The energy-momentum tensor near a black hole

The energy-momentum tensor for a conformally invariant scalar field near a Schwarzschild black hole in thermal equilibrium with radiation is found by a combination of analytical and numerical techniques. Calculations are performed in the Euclidean section of the spacetime, and divergences isolated using the heat kernel expansion. It is found that the results agree well with those of Candelas [1], but that there are significant differences from the Gaussian approximation of Page [2].     

Some aspects of discreteness-of-charge and ion-size effects for ions adsorbed at charged metal/aqueous electrolyte interfaces

It is argued that the self-image potential of an ion adsorbed on a charged metal from an aqueous electrolyte is described in terms of multiple imaging and not single imaging in the metal as proposed by Bockris. The image potential of an isolated ion situated on the i.H.p. in the inner region with a continuously and smoothly varying dielectric profile is calculated. This is compared with the corresponding potential for an inner region model with a discontinuous dielectric profile. It is shown that when the position of the i.H.p. relative to the o.H.p. is changed, the two potentials will in general cross each other such that the discontinuous model has the more negative self-image potential when the i.H.p. approaches the o.H.p. The scaled-particle expression for the entropic contribution due to ion-size effects in the adsorption isotherm of an ion in the inner region is compared with the corresponding Flory-Huggins formula. It is demonstrated that the two theories can give very different results. In particular, when the adsorbed ions are considerably larger than the solvent molecules, it is possible that scaled-particle theory leads to a ‘negative’ ion-size entropy term, which decreases with increase in density of adsorbed ion.     

A surprising steric effect on a tandem cycloaddition/ring-opening reaction: rapid syntheses of difluorinated analogues of (hydroxymethyl)conduritols

Difluorinated analogues of (hydroxymethyl)conduritols can be synthesised from selected furans and a difluorinated dienophile in two reaction steps.     

Synthesis of 4,4-difluoroglycosides using ring-closing metathesis

4-Deoxy-4,4-difluoro-glycosides have been synthesised for the first time via a direct sequence involving ring-closing metathesis and indium-mediated difluoroallylation with 1-bromo-1,1-difluoropropene in water. Two protecting group strategies were explored, one to allow protection of the primary C-6 hydroxyl group throughout the sequence, while the second was intended to allow deprotection after RCM and before dihydroxylation. The benzyl ether could be used in the first role, and pivaloyl is effective in the second. Dihydroxylations were highly stereoselective and controlled by the orientation of the glycosidic C-O bond.     

Highly-functionalised difluorinated (hydroxymethyl)conduritol analogues via the Diels-Alder reactions of a difluorinated dienophile

A difluorodienophile, synthesised using a Stille coupling reaction underwent tin(iv)-catalysed cycloaddition with three furans to afford oxa[2.2.1]bicycloheptenes in good yield. Reduction of ester and carbamate carbonyl groups and diol protection as the acetonide set the stage for palladium-catalysed hydrostannylation in two cases. Treatment of the stannanes with methyllithium triggered ring-opening to afford highly-functionalised difluorinated cyclohexenols which could be deprotected to afford (hydroxymethyl)conduritol analogues.     

A potentially divergent and rapid route to analogues of deoxycyclitols, pentopyranoses, 6-deoxyhexoses, and hexoses

Direct precursors to analogues of pentopyranoses, 6-deoxyhexoses, and hexoses, in which a CF(2) center replaces the pyranose oxygen, have been synthesized rapidly from trifluoroethanol. A simple scaleable allylation reaction delivers ethers which undergo dehydrofluorination/metalation, followed by addition to either acrolein or cinnamaldehyde, to afford allylic alcohols. Fluorine-assisted [3,3]-rearrangement followed by reduction with sodium borohydride delivers diols, which undergo RCM smoothly to afford cyclohexene diols.     

Scattering from a partially fluid-filled, elastic-shelled sphere

In this article a sphere is taken to be partially filled with fluid so that its interior is part fluid and part air. A set of basis of functions, based upon an origin at the fluid/air interface, is used for the interior and a set of basis functions based upon the center of the sphere is used for the shell and exterior of the sphere. These sets of basis functions are coupled at the shell/interior interface and the resulting coupled system of equations solved to yield the scattered field. Numerical computations using this approach are presented for varying amounts of fluid-fill and for varying incident plane waves.     

Structures of three molybdenum(0)–tetracarbonyl–Schiff base compounds

The structures of three molybdenum(0)–tetracarbonyl–Schiff base compounds, determined by X-ray diffraction techniques, are reported. The Schiff bases are those derived from 2-acetylpyridine and 4-methoxyaniline, 4-trifluoromethoxyaniline, or 3-fluoro-4-methylaniline. The structure of the Schiff base ligand has also been determined for the ligand derived from 4-trifluoromethoxyaniline. Comparisons are made between metal–nitrogen bond distances, and carbon–nitrogen and carbon–carbon bond distances in the chelate rings, for these and a number of related molybdenum(0)–tetracarbonyl-diimine compounds. Comparisons are also made between ligand geometry in the free and coordinated states.