Organotin derivatives of alpha-[XIIIW9O33]9- (X = As,Sb) heteropolytungstates. Solution- and solid-state characterization of [[C6H5Sn)2O]2H(alpha-AsW9O33)2]9- and [(C6H5Sn)3Na3(alpha-SbW9O33)2]6-

The tris(phenyltin)-substituted tungstoantimonate(III) Cs6[(PhSn)3Na3(alpha-SbW9O33)2].20H2O (1) and the tetrakis-(phenyltin)-substituted tungstoarsenate(III) Na9[[(PhSn)2O]2H(alpha-AsW9O33)2].20H2O (2) have been prepared by reaction of phenyltin trichloride with Na9[alpha-SbW9O33].19.5H2O and Na9[alpha-AsW9O33].19.5H2O, respectively, in aqueous solution. The products were characterized by elemental analysis, X-ray crystallography, multinuclear NMR, and infrared spectroscopy. Crystals of 1 are monoclinic, space group P2(1)/n, with a = 13.7952(1) A, b = 22.3133(2) A, c = 34.4493(2) A, beta = 90.933(1) degrees, and Z = 4. Anion 1 has nominal D3h symmetry and contains three PhSn3+ groups and three sodium ions sandwiched between [alpha-SbW9O33]9- units. Crystals of 2 are triclinic, space group P1, with a = 15.272(6) A, b = 15.303(6) A, c = 16.760(7) A, alpha = 93.59(3) degrees, beta = 106.187(19) degrees, gamma = 112.23(3) degrees, and Z = 1. Anion 2 has nominal C2h symmetry and contains four PhSn3+ groups sandwiched between two [alpha-AsW9O33]9- units.     

Diffusion in stochastic sandpiles

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity density, so that it represents an alternative definition of an order parameter. The critical behavior of the unrestricted sandpile is very similar to that of its restricted counterpart, including the fact that a data collapse of the order parameter as a function of the particle density is possible, but with a narrow scaling region. We also develop a series expansion, in inverse powers of the density, for the collective diffusion coefficient in a variant of the stochastic sandpile in which the toppling rate at a site with n particles is n(n-1), and compare the theoretical prediction with simulation results.     

Activated Random Walkers: Facts, Conjectures and Challenges

We study a particle system with hopping (random walk) dynamics on the integer lattice ? ^d . The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of particles; there is no limit on the number of particles at a given site. Isolated active particles fall asleep at rate λ>0, and then remain asleep until joined by another particle at the same site. The state in which all particles are inactive is absorbing. Whether activity continues at long times depends on the relation between the particle density ζ and the sleeping rate λ. We discuss the general case, and then, for the one-dimensional totally asymmetric case, study the phase transition between an active phase (for sufficiently large particle densities and/or small λ) and an absorbing one. We also present arguments regarding the asymptotic mean hopping velocity in the active phase, the rate of fixation in the absorbing phase, and survival of the infinite system at criticality. Using mean-field theory and Monte Carlo simulation, we locate the phase boundary. The phase transition appears to be continuous in both the symmetric and asymmetric versions of the process, but the critical behavior is very different. The former case is characterized by simple integer or rational values for critical exponents (β=1, for example), and the phase diagram is in accord with the prediction of mean-field theory. We present evidence that the symmetric version belongs to the universality class of conserved stochastic sandpiles, also known as conserved directed percolation. Simulations also reveal an interesting transient phenomenon of damped oscillations in the activity density.     

The 20-Tungsto-4-Tellurate(IV) [H2Te4W20O80]22− and the 15-Tungstotellurate(IV) [NaTeW15O54]13−

The 20-tungsto-4-tellurate(IV) polyanion [H₂Te₄W₂₀O₈₀]^22? (1) has been synthesized and isolated in the form of its hydrated sodium salt Na₂₂[H₂Te₄W₂₀O₈₀]·64H₂O (Na-1). Na-1 has been characterized in the solid state by FTIR and TGA. Single-crystal X-ray diffraction analysis revealed that Na-1 crystallizes in the triclinic space group P ${\bar 1}The 20-tungsto-4-tellurate(IV) polyanion [H₂Te₄W₂₀O₈₀]²²⁻ (1) has been synthesized and isolated in the form of its hydrated sodium salt Na₂₂[H₂Te₄W₂₀O₈₀]·64H₂O (Na-1). Na-1 has been characterized in the solid state by FTIR and TGA. Single-crystal X-ray diffraction analysis revealed that Na-1 crystallizes in the triclinic space group P , with a = 12.741(2) ?, b = 16.842(3) ?, c = 17.197(4) ?, α = 93.961(10)°, β = 107.466(8)°, γ = 108.548(8)°, V = 3281.5(11) ?³ and Z = 1. The polyanion 1 comprises two [HTe₂W₁₀O₄₀]¹¹⁻ fragments, connected through Te−O–W μ₂-oxo bridges, and each containing a pair of face-shared WO₆ octahedra. Furthermore, the 15-tungstotellurate(IV) polyanion [NaTeW₁₅O₅₄]¹³⁻ (2) was synthesized and crystallized as a sodium salt in the orthorhombic space group Pccn, with a = 11.8841(5) ?, b = 20.8934(11) ?, c = 31.801(2) ?, V = 7896.3(7) ?³ and Z = 4. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. Dedicated to Professor C. N. R. Rao on the occasion of his 75th birthday     

Synthesis and structure of asymmetric zirconium-substituted silicotungstates, [Zr6O2(OH)4(H2O)3(beta-SiW10O37)3]14- and [Zr4O2(OH)2(H2O)4(beta-SiW10O37)2]10-

The reaction of ZrCl4 with [gamma-SiW10O36]8- in a potassium acetate buffer results in two different products depending on the reactant ratios. The trimeric species [Zr6O2(OH)4(H2O)3(beta-SiW10O37)3]14- (1) consists of three beta23-SiW10O37 units linked by an unprecedented Zr6O2(OH)4(H2O)3 cluster with C1 point group symmetry. The dimeric species [Zr4O2(OH)2(H2O)4(beta-SiW10O37)2]10- (2) consists of beta22- and beta12-SiW10O37 units sandwiching a Zr4O2(OH)2(H2O)4 cluster, which also has C1 symmetry. Polyanion 1 contains more zirconium centers than any other polyoxometalate known to date.     

Structural characterization of mono-ruthenium substituted Keggin-type silicotungstates

We have synthesized the mono-ruthenium substituted Keggin-type silicotungstate [SiW(11)O(39)Ru(III)(H(2)O)](5-) (1a) by reaction of the mono-lacunary silicotungstate precursor [SiW(11)O(39)](8-) with Ru(acac)(3) under hydrothermal conditions and isolated as the caesium salt Cs(5)[SiW(11)O(39)Ru(III)(H(2)O)] (1). The DMSO-coordinated complex [SiW(11)O(39)Ru(III)(DMSO)](5-) (2a) was prepared by reaction of 1a with DMSO in aqueous solution at 353 K and isolated as the caesium-potassium mixed salt Cs(4.9)K(0.1)[SiW(11)O(39)Ru(III)(DMSO)] (2). Both compounds 1 and 2 were characterized by single-crystal X-ray structure analysis, powder X-ray structure analysis, UV-Vis spectroscopy, cyclic voltammetry, IR-spectroscopy and elemental analysis. 1 crystallized in the tetragonal space group P4(2)/ncm with a = 20.9299(4), c = 10.3603(4) Angstrom, Z = 4. The ruthenium atom in the Keggin unit could not be distinguished from the tungsten due to disorder. The structural analysis of 2 (monoclinic, P2(1)/c, a = 13.5850(4), b = 20.2764(7), c = 18.1326(4) Angstrom, beta = 90.8730(10) degrees , Z = 4) successfully revealed that the incorporated ruthenium atom is coordinated by DMSO through a Ru-S bond. Polyanion 2a represents the first mono-substituted Keggin ion in which the ruthenium center is not crystallographically disordered. UV-Vis spectroscopy combined with controlled potential electrolysis confirmed that the incorporated rutheniums in 1 and 2 have a valence state of +3. The IR spectra of both 1 and 2 were very similar. All these data indicate that 1 synthesized by reaction of the mono-lacunary silicotungstate K(8)[SiW(11)O(39)] with Ru(acac)(3) under hydrothermal conditions is truly the mono-ruthenium substituted Keggin-type silicotungstate.     

Reweighting in nonequilibrium simulations

A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier reweighting schemes, the present approach does not require knowledge of the stationary probability distribution, and so is applicable out of equilibrium. The method is applied to the contact process in two and three dimensions, yielding the critical parameter and spreading exponents to unprecedented precision.