When is a symmetric pin-jointed framework isostatic?

Maxwell’s rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.     

Comparison of the pharmacokinetics and phototoxicity of protoporphyrin IX metabolized from 5-aminolevulinic acid and two derivatives in human skin in vivo

Our novel approach was to compare the pharmacokinetics of 5-aminolevulinic acid (ALA), ALA-n-butyl and ALA-n-hexylester induced protoporphyrin IX (PpIX), together with the phototoxicity after photodynamic therapy (PDT) in human skin in vivo, using iontophoresis as a dose-control system. A series of four increasing doses of each compound was iontophoresed into healthy skin of 10 volunteers. The kinetics of PpIX metabolism (n = 4) and the response to PDT (n = 6) performed 5 h after iontophoresis, were assessed by surface PpIX fluorescence and post-irradiation erythema. Whilst ALA-induced PpIX peaked at 7.5 h, highest PpIX fluorescence induced by ALA-n-hexylester was observed at 3-6 h and no clear peak was seen with ALA-n-butylester. With ALA-n-hexylester, more PpIX was formed after 3 (P < 0.05) and 4.5 h, than with ALA or ALA-n-butylester. All compounds showed a linear correlation between logarithm of dose and PpIX fluorescence/phototoxicity at 5 h, with R-values ranging from 0.87 to 1. In addition, the ALA-n-hexylester showed the tendency to cause greater erythema than ALA and ALA-n-butylester. Fluorescence microscopy (n = 2) showed similar PpIX distributions and penetration depths for the three drugs, although both ALA esters led to a more homogeneous PpIX localization. Hence, ALA-n-hexylester appears to have slightly more favorable characteristics for PDT than ALA or ALA-n-butylester.     

Oxidation state and local environment of selenium in alkali borosilicate glasses for radioactive waste immobilisation

The oxidation state and local environment of selenium in alkali borosilicate glasses for high level radioactive waste (HLW) immobilisation were studied by Se K-edge XANES and EXAFS spectroscopy. An inactive surrogate of the UK's “MW” HLW-loaded glass and two waste-free glasses were investigated. Results confirm that the predominant Se oxidation state in all air-melted glasses is Se⁴⁺. Low levels (< 10% each of Se⁰ and Se⁶⁺) were also detected in the simulated HLW-loaded glass. The presence of Se⁶⁺ is consistent with moderately oxidising melting conditions arising from decomposition of nitrates in the waste. Results also suggest small but measurable Fe-Se redox interactions. Imposed atmospheres of air, N₂, or H₂ during melting resulted in increasingly reduced average Se valence as expected. Linear combination XANES fitting to quantify the relative abundances of these species was restricted by the limited availability of appropriate XANES standards for reduced Se species. EXAFS of all air-melted glasses provided robust fits indicating Se-O bond lengths of 1.71 ± 0.1 Å and CN = 3 ± 0.3, consistent with Se⁴⁺ being present in SeO₃²⁻ selenite groups. Therefore, ⁷⁹Se in UK alkali borosilicate HLW glasses is expected to occur predominantly as Se⁴⁺ in SeO₃²⁻ selenite groups.     

Characterization of a Palladium Dihydrogen Complex

The preparation and isolation of the first palladium dihydrogen complex is described. NMR spectroscopy reveals a very short H? H bond length, but the hydrogen molecule is activated toward heterolytic cleavage. An X‐ray crystal structure suggests that proton transfer to the ^tBuPCP (κ³‐2,6‐(^tBu₂PCH₂)₂C₆H₃) pincer ligand is possible. The basicity of the ipso‐carbon atom of the pincer ligand was investigated in a related complex.     

The effect of micro-CN linkage isomerism and ancillary ligand set on directional metal-metal charge-transfer in cyanide-bridged dimanganese complexes

The reaction of [Mn(CN)L'(NO)(eta(5)-C(5)R(4)Me)] with cis- or trans-[MnBrL(CO)(2)(dppm)], in the presence of Tl[PF(6)], gives homobinuclear cyanomanganese(i) complexes cis- or trans-[(dppm)(CO)(2)LMn(micro-NC)MnL'(NO)(eta(5)-C(5)R(4)Me)](+), linkage isomers of which, cis- or trans-[(dppm)(CO)(2)LMn(micro-CN)MnL'(NO)(eta(5)-C(5)R(4)Me)](+), are synthesised by reacting cis- or trans-[Mn(CN)L(CO)(2)(dppm)] with [MnIL'(NO)(eta(5)-C(5)R(4)Me)] in the presence of Tl[PF(6)]. X-Ray structural studies on the isomers trans-[(dppm)(CO)(2){(EtO)(3)P}Mn(micro-NC)Mn(CNBu(t))(NO)(eta(5)-C(5)H(4)Me)](+) and trans-[(dppm)(CO)(2){(EtO)(3)P}Mn(micro-CN)Mn(CNBu(t))(NO)(eta(5)-C(5)H(4)Me)](+) show nearly identical molecular structures whereas cis-[(dppm)(CO)(2){(PhO)(3)P}Mn(micro-NC)Mn{P(OPh)(3)}(NO)(eta(5)-C(5)H(4)Me)](+) and cis-[(dppm)(CO)(2){(PhO)(3)P}Mn(micro-CN)Mn{P(OPh)(3)}(NO)(eta(5)-C(5)H(4)Me)](+) differ, effectively in the N- and C-coordination respectively of two different optical isomers of the pseudo-tetrahedral units (NC)Mn{P(OPh)(3)}(NO)(eta(5)-C(5)H(4)Me) and (CN)Mn{P(OPh)(3)}(NO)(eta(5)-C(5)H(4)Me) to the octahedral manganese centre. Electrochemical and spectroscopic studies on [(dppm)(CO)(2)LMn(micro-XY)MnL'(NO)(eta(5)-C(5)R(4)Me)](+) show that systematic variation of the ligands L and L', of the cyclopentadienyl ring substituents R, and of the micro-CN orientation (XY = CN or NC) allows control of the order of oxidation of the two metal centres and hence the direction and energy of metal-metal charge-transfer (MMCT) through the cyanide bridge in the mixed-valence dications. Chemical one-electron oxidation of cis- or trans-[(dppm)(CO)(2)LMn(micro-NC)MnL'(NO)(eta(5)-C(5)R(4)Me)](+) with [NO][PF(6)] gives the mixed-valence dications trans-[(dppm)(CO)(2)LMn(II)(micro-NC)Mn(I)L'(NO)(eta(5)-C(5)R(4)Me)](2+) which show solvatochromic absorptions in the electronic spectrum, assigned to optically induced Mn(I)-to-Mn(II) electron transfer via the cyanide bridge.     

Vortex lattice transitions in YNi2B2C

We have performed extensive small-angle neutron scattering (SANS) diffraction studies of the vortex lattice in single crystal YNi₂B₂C for B‖c. High-resolution SANS, combined with a field-oscillation vortex lattice preparation technique, allows us to separate Bragg scattered intensities from two orthogonal domains and accurately determine the unit cell angle, β. The data suggest that upon increasing field there is a finite transition width where both low- and high-field distorted hexagonal vortex lattice phases, mutually rotated by 45°, coexist. The smooth variation of diffracted intensity from each phase through the transition corresponds to a redistribution of populations between the two types of domains.     

Dynamic model of slow light in a tensile-strained semiconductor optical amplifier

The slow light effect in semiconductor optical amplifiers has many potential applications in microwave photonics such as phase shifting and filtering. Models are needed to predict the slow light effect in SOAs and its dependence on the bias current, wavelength, and power and modulation index. In this paper we predict the slow light characteristics of a tensile-strained SOA by using a detailed time-domain model. The model includes full band-structure based calculations of the material gain, bimolecular recombination and spontaneous emission, a detailed carrier density rate equation and travelling-wave equations for the amplitude modulated signal and amplified spontaneous emission. The slow light parameters of interest include the beat signal phase shift and amplitude response. The model predictions show good agreement with experimental trends reported in the literature.