Theory of chirality functions,generalized for molecules with chiral ligands

The theory of chirality functions described in a previous publication is generalized to allow for chiral ligands. In the earlier theory, all symmetry operations of the molecular frame could be thought of as permutations of the ligands among the sites; in the present work, improper rotations not only permute the ligands, but convert them into mirror images. The group that generates all isomers from a given ordered molecule belonging to a frame with n sites is now the hyperoctahedral group of order 2ⁿ n! consisting of all possible combinations of permutations and site reflections. The representation theory of these groups is described, and applied to the problem of constructing qualitatively complete chirality functions, and of deciding which ligand partitions, and which isomer mixtures, are chiral. It is found useful to classify chiral representations of the covering group as ligand specific and class specific. The ligand specific representations describe chiral properties which are common to all frames and arise purely from the chirality of the ligands, while the class specific representations describe the chiral properties of the frame. A number of examples are explicitly worked out.     

The robinson annulation of some medium ring size 2-hydroxymethylenecyclanones

The adducts formed from methyl vinyl ketone and the 2-hydromethylene derivatives of cyclooctane and cyclodecanone can be cyclised to spiroketones containing the same number of C atoms. The spiroketone from cyclooctanone possesses a single UV maximum at 227 nm; the cyclodecanone compound has a further absorption at ca 246 nm. The constitution and stereochemistry of the ketols produced from the adducts under mild cyclising conditions have been investigated.     

Sign changes in the prime number theorem

The Ramanujan Journal - Let V(T) denote the number of sign changes in $$\psi (x) - x$$ for $$x\in [1, T]$$ . We show that $$\liminf _{T\rightarrow \infty } V(T)/\log T\ge \gamma _{1}/\pi +...     

The entropy of small clusters of atoms using an Einstein model

We present a generalized Einstein model for calculating thermodynamic properties of small clusters of atoms and demonstrate its validity by comparing its predictions with Burton's exact calculations. The simplicity of the method enables one to easily compute thermodynamic quantities for many systems beyond those previously considered.     

Effect of trace amounts of water on organic solvent transport through gamma-alumina membranes with varying pore sizes

The transport behavior of toluene and n-hexane in gamma-alumina membranes with different pore diameters was studied. It was shown that the permeability of water-lean hexane and toluene is in agreement with Darcy's law down to membrane pore diameters of 3.5 nm. The presence of molar water fractions of 5-8 x 10(-4) in these solvents led to a permeability decrease of the gamma-alumina layer by a factor of 2-4 depending on pore size. In general, a lower permeability was found for hexane than for toluene. Moreover, in the presence of water a minimum applied pressure of 0.5-1.5 bar was required to induce net liquid flow through the membrane. These phenomena were interpreted in terms of capillary condensation of water in membrane pores with a size below a certain critical diameter. This is thought to lead to substantial blocking of these pores for transport, so that the effective tortuosity of the membrane for transport of hydrophobic solvents increases.     

Selective pervaporation of water through a nonselective microporous titania membrane by a dynamically induced molecular sieving mechanism

Pervaporation experiments were performed on microporous titania membranes using several binary liquids containing 2-20 wt % water. The membrane was nonselective in the separation of water from alcohols and p-dioxane but showed a remarkably high selectivity in the separation of water from ethylene glycol/water mixtures with < or =15 mol % water. The absence of selectivity under most conditions is explained by the large pore size (0.9 nm) of microporous titania. The high selectivity for water in the separation from ethylene glycol can be explained by the formation of a hydrogen-bonded network of ethylene glycol in the micropores, which blocks transport of ethylene glycol, while water can still permeate through. These networks are disrupted by water at higher concentrations, leading to full loss of membrane selectivity.     

1,3‐Dimethyl‐2‐oxo‐4,6‐diphenyl‐1,2,3,4‐tetrahydropyridine‐3‐carbonitrile

The crystal structure of the title compound, C₂₀H₁₈N₂O, reveals a distorted half‐chair conformation of the central tetra­hydro­pyridine (THP) ring, with the cyano‐ and adjacent phenyl‐substituted C atoms displaced by 0.329 (1) and ?0.315 (1) Å, respectively, from the THP best plane. Steric interactions force the phenyl rings out of the THP plane by 49.21 (9) and 65.76 (5)°. The cyano moiety is coplanar with the THP plane.     

Potassium carbonate,a support for the green synthesis of azoles and diazines

A novel potassium carbonate mediated synthesis of 2‐amino‐1,3‐thia/oxa zoles, 2‐amino‐1,3,4‐thia/oxa diazines and 2‐hydrazino‐1,3,4‐thiadiazines has been described here. The use of K₂CO₃ allows for an aqueous workup thereby eliminating the organic solvent from both the reaction step and post reaction stage, without compromising the yield and reaction time.     

Large‐scale extrusion processing and characterization of hybrid nylon‐6/SiO2 nanocomposites

Solution impregnations, pulltrusion and film stacking are widely used methods to prepare thermoplastic composite materials. Extruders are used to melt the polymer and to incorporate fibers into the polymer in order to modify physical properties. In this article, the compounding of colloidal silica nanoparticles filled polyamide‐6 (PA‐6) is achieved using a twin‐screw extruder, which has a significant market share due to its low cost and easy maintenance. The experiments were performed at 250 rpm and the bulk throughput was 6 kg h^?1 with a pump pressure of 30 bars. The composites were characterized with nuclear magnetic resonance (NMR), wide angle X‐ray diffraction (WAXD), differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). As determined by WAXD, the PA‐6 showed higher amounts of γ‐phase when compared to other synthesis methods such as in situ polymerization. TEM pictures showed that the silica particles aggregated nevertheless, upon addition of 14% (w/w) silica the E‐modulus increased from 2.7 to 3.9 GPa indicating that an effective mechanical coupling with the polymer was achieved. The behavior, illustrated with dynamic mechanical analysis (DMA) curves, indicated that in general when a filled system is compared to unfilled material, the values of the moduli (E′ and E″) increased and tan δ decreased. Determination of molecular mass distribution of the samples by means of size exclusion chromatography (SEC) coupled to a refractive index (RI), viscosity (DV) and light scattering (LS) detector revealed that the addition of silica did not decrease the average molecular weight of the polymer matrix, which is of importance for composite applications. Copyright © 2004 John Wiley & Sons, Ltd.