Permeation in cholesteric liquid crystals

It is shown that permeation in cholesteric liquid crystals can be derived quite generally from Leslie's linearized equations for the conservation of linear and angular momentum.     

Depolymerization behavior of thermoplastic poly(urethane) (TPU) and its dependence on initial molecular weight

The quantitative and qualitative depolymerization behavior of thermoplastic poly(urethane) (TPU) consisting of 4,4′-methylenediphenyldiisocyanate (MDI), 1,6-hexanediol (HD) and 1-hexanol (HEX) was described using temperature-modulated differential scanning calorimetry and Fourier transform infrared (FT-IR) spectroscopy. The depolymerization behavior could be altered by lowering the starting molecular weight. This resulted not only in a higher ceiling temperature, but also in a faster decrease of the molecular weight as a function of temperature once the depolymerization has started. The increase in the ceiling temperature for low molecular weight TPUs is attributed to the lower entropy of polymerization for these compounds compared to high molecular weight TPUs.     

Application of FTIR Microscopy in Combinatorial Experimentation on Polymer Blends

Summary: A novel combinatorial, high-throughput experimentation (HTE) setup has been developed, which allows for rapid mapping of the phase behavior of blends of homopolymers and block copolymers. The principle is based on the preparation of composition (ϕ)-temperature (T) gradient films. Linear ϕ gradients were obtained over a large composition range, as shown by FTIR microscopy. The applicability of this combinatorial approach was demonstrated by studying the phase behavior of a poly(styrene-co-acrylonitrile) (SAN)/poly(methyl methacrylate-co-ethyl acrylate) (PMMA-EA) blend with varying EA content and a poly(styrene-b-butadiene-b-methyl methacrylate) (SBM) triblock copolymer.     

Vapour diffusion growth and characterisation of fully deuterated triglycine sulphate (ND2CD2COOD)3D2SO4

A new vial-in-vial vapour diffusion method for growing single crystals of fully deuterated triglycine sulphate (TGS) has been developed. Single crystals of hydrogenous TGS were also grown for comparison purposes. The crystals have been characterised using x-ray diffraction and differential scanning calorimetry. The phase transition temperature was 334.0±0.5 K for fully deuterated TGS compared to 322.3±0.3 K for hydrogenous TGS. These values compare well with the expected T_C.     

Double-Gyroid Nanostructure Formation by Aggregation-Induced Atropisomerization and Co-Assembly of Ionic Liquid-Crystalline Amphiphiles

We report a new molecular-design principle for creating double-gyroid nanostructured molecular assemblies based on atropisomerization. Ionic amphiphiles containing two imidazolium rings close to each other were designed and synthesized. NMR data revealed that the rotation of the imidazolium rings is restricted, with an activation energy as high as 63 kJ mol⁻¹ in DMSO-d₆ solution (DFT prediction for a model compound in the vacuum: 90–100 kJ mol⁻¹). Due to the restricted rotation, the amphiphiles feature “double” atropisomeric axes in their ionic segments and form three stable atropisomers: meso, R, and S. These isomers co-organize into -type bicontinuous cubic liquid-crystalline mesophases through nanosegregation of the ionic and non-ionic parts. Considering the intrinsic characteristic of -type bicontinuous cubic structures that they are composed of intertwined right- and left-handed single gyroids, we propose that the simultaneous presence of both R- and S-atropisomers is an important contributor to the formation of double-gyroid structures.     

The approximability of three-dimensional assignment problems with bottleneck objective

We discuss two special cases of the three-dimensional bottleneck assignment problem where a certain underlying cost function satisfies the triangle inequality. We present polynomial time 2-approximation algorithms for the broadest class of these special cases, and we prove that (unless P = NP) this factor 2 is best possible even in the highly restricted setting of the Euclidean plane.     

Shock wave induced evaporation of water droplets in a gas-droplet mixture

A model is presented for the droplet evaporation process induced by a shock wave propagating in a fog. The model is based on the existence of a quasi-steady wet bulb state of the droplets during evaporation. It is shown that for moderate shock strength, Ma = < 2, and droplet radii in the range of 1–5 the, the major part of the evaporation process is governed by a balance between heat conduction and vapour diffusion. The formation of a fog by means of an unsteady adiabatic expansion of humid nitrogen is described. Experimental results of shock induced evaporation are shown for shock Mach numbers from 1.2 to 2.1, droplet mass fraction of 5 · 10^-3, and initial droplet radii of 1–1.4 m. The expected linear relation between droplet radius squared and time during evaporation is observed. Characteristic evaporation times appear to be strongly dependent on shock strength. A variation of about two decades, predicted by theory, was experimentally observed for the Mach number range studied.     

Characterization of the morphology of co-extruded, thermoplastic/rubber multi-layer tapes

Tapes with alternating semi-crystalline thermoplastic/rubber layers with thicknesses varying from 100 nm up to several μm were prepared by multi-layer co-extrusion. The variation in layer thickness was obtained by varying the thermoplastic/rubber feed ratio. A systematic study on the use of various microscopy techniques to visualize the morphology of the layered systems is presented. The relatively large length scales and the sample preparation make optical microscopy (OM) unsuitable to study the morphology of the multi-layer tapes. Although excellent contrast between the thermoplastic and rubber layers can be obtained, the usually applied, relatively large magnifications limit the use of transmission electron microscopy (TEM) and atomic force microscopy (AFM) to small sample areas. The large range of applicable magnifications makes scanning electron microscopy (SEM) the most suitable technique to study the morphology of the multi-layer tapes. The sample preparation for SEM with a secondary electron (SE) detector is often based on the removal of one of the components, which may induce changes in the morphology. SEM with a back-scattered electron (BSE) detector is a very convenient method to study the morphology over a wide range of length scales, where the contrast between the different layers can be enhanced by chemical staining. Finally, the nucleation behavior (homogeneous versus heterogeneous) of the semi-crystalline layers, as probed by differential scanning calorimetry (DSC), provides valuable information on the layered morphology. The use of relatively straightforward DSC measurements shows a clear advantage with respect to the discussed microscopy techniques, since no sample preparation is required and relatively large samples can be studied, which are more representative for the bulk.     

The transportation problem with exclusionary side constraints

We consider the so-called Transportation Problem with Exclusionary Side Constraints (TPESC), which is a generalization of the ordinary transportation problem. We confirm that the TPESC is NP-hard, and we analyze the complexity of different special cases. For instance, we show that in case of a bounded number of suppliers, a pseudo-polynomial time algorithm exists, whereas the case of two demand nodes is already hard to approximate within a constant factor (unless P = NP). This research was partially supported by FWO Grant No. G.0114.03.