Speciation of Copper(II)-Betaine Complexes as Starting Point for Electrochemical Copper Deposition from Ionic Liquids

The application of ionic liquids for the dissolution of metal oxides is a promising field for the development of more energy- and resource-efficient metallurgical processes. Using such solutions for the production of valuable chemicals or electrochemical metal deposition requires a detailed understanding of the chemical system and the factors influencing it. In the present work, several compounds are reported that crystallize after the dissolution of copper(II) oxide in the ionic liquid [Hbet][NTf₂]. Dependent on the initial amount of chloride, the reaction temperature and the purity of the reagent, copper crystallizes in complexes with varying coordination geometries and ligands. Subsequently, the influence of these different complex species on electrochemical properties is shown. For the first time, copper is deposited from the ionic liquid [Hbet][NTf₂], giving promising opportunities for more resource-efficient copper plating. The copper coatings were analyzed by SEM and EDX measurements. Furthermore, a mechanism for the decomposition of [Hbet][NTf₂] in the presence of chloride is suggested and supported by experimental evidence.     

Synthesis and Optoelectronic Properties of a Quinoxalino-Phenanthrophenazine (QPP) Extended Tribenzotriquinacene (TBTQ)

A six-step synthesis towards a tribenzotriquinacene (TBTQ) bearing three quinoxalinophenanthrophenazine (QPP) units is presented. The optoelectronic properties are investigated and the effect of the three-dimensional arrangement of the individual QPP planes is examined using optical spectroscopy, electrochemical analysis and quantum-chemical calculations.     

Inhomogeneous ‘longitudinal’ plane waves in a deformed elastic material

By definition, a homogeneous isotropic compressible Hadamard material has the property that an infinitesimal longitudinal homogeneous plane wave may propagate in every direction when the material is maintained in a state of arbitrary finite static homogeneous deformation. Here, as regards the wave, homogeneous means that the direction of propagation of the wave is parallel to the direction of eventual attenuation; and longitudinal means that the wave is linearly polarized in a direction parallel to the direction of propagation. In other words, the displacement is of the form u = ncos k(n · x – ct), where n is a real vector. It is seen that the Hadamard material is the most general one for which a longitudinal inhomogeneous plane wave may also propagate in any direction of a predeformed body. Here, inhomogeneous means that the wave is attenuated, in a direction distinct from the direction of propagation; and longitudinal means that the wave is elliptically polarized in the plane containing these two directions, and that the ellipse of polarization is similar and similarly situated to the ellipse for which the real and imaginary parts of the complex wave vector are conjugate semi-diameters. In other words, the displacement is of the form u = {S exp i(S · x – ct)}, where S is a complex vector (or bivector). Then a Generalized Hadamard material is introduced. It is the most general homogeneous isotropic compressible material which allows the propagation of infinitesimal longitudinal inhomogeneous plane circularly polarized waves for all choices of the isotropic directional bivector. Finally, the most general forms of response functions are found for homogeneously deformed isotropic elastic materials in which longitudinal inhomogeneous plane waves may propagate with a circular polarization in each of the two planes of central circular section of the ⁿ -ellipsoid, where is the left Cauchy-Green strain tensor corresponding to the primary pure homogeneous deformation.     

A Method for Determining Model‐Structure Errors and for Locating Damage in Vibrating Systems

A method is proposed for the determination of natural frequencies and mode shapes of a system which is constrained so that unknown stiffnesses are replaced by rigid connections. The constraint is not imposed physically but only in mathematics so that the behaviour of the constrained system is inferred from the unconstrained measurements. Since stiffnesses which are made rigid cannot experience any elastic strain they can have no effect on the inferred measurements. A procedure for comparing the inferred measurements with similarly constrained finite element predictions can be used to determine modelstructure errors. Damage, such as a crack in a beam, can be located by comparing the inferred measurements from the structure in its undamaged and current states. It is demonstrated how unmeasured rotations may be constrained by using rigidbody modes and a reduction/expansion transformation from a finite element model.Sommario. Viene proposto un metodo per la determinazione delle frequenze proprie e dei modi di vibrazione di un sistema vincolato in modo tale che alcuni elementi elastici siano sostituiti da collegamenti rigidi. Il vincolo non viene imposto fisicamente, ma solo matematicamente, e pertanto il comportamento del sistema vincolato viene dedotto dalle misure sul sistema non vincolato. Poiché gli elementi che sono resi rigidi non possono subire alcuna deformazione elastica, essi non hanno certamente alcun effetto sulle misure dedotte per il sistema vincolato. Una procedura che mette a confronto le misure dedotte per il sistema vincolato con le previsioni fornite da un modello ad elementi finiti con analoghi vincoli, può essere utilizzata per determinare errori nella struttura del modello. Danni del tipo di una cricca su una trave possono essere localizzati confrontando le misure dedotte – per sistemi analogamente vincolati – da quelle effettuate sulla struttura non danneggiata e sulla struttura danneggiata. Si dimostra come si possono imporre vincoli sulle rotazioni (non misurate) utilizzando i modi di corpo rigido dell'elemento e una tecnica di riduzione/espansione dei gradi di libertà di un modello ad elementi finiti.     

On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure

We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result of Zhou [28].     

Determination of stress levels for dynamic fracture of oil shale

The dynamic tensile-stress amplitudes necessary to cause complete spall in unconfined oil-shale samples were experimentally determined in the laboratory for pulse durations typically encountered in the field (60–100 μs). Tensile stresses were generated by free-surface reflection of compressive pulses, and the stress-time history at the free surface was obtained by numerically differentiating the displacement-time history monitored by a fiber-optic proximity sensor. A computer code was written to display the stress profile, obtained experimentally, over the length of the specimen as time increased. In this manner, the amplitude of the resultant stress wave (incident plus reflected) was determined at the measured spall plane. By using many specimens, the fracture thresholds for these pulse durations were determined. Spall thresholds for competent shale of 25-gal/ton yield were found to be approximately 1800 psi (12.4 MPa) for pulses propagating normal to the bedding plane, and nearly 5,000 psi (34.5 MPa) for pulses propagating parallel to the bedding plane. For shale of 34 gal/ton yield, the spall-threshold levels were found to be 1200 psi (8.3 MPa) and 2700 psi (18.6 MPa) for pulses propagating normal and parallel, respectively, to the bedding plane.     

Asymptotic behavior of Toeplitz matrices and determinants

We consider the inverse X _N and determinant D_N(c) of an N×N Toeplitz matrix C_N=[c_i?j] ₀ ^N?1 as N ar∞. Under the condition that there exists a monotonic decreasing summable bound b _n ≧|c _n |+|c _?n |, and that the generating function \(c(\theta ) = \sum\limits_{n = - \infty }^\infty {c_n e^{i{\text{ }}n{\text{ }}\theta } }\) does not vanish, we construct a matrix iterative process which yields (i) explicit asymptotic formulae for the elements of X_N when v(c) = (2π)^?1 [arg{c(2π)}?arg{c(0)}] is zero. Thence we obtain (ii) expressions for the constants, and bounds on the remainder, in the asymptotic formula $$\ln D_N (c) = N{\text{ }}k_0 (c) + E_0 (c) + E_{1,N} (c) + \mathcal{R}_N (c),$$ and (iii) the extension of this formula to the case of general integral v(c). Under certain further conditions the monotonicity of E_1,N+?_N is proved. We discuss various identities for D_N which apply when c(θ) is a rational function of e^iθ and mention a conjecture for D _N when c(θ) has zeros, and is discontinuous with arbitrary v(c).     

A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations

A minimal two degree of freedom model is used to clarify from an intuitive perspective the physical mechanisms underlying the mode-coupling instability of self-excited friction induced oscillations. It is shown that simultaneous out-of-phase oscillations of friction force and displacement tangential to the friction force may lead to energy transfer from the frictional system to vibrational energy. Also it is shown that the friction force acts like a cross-coupling force linking motion normal to the contact surface to motion parallel to it and that a necessary condition for the onset of instability is that these friction-induced cross-coupling forces balance the corresponding structural cross-coupling forces of the system. Finally the origin and the role of phase shifts between oscillations normal and parallel to the contact surface is clarified with respect to the mode-coupling instability. It may be expected that the intuitive picture gained will be of considerable help for practical design purposes.