Heterometallic hexanuclear isobutyrate clusters based on di- and tripodal alcohols

Four hexanuclear coordination clusters containing $\{{\mathrm{M}}_4^{\mathrm{II}}{\mathrm{M}}_2^{\mathrm{III}}\}$ cores of edge-sharing coordination octahedra exemplify how mixed-spin derivatives of a homonuclear parent structure, [${\mathrm{Mn}}_4^{\mathrm{II}}{\mathrm{Mn}}_2^{\mathrm{III}}{\mathrm{L}}_8$(N–O)₄], can be realized by a ligand ‘shrink-wrapping’ approach, resulting in [${\mathrm{Mn}}_2^{\mathrm{II}}{\mathrm{Co}}_2^{\mathrm{II}}{\mathrm{Mn}}_2^{\mathrm{III}}{\mathrm{L}}_8$(N–O)₄]- and [${\mathrm{Co}}_4^{\mathrm{II}}{\mathrm{Fe}}_2^{\mathrm{III}}{\mathrm{L}}_8$(N-O)₄]-type clusters (L = isobutyrate, N–O = methyldiethanolamine, n-butyldiethanolamine, or triethanolamine). The resulting core structures are either virtually isostructural to the parent structure or differ in the placement of the peripheral metal ions, depending on the mix of structure-directing carboxylate and alkoxyamine ligands with large, flexible alkyl chains. Whereas the $\{{\mathrm{Mn}}_4^{\mathrm{II}}{\mathrm{Mn}}_2^{\mathrm{III}}\}$ and {${\mathrm{Co}}_4^{\mathrm{II}}{\mathrm{Fe}}_2^{\mathrm{III}}$} complexes show dominant antiferromagnetic exchange, ferrimagnetic coupling features are exhibited by two {${\mathrm{Mn}}_2^{\mathrm{II}}{\mathrm{Co}}_2^{\mathrm{II}}{\mathrm{Mn}}_2^{\mathrm{III}}$} clusters.     

[Cr8(PhCO2)16O4]·4CH3CN·2H2O: structural origin of magnetic anisotropy in a molecular spin cluster

The Cr₄O₄ hetero‐cubane‐centered octachromium(III) cluster [Cr₈(PhCO₂)₁₆O₄] crystallizes from fluorobenzene–acetonitrile as dodeca‐μ₂‐benzoato‐tetrabenzoatotetra‐μ₄‐oxido‐octachromium(III) acetonitrile tetrasolvate dihydrate, [Cr₈(C₇H₅O₂)₁₆O₄]·4C₂H₃N·2H₂O, (I). Crystals produced by this method are significantly more stable than the originally published dichloromethane pentasolvate, [Cr₈(PhCO₂)₁₆O₄]·5CH₂Cl₂ [Atkinson et al. (1999). Chem. Commun. pp. 285–286], leading to a significantly higher quality structure and allowing the production of large quantities of high‐quality nondeuterated and deuterated material suitable for inelastic neutron scattering (INS) measurements. Compound (I) reveals a higher symmetry structure in which the cluster sits on a twofold rotation axis, and is based on an asymmetric unit containing four crystallographically independent Cr positions, two oxide ligands, eight benzoate ligands, two acetonitrile solvent molecules and one disordered water molecule. All the Cr atoms are six‐coordinate, with an octahedral geometry for the inner cubane and a more highly distorted coordination environment in the outer positions. Despite the higher symmetry, the coordination geometries observed in (I) are largely similar to the dichloromethane pentasolvate structure, indicating that crystal‐packing effects have little influence on the molecular structure of [Cr₈(PhCO₂)₁₆O₄]. Close structural analysis reveals that the high magnetic anisotropy observed in the INS measurements is a consequence of the distorted coordination geometry of the four outer Cr atoms.     

Reconstructing phase dynamics of oscillator networks

We generalize our recent approach to the reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from a multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. Partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling.     

Attractor of Smale - Williams type in an autonomous distributed system

We consider an autonomous system of partial differential equations for a one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases transformed from one stage of activity to another by the doubly expanding circle map. So, the attractor in the Poincaré section is uniformly hyperbolic, a kind of Smale - Williams solenoid. Finite-dimensional models are derived as ordinary differential equations for amplitudes of spatial Fourier modes (the 5D and 7D models). Correspondence of the reduced models to the original system is demonstrated numerically. Computational verification of the hyperbolicity criterion is performed for the reduced models: the distribution of angles of intersection for stable and unstable manifolds on the attractor is separated from zero, i.e., the touches are excluded. The example considered gives a partial justification for the old hopes that the chaotic behavior of autonomous distributed systems may be associated with uniformly hyperbolic attractors.     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.     

Study of the multilayer PCB CTEs by moiré interferometry

Microelectronics packaging has been developing rapidly due to the demands for faster, lighter and smaller products. Printed circuit boards (PCBs) provide mechanical support and electrical interconnection for electronic devices. Many types of composite PCBs have been developed to meet various needs. Recent trends in reliability analysis of PCBs have involved development of the structural integrity models for predicting lifetime under thermal environmental exposure; however the theoretical models need verification by the experiment.

The objective of the current work is the development of an optical system and testing procedure for evaluation of the thermal deformation of PCBs in the wide temperature range. Due to the special requirements of the specimen and test condition, the existing technologies and setups were updated and modified. The discussions on optical methods, thermal loading chambers, and image data processing are presented. The proposed technique and specially designed test bench were employed successfully to measure the thermal deformations of PCB in the −40°C to +160°C temperature range. The video-based moiré interferometry was used for generating, capturing and analysis of the fringe patterns. The obtained information yields the needed coefficients of thermal expansion (CTE) for tested PCBs.     

Direct Bioelectrocatalysis by NADP‐Reducing Hydrogenase from Pyrococcus furiosus

The direct bioelectrocatalysis by an NAD(P)‐reducing hydrogenase is reported for the first time. In contrast to previous attempts to involve similar enzymes in bioelectrocatalysis [1–4], which were in fact unsuccessful, in our report an effective electrocatalysis by Pyrococcus furiosus hydrogenase is convincingly shown by (i) achievement of the hydrogen equilibrium potential and (ii) a high current of hydrogen oxidation (0.3 mA cm^?2 at 100 mV overpotential and at 75 °C). The latter is just a few times lower compared to enzyme electrodes based on NAD(P)‐independent hydrogenases.