Dielectric Properties of 2,3-Dicyano-4-pentyloxyphenyl 4′-pentyloxybenzoate (DPP) Mixtures with Non-polar Liquid Crystals (LC)

The static dielectric properties of four binary mixtures of DPP and non-polar LC were investigated. For each system the effective dielectric anisotropy of DPP was calculated by means of linear extrapolation. The essential influence of the polarizability of non-polar LC molecule on the effective value of DPP dielectric anisotropy was shown. The influence of non-polar LC matrix on the effective value of the dielectric permittivity of DPP is discussed.     

Merging and splitting in cooperative games: some (im)possibility results

Allocation rules for cooperative games can be manipulated by coalitions merging into single players, or, conversely, players splitting into a number of smaller units. This paper collects some (im)possibility results on merging- and splitting-proofness of (core) allocation rules for cooperative games with side-payments.     

Intermolecular exchange-induction energies without overlap expansion

An approach to evaluate the second-order exchange-induction energies of symmetry-adapted intermolecular perturbation theory (SAPT) for single-determinant ground-state monomer wavefunctions has been derived. This approach is correct to all orders of the intermonomer overlap, that is, it takes multiple electron exchange between the monomers into account. The resulting formulae can be written in a compact way and implemented efficiently. Here, the method is employed to investigate the performance of the S ²- or single-exchange approximation at the Hartree-Fock-SAPT level. The list of test systems comprises the prototypical van der Waals- and hydrogen-bridge complexes Ne₂, Ar–HF, and (H₂O)₂, but also the systems HeCl^?, NeNa⁺ and Li⁺F^? involving closed-shell ions. It was found that the errors introduced by the S ²-approximation are more pronounced for the second-order exchange-induction energy than for the first-order exchange energy. While these errors tend to be negligible throughout the well region of complexes such as the neon dimer, they start to be significant in the repulsive part of the well regions of systems such as the water dimer, and in particular for the ionic lithium fluoride molecule. The consequences of these findings for the Hartree-Fock level estimate of higher-order induction plus exchange-induction energies, which is frequently employed in SAPT are also discussed.     

‘New mathematics’ and teaching

Inside the scientific world it is not always understood that the mood of mathematics, which is a product and a part of culture, can change with time. This is partly why many have been surprised by the coming of the so‐called new mathematics.

In the truly creative mathematical mind two opposite tendencies coexist: the logical and the imaginative. Apparently it seems that new mathematics can be reduced to a purely logical machinery. In fact it contains as much imaginative contributions as classical mathematics. But it is difficult to show simultaneously the logical sequence of propositions and the clumsy progression of research itself. Mathematical exposition does not always follow the ‘ most natural slopes’ of the mind. Unfamiliar presentations often give an impression of ‘ abstraction ‘, more familiar ones an impression of concreteness ‘.

So it appears that difficulties with new mathematics are mostly of psychological origin. Misuses of it can easily raise up intolerance reactions and emotional blocks. Perhaps insisting upon the fact that, here as elsewhere, it is important to be able to guess, to realize that intuition and imagination are essential, could help to make new mathematics better understood, more useful and more able to be considered as a unifing element among sciences.     

Thermal transformation of polyacrylonitrile deposited on SBA-15 type silica

Thermogravimetry, diffuse reflectance infrared Fourier transform spectroscopy, and X-ray photoelectron spectroscopy (XPS) were used for the studying of thermally induced structural changes of polyacrylonitrile (PAN) deposited on the surface of SBA-15 type mesoporous silica. Polymer was introduced onto the support by the precipitation polymerization of acrylonitrile in aqueous suspension of SBA-15. Low temperature transformation (to 723?K) of the deposited PAN was analyzed. It was found that at about 523?K, exothermic cyclization of polymer chains to the so-called ladder form of PAN occurred. However, the total cyclization of PAN required higher carbonization temperatures, at which gradual dehydrogenation followed by graphitization was initiated. XPS revealed that the cyclic form of PAN and a relatively large amount of carbonyl species, formed during the carbonization of the PAN/SBA-15 composite at 623?K, were responsible for the high sorption capacity in the methyl?Cethyl ketone (MEK) vapor elimination. The efficiency in the MEK adsorption was also influenced by the content of PAN-derived carbon deposited on the SBA-15 surface.