The Ru(II)-supported heptatungstates [HXW7O28Ru(dmso)3]6-(X=P, As)

The ruthenium(II)-supported heteropolyanions [HXW7O28Ru(dmso)3]6-(X=P, 1; As, 2) are composed of a Ru(dmso)3 group attached to an unprecedented heptatungstate fragment via two Ru-O-W bonds and one Ru-O-X bond, which represents a fundamentally novel mode of Ru-coordination to a polyoxoanion framework. Multinuclear 183W, 31P, 13C, and 1H NMR studies indicate high stability of 1 and 2 in solution.     

A rapid technique to determine the internal area function of finite-length ducts using maximum length sequence analysis

This paper describes a rapid technique for reconstruction of the internal area function of a duct using blockage-induced eigenvalue shifts determined from eigenfrequencies measured under two sets of duct termination boundary conditions. A single broad band maximum length sequence (MLS) measurement of short duration is utilized to obtain the transfer function of the duct, which in turn can be utilized to determine its eigenvalue shifts and subsequently its internal area function using an inverse perturbation technique. The reconstruction results display the same order of accuracy as those obtained previously using swept sine measurements of extended duration. An expression for the determination of the area function is presented utilizing resonant frequency information alone, thus rendering duct length determination unnecessary. A computational routine further simplifies the process such that the accuracy of the technique could be ascertained for a range of configurations including longer ducts and ducts that initially have nonuniform internal cross section over their length. Development of a relationship between obstacle length and wavelength of the lowest eigenfrequency required for successful reconstruction is also described. This is an important result for longer ducts where measurement of lower eigenfrequencies may present problems using standard measurement equipment.     

Noise-driven nonlinear sigma model

We present a noise-driven model for obtaining the gap and line-width as functions of the temperature in the nonlinear sigma model. The method is phenomenological and rests on the following physical idea: a classical external stochastic field is introduced representing the coupling of the sigma field with a noise source. Moreover, we assume that the inelastic scattering length is much longer than the elastic one, justifying the neglect of dissipation for temperatures such that the nonlinear sigma model is a good approximation for antiferromagnetic spin chains. This phenomenological approach is justified by comparison with other theoretical predictions and with experiment.     

A scaling theory of clusters in the lattice gas

It is proposed that the number ofp-particle,k-bond lattice gas cluster configurations is of the form exp{σpf(k/p)} in the limitp→t8. A simple modification permits application to finite clusters, with the consequence that asymptotically the cluster partition function is of the droplet form, i.e., Z _p =exp[kp{itμp^1?1/d }+O(ln p)]. The scaling function for two-dimensional lattices is determined numerically and is found to be qualitatively universal. The scaling theory is used to investigate the size dependence of the surface free energy. The surface tension of small clusters can significantly exceed its limiting value. For intermediate cluster sizes (～100 particles) there is a modest reduction in surface tension, in accord with Tolman's prediction and the results of recent Monte Carlo studies.     

Mixed-Valence 24-Vanadophosphate Decorated with Six RuII(dmso)3 Groups: [{RuII3(dmso)9PVV11VIVRuIIIO37(OH)3}2]8?

The mixed-valence 24-vanadophosphate (1) has been synthesized and characterized in the solid state by IR, magnetism, EPR, XPS, and elemental analysis. Single-crystal X-ray analysis was carried out on (Na-1), which crystallizes in the triclinic system, space group , with a = 17.168(3) ?, b = 18.1971(14) ?, c = 20.1422(13) ?, α = 114.753(3)°, β = 99.390(4)°, γ = 95.124(4)°, and Z = 2. Polyanion 1 has an unusual, open structure composed of 2 Ru^IIIO₆ octahedra, 2 V^IVO₆ octahedra, 14 V^VO₅ square-pyramids, 8 V^VO₄ tetrahedra, and 2 PO₄ tetrahedra which are all directly linked via edges and corners. The outer surface of 1 is decorated with six Ru^II(dmso)₃ groups. XPS studies on Na-1 confirm the presence of 2 Ru^III and 6 Ru^II as well as 22 V^V and 2 V^IV centers. Magnetic susceptibility data on Na-1 show that the V^IV–Ru^III pairs are coupled antiferromagnetically, with J ₁ = −13 K and J ₂ ∼ −3 K. We did not detect any peak in our EPR measurements on Na-1, thus supporting the conclusion that Na-1 is diamagnetic in its ground state. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. In Memoriam Prof. F. A. Cotton     

Two iron-containing tungstogermanates: [K(H2O)(beta-Fe2GeW10O37(OH))(gamma-GeW10O36)]12- and [{beta-Fe2GeW10O37(OH)2}2]12-

Interaction of the dilacunary polyanion precursor [gamma-GeW(10)O(36)](8-) with Fe(3+) ions in aqueous buffer medium (pH 4.8) results in the formation of two dimeric tungstogermanates depending on the reactant ratios. When using an Fe3+ to [gamma-GeW(10)O(36)](8-) ratio of 1:1, the asymmetric anion [K(H(2)O)(beta-Fe(2)GeW(10)O(37)(OH))(gamma-GeW(10)O(36))](12-) (1) is formed, whereas [{beta-Fe(2)GeW(10)O(37)(OH)2}2]12- (2) is formed when using a ratio of 2:1. Single-crystal X-ray analyses were carried out on Cs(3)K(9)[K(H(2)O)(beta-Fe(2)GeW(10)O(37)(OH))(gamma-GeW(10)O(36))].19H(2)O (CsK-1), which crystallizes in the triclinic system, space group P1, a = 11.4547(2), b = 19.9181(5), c = 21.0781(6) A, alpha = 66.7977(12), beta = 89.1061(12), gamma = 84.4457(11) degrees, and Z = 2 and on Cs(7)K(4)Na[{beta-Fe(2)GeW(10)O(37)(OH)(2)}(2)].39H(2)O (CsKNa-2), which crystallizes in the monoclinic system, space group C2/m, a = 32.7569(13), b = 12.2631(5), c = 14.2895(5) A, beta = 104.135(2) degrees , and Z = 2. Polyanion 1 consists of (beta-Fe(2)GeW(10)O(37)) and (gamma-GeW(10)O(36)) units linked via two Fe-O-W bridges and a central potassium ion. Two equivalent FeO(6) octahedra complete the belt of the beta-Keggin unit and link to the (gamma-GeW(10)O(36)) fragment. On the other hand, 2 consists of two {beta-Fe(2)GeW(10)O(37)(OH)(2)} units with four bridging hydroxo groups linking the four Fe(3+) ions, forming an eight-membered ring. The magnetic properties of CsK-1 and CsKNa-2 have been studied by magnetic susceptibility and magnetization measurements and fitted according to an isotropic exchange model. Both polyanions 1 and 2 exhibit diamagnetic ground states with a small amount of paramagnetic impurity. Electrochemistry studies on 1 and 2 were carried out in a pH 5 acetate medium. The two polyanions have in common the simultaneous reduction of all of their Fe(3+) centers. This observation suggests the existence of identical or almost-identical influences on these centers and their equivalence, especially in the reduced state. Controlled potential coulometry results indicate the presence of two Fe(3+) centers in 1 and four in 2. The splitting of the tungsten wave of 1 compared to the single tungsten wave of 2 is attributed to a difference in acid-base properties of the polyanions. Voltammetric peak-potential shifts as a function of pH were studied in the case of 2.