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.     

Increased torque transducer sensitivity via oversampling

The sensitivity of a commercial torque transducer under oscillatory shear conditions is extended by about a factor 3–5 into the small torque region. This increased sensitivity is a result of a straightforward data treatment in the time domain termed “on the fly oversampling”. This method is enabled by the emergence of modern ADC-cards. The underlying ideas of oversampling together with a first experimental verification of this method are described in detail. Received: 22 August 2000 Accepted: 14 November 2000     

Threshold Phenomenon for the Quintic Wave Equation in Three Dimensions

For the critical focusing wave equation ${\square u = u^5 \, {\rm on} \, \mathbb{R}^{3+1}}$ in the radial case, we establish the role of the “center stable” manifold ${\Sigma}$ constructed in Krieger and Schlag (Am J Math 129(3):843–913, 2007) near the ground state (W, 0) as a threshold between blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizoń et al. (Nonlinearity 17(6):2187–2201, 2004). The underlying topology is stronger than the energy norm.     

Tuning the electronic coupling in a low-bandgap donor-acceptor copolymer via the placement of side-chains

We present a spectroscopic and theoretical investigation of the effect of the presence and position of hexyl side-chains in the novel low-bandgap alternating donor-acceptor copolymer poly[bis-N,N-(4-octylphenyl)-bis-N,N-phenyl-1,4-phenylenediamine-alt-5,5'-4',7',-di-2-thienyl-2',1',3'-benzothiadiazole] (T8TBT). We use electronic absorption and Raman spectroscopic measurements supported by calculations of chain conformation, electronic transitions, and Raman modes. Using these tools, we find that sterically demanding side-chain configurations induce twisting in the electronic acceptor unit and reduce the electronic interaction with the donor. This leads to a blue-shifted and weakened (partial) charge-transfer absorption band together with a higher photoluminescence efficiency. On the other hand, sterically relaxed side-chain configurations promote coupling between donor and acceptor units and exhibit enhanced absorption at the expense of luminescence efficiency. The possibility of tuning the donor-acceptor character of conjugated polymers by varying the placement of side-chains has very important ramifications for light emitting diode, Laser, display, and photovoltaic device optimization.     

Ultrasound Emulsification—An Overview

Fundamentals and applications of ultrasound emulsification are reviewed. The importance of cavitation is stressed, as also is power input to the multiphase fluid. The influence of surfactants, polymeric stabilizers, temperature, pressure, and ultrasonic parameters such as frequency, residence time, acoustic intensity, and energy density are described. The effects of other physicochemical parameters such as emulsifier concentration, disperse phase volume fraction, and viscosity are discussed. Applications to both water-in-oil and oil-in-water emulsions are discussed.     

Crystal structures of a calix[4]arene controlled by two affixed pyrene units

The synthesis and crystal structures of a calix[4]arene (1) with two affixed pyrene units and its corresponding inclusion compound with chloroform (1a) are reported. In both cases, stacking structures resulting from the influencing control of the pyrene units are observed. The occurrence of infinite or dimeric stack motifs of the pyrene units is dependent on the absence or presence of the included guest solvent.

     

Total Gaussian curvature,drop shapes and the range of applicability of drop shape techniques

Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The new definition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.     

Oscillatory shear and high-pressure dielectric study of 5-methyl-3-heptanol

The monohydroxy alcohol 5-methyl-3-heptanol is studied using rheology at ambient pressure and using dielectric spectroscopy at elevated pressures up to 1.03 GPa. Both experimental techniques reveal that the relaxational behavior of this liquid is intermediate between those that show a large Debye process, such as 2-ethyl-1-hexanol, or a small Debye-like feature, such as 4-methyl-3-heptanol, with which comparisons are made. Various phenomenological approaches assigning a time scale for the rheological signature of supramolecular dynamics in monohydroxy alcohols are discussed.     

Tan relations in one dimension

We derive exact relations that connect the universal C/k⁴-decay of the momentum distribution at large k with both thermodynamic properties and correlation functions of two-component Fermi gases in one dimension with contact interactions. The relations are analogous to those obtained by Tan in the three-dimensional case and are derived from an operator product expansion of the one- and two-particle density matrix. They extend earlier results by Olshanii and Dunjko (2003) [24] for the bosonic Lieb–Liniger gas. As an application, we calculate the pair distribution function at short distances and the dimensionless contact in the limit of infinite repulsion. The ground state energy approaches a universal constant in this limit, a behavior that also holds in the three-dimensional case. In both one and three dimensions, a Stoner instability to a saturated ferromagnet for repulsive fermions with zero range interactions is ruled out at any finite coupling.