Optical properties of electron beam- and UV-cured polypropyleneglycoldiacrylate/liquid crystal E7 systems

This contribution focuses on a detailed investigation of the relationship between the method of polymerisation/cross-linking, such as slow and rapid UV radiation, and high voltage accelerated electron beam (EB), and the obtained physical properties including phase diagrams, polymerisation and phase separation kinetics, morphologies and electro-optic responses of polypropyleneglycoldiacrylate (PPGDA) monomers, in the presence of the nematic liquid crystal E7. The longer the spacing between double bonds, the more rapid was the photopolymerisation under both UV systems; however, the reverse was proved under EB. More homogenous and regular morphologies were obtained under EB curing.

The electro-optical responses of various polymer dispersed liquid crystals (PDLCs) systems exhibited remarkable differences between the UV-cured samples and those cured by the EB technique. It was found that the threshold and saturation voltages considerably increased in the case of the UV-cured systems. Other results involving the contrast ratio, which is higher for EB-cured systems, confirm their higher quality, although the rapid photopolymerisation UV source was employed, which slightly improved the electro-optical responses. Moreover, EB curing leads to high enough conversions without a photoinitiator, which may act as an impurity that might have a strong impact on the electro-optical performance of the obtained PDLCs.     

Palladium catalyzed oxidation of allylsilanes with U.V. light and molecular oxygen (1)

Photolysis of oxygenated acetone solutions of allylsilanes containing small amounts of palladium led to α,β-ethylenic alcohols, aldehydes or ketones. Efficient regiospecific oxidation can be observed when the allylsilane was substituted by an arylsulphonyl group.     

On the range of the sum of monotone operators in general Banach spaces

The purpose of this paper is to generalize the Brézis-Haraux theorem on the range of the sum of monotone operators from a Hilbert space to general Banach spaces. The result obtained provides that the range is topologically almost equal to the sum where is a compatible topology in as proposed by Gossez. To illustrate the main result we consider some basic properties of densely maximal monotone operators.

     

One pot diastereoselective synthesis of new chiral spiro‐1,3,4‐thiadiazoles and 1,4,2‐oxathiazoles from (1R)‐thiocamphor

Herein we report an efficient one pot synthesis of new chiral 4,5‐dihydro‐4‐arylspiro[1,3,4‐thiadiazole]‐5,2′‐camphane‐2‐carboxylic acid ethyl esters 5–7 and 4,5‐dihydro‐3‐arylspiro[1,4,2‐oxathiazole]‐5,2′‐camphane 11–13 , using 1,3‐dipolar cycloaddition of nitrilimines 2–4 and nitrile oxides 8–10 to (1R)‐thiocamphor 1 respectively. The structure of the newly prepared 1,3,4‐thiadiazoles 5–7 (obtained as pure diastereoisomers) were fully established via spectroscopic analysis and X‐ray structural analysis which proved the absolute configuration of the C5 spiranic carbon to be (R). NMR spectral analysis were also very useful to show the new 1,4,2‐oxathiazoles 11–13 are mixtures of two (5R)/(5S) diastereoisomers with the ratio 6:4,7:3 and 6:4 respectively.     

On convection with nearly insulating boundaries in a low Prandtl number fluid

Summary For the Prandtl numberP in the rangeP ^1/3 1 ( is the ratio between the thermal conductivities of the boundary and of the fluid) two-dimensional rolls are preferred in contrast to square-pattern convection that represents the preferred stable convection in the rangeP ^1/3.

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Zussammenfasung Für PrandtlzahlenP, die der RelationP ^1/3 1 genügen (\ ist das Verhältnis zwischen den thermischen Leitfähigkeiten der Wand und des Fluid), sind zweidimensionale Rollen bevorzugt im Gegensatz zur quadratartigen Konvektion, welche die bevorzugte stabile Konvektionsform im BereichP ^1/3 darstellt.

     

Effect of Low Rotation Rate on Steady Convection During the Solidification of a Ternary Alloy

We consider the problem of steady convective flow during the directional solidification of a horizontal ternary alloy system rotating at a constant and low rate about a vertical axis. Under the limit of large far-field temperature, the flow region is modeled to be composed of two horizontal mushy layers, which are referred to here as a primary layer over a secondary layer. We first determine the basic state solution and then carry out linear stability analysis to calculate the neutral stability boundary and the critical conditions at the onset of motion. We find, in particular, that there are two flow solutions and each solution exhibits two neutral stability boundaries, and the flow can be multi-modal in the low rotating rate case with local minima on each neutral boundary. The critical Rayleigh number and the wave number as well as the vertical volume flux increase with the rotation rate, but the flow is found to be less stabilizing as compared to the binary alloy counterpart flow. The effects of low rotation rate increase the solid fraction and the liquid fraction at certain vertically oriented fluid lines, and the highest value of such increase is at a horizontal level close to the interface between the two mushy layers.     

On non-linear magneto convection in a mushy layer with joule heating

This paper studies the flow pattern of non-linear magneto convection that can be realized in a horizontal mushy layer and in the presence of joule heating, which is the amount of heat produced by the induced magnetic field. We consider the appropriate system of equations and the associated boundary conditions for the flow in the mushy layer subjected to a vertical magnetic field of uniform strength. Under certain assumptions and conditions, we determine the stable finite-amplitude solutions of the resulting system using a perturbation approach and stability analysis. We find, in particular, that for a wide range of values of the joule heating parameter and sufficiently small amplitude of the flow, the only stable convective flow is in the form of subcritical down-hexagons with down-flow at the cells' centers and up-flow at the cells' boundaries. This result is in sharp contrast to the case in the absence of joule heating where instead the subcritical up-hexagons with up-flow at the cells' centers and down-flow at the cells' boundaries can be stable. In the presence of joule heating the stable subcritical down-hexagons were found to be enhanced with increasing the strength of the externally imposed magnetic field.     

Numerical Investigation on Marginal Stability and Convection with and without Magnetic Field in a Mushy Layer

In this article, an investigation is conducted to analyze the marginal stability with and without magnetic field in a mushy layer. During alloy solidification, such mushy layer, which is adjacent to the solidification front and composed of solid dendrites and liquid, is known to produce vertical chimneys. Here, we carry out numerical investigation for particular range of parameter values, which cover those of available experimental studies, to determine the convective flow at the onset of motion. The governing coupled non-linear partial differential equations are non-dimensionalised and solved to get the steady basic-state solution. The thickness of the mushy layer is determined as a part of the solution. Using multiple shooting technique, we determine the steady-state solutions in a range of critical Rayleigh number. We analyse the effect of several parameters, Chandrasekhar number Q, and Robert’s number τ on the problem. It was found that an increase in Q has a stabilizing effect on solidification and the critical Rayleigh number increases on increasing Q. It was also found that for moderate or small values of Robert’s number τ the critical Rayleigh number is mostly insensitive.     

On Perturbation and Marginal Stability Analysis of Magneto-Convection in Active Mushy Layer

This present study considers the problem of steady magneto-convection in a horizontal mushy layer with variable permeability and an impermeable mush–liquid interface during directional solidification of binary alloys. We model the flow by introducing a uniform magnetic field in the mushy layer which is considered as a porous medium where Darcy’s law holds and the permeability is a function of the local solid volume fraction. Basic-state solutions are obtained analytically using the no-flow condition. With the help of multiple shooting techniques, we obtain numerical solutions to the linear perturbation system for non-magnetic and magnetic cases. Numerical results are presented showing the effects of the magnetic field and the permeability of the layer. These results demonstrate that the application of an external magnetic field has stabilizing effects on the convection and can reduce the tendency for chimney formation in the mushy layer. In addition, variable permeability, which corresponds to an active mushy layer, indicates more stable and realizable flow system as compared to the case of constant permeability.