Space-resolved dynamics of a tracer in a disordered solid

The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test particle by extensive molecular dynamics simulations and characterize the spatio-temporal transport in terms of two-time correlation functions, including the time-dependent diffusion coefficient, the frequency-dependent conductivity, as well as the wavenumber-dependent intermediate scattering function. We rationalize our findings within the framework of critical phenomena and compare our data to a dynamic scaling theory.     

2H NMR calculations on polynuclear transition metal complexes: on the influence of local symmetry and other factors

It is now well-known that (2)H solid-state NMR techniques can bring a better understanding of the interaction of deuterium with metal atoms in organometallic mononuclear complexes, clusters or nanoparticles. In that context, we have recently obtained experimental quadrupolar coupling constants and asymmetry parameters characteristic of deuterium atoms involved in various bonding situations in ruthenium clusters, namely D(4)Ru(4)(CO)(12), D(2)Ru(6)(CO)(18) and other related compounds [Gutmann et al., J. Am. Chem. Soc., 2010, 132, 11759], which are model compounds for edge-bridging (μ-H) and face-capping (μ(3)-H) coordination types on ruthenium surfaces. The present work is in line with density functional theory (DFT) calculations of the electric field gradient (EFG) tensors in deuterated organometallic ruthenium complexes. The comparison of quadrupolar coupling constants shows an excellent agreement between calculated and observed values. This confirms that DFT is a method of choice for the analysis of deuterium NMR spectra. Such calculations are achieved on a large number of ruthenium clusters in order to obtain quadrupolar coupling constants characteristic of a given coordination type: terminal-D, η(2)-D(2), μ-D, μ(3)-D as well as μ(4)-D and μ(6)-D (i.e. interstitial deuterides). Given the dependence of such NMR parameters mainly on local symmetry, these results are expected to remain valid for large assemblies of ruthenium atoms, such as organometallic ruthenium nanoparticles.     

A reactive Si4 cage: K(SitBu3)3Si4

KR∗₃Si₄, 2, (R∗ = SitBu₃), formed by the reaction of R∗₄Si₄ with 2 KC₈, is an orange red solid stable at r.t. but decomposes in solution into R∗₄Si₄ and a compound that reacts with excess Me₃SiCl to form (Me₃Si)₄R∗₃ClSi₈. Compound 2 is very sensitive to air and moisture. Its alcoholysis does not stabilize the protonated species HR∗₃Si₄ and ends up in R∗₃Si₃H₃. Compound 2 reacts with 1/2 equivalent ICl to form a violet solid R∗₆Si₈. A 1:1 reaction of 2 with SiBr₄ runs differently to form ditetrahedranyl, R∗₃Si₄-Si₄R∗₃ which is stable at r.t. but transforms into its violet isomer R∗₆Si₈ at higher temperatures. Compound 2 crystallizes as R∗₃Si₄K(18-crown-6) and its crystal structure shows a Si₄-cage with a short Si-K linkage. It opens up at higher temperatures to acquire a unique structure in which a -CH₂-CH₂- group detaches itself from an ether to insert into Si-Si linkage of Si₄-unit to form a bicyclic ring. The residual chain (CH₂)₁₀O₆ closes itself on to a Si atom to form R∗₃Si₃(CH₂-CH₂)Si(C₁₀H₂₀O₆)K(18-C-6).     

Redox-active silica nanoparticles. Part 4. Synthesis, size distribution, and electrochemical adsorption behavior of ferrocene- and (diamine)(diphosphine)-ruthenium(II)-modified Stöber silica colloidal particles

Stöber silica nanoparticles with a diameter of approximately 800 nm are covalently modified by redox-active ferrocene or (diamine)(diphosphine) ruthenium(II) units attached to a spacer. The particles are characterized by NMR spectroscopic and chemical techniques. Two variants of modification by condensation are compared. Besides an estimation of the size and the particle porosity, the agglomeration behavior in solvents of different polarity is investigated. The adsorption of the particles to an electrode surface is followed.     

Note on Vector Translation with Respect to Thompson’s Metric

It is known that vector translations are contractive with respect to Thompson’s part metric. Here, we give a simple proof, based on a representation of Thompson’s metric through positive functionals. Moreover, we use contractivity of translations to prove a fixed point result for mappings that are Lipschitz continuous with respect to Thompson’s metric with Lipschitz constant r>1. The case r = 1 for order preserving or order reversing mappings has been recently studied by Lawson and Lim. We apply our result to a nonlinear boundary value problem.