transform rheology (FTR) and melt state nuclear magnetic resonance (NMR) is applied for the detection and quantification of branching topology (number of branches per molecule), for industrial polyethylenes of various molecular weight and molecular weight distributions. FT rheology consists of studying the development of higher harmonics contribution of the stress response to a large amplitude oscillatory shear deformation. In particular, when applying large-amplitude oscillatory shear (LAOS), one observes the development of mechanical higher harmonic contributions at 3ω ₁, 5ω ₁,..., in the shear stress response. We correlate the relative intensity, I _3/1, and phase Φ ₃ of these harmonics with structural properties of industrial polyethylene, i.e. polymer topology and molecular weight distribution. Experiments are complemented by numerical simulations, using a multimode differential Pom-pom constitutive model (DCPP formulation), by fitting to the experimental linear and nonlinear viscoelastic behaviours. Simulation results in the nonlinear regime are correlated with molecular properties of the “pom-pom” macromolecular architecture. Qualitative agreement is found between predicted and experimental FT rheology results.     

Extensions of the disc algebra and of Mergelyanʼs theorem

We investigate the uniform limits of the set of polynomials on the closed unit disc $\overline{D}$ with respect to the chordal metric χ. More generally, we examine analogous questions replacing $\mathbb{C}\cup \{\infty \}$ by other metrizable compactifications of $\mathbb{C}$.     

Coupling Deterministic and Stochastic Simulation to Model the Polymeric Microstructure of LDPE

Summary: Simulation based process development of new LDPE grades often requires a deep insight into the exact microstructure of individual macromolecules. Therefore, we developed an approach, which combines the advantages of the deterministic (low computational time and high accuracy) and stochastic simulation (individual macromolecules with distinct microstructure). The approach can be used for the modeling of continuously driven autoclave and tubular reactors. First results visualize the random conformation of a distinct macromolecule as well as the resulting contraction factor.     

Predicting extrusion instabilities of commercial polyethylene from non-linear rheology measurements

Processing at the highest possible throughput rates is essential from an economical point of view. However, various flow instabilities and extrudate distortions like sharkskin, stick slip, and gross melt fracture (GMF) may limit the production rate of high-quality products. Predicting the process conditions leading to the occurrence of rheological instabilities is the key for improving product quality, process control, and optimization. Large-amplitude oscillatory shear (LAOS) and FT-rheology were used to quantify the non-linear rheological behavior and instabilities of a series of well-characterized commercial polyethylene (PE). From the latter, we derive the critical non-linearity parameter, F _0,c, which corresponds to the normalized intensity of the third harmonic at the critical strain amplitude, γ _0,C (defined by the appearance of the second harmonic), normalized by γ _0,C . The F _0,c is correlated with the high molecular mass fraction of the polymers and with the Deborah numbers. Linear rheological parameters and molecular structures were related to F _0,c. An experimental correlation between F _0,c of commercial PE melts and pressure fluctuations associated with flow instabilities (sharkskin) was established both for capillary rheometry and extrusion.     

Laplacians and Spectrum for Singular Foliations

The author surveys Connes＇ results on the longitudinal Laplace operator along a （regular） foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it is proved that the Laplacian of a singular foliation is an essentially self-adjoint operator （unbounded） and has the same spectrum in every （faithful） representation, in particular, in L2 of the manifold and L2 of a leaf. The author also discusses briefly the relation of the Baum-Connes assembly map with the calculation of the spectrum.