Stöber silica particles as basis for redox modifications: particle shape, size, polydispersity, and porosity

The synthesis of Stöber silica particles as basis for redox modifications is optimized for desired properties, in particular diameter in a wide sub-micrometer range, spherical shape, monodispersity, the absence of porosity, and aggregation free isolability for characterization and later covalent modification. The materials are characterized by SEM, DLS, nitrogen sorption isotherms, helium as well as Gay-Lussac (water) pycnometry, and DRIFT spectroscopy. Particles with diameters between approximately 50 and 800 nm are obtained by varying the concentrations of the reagents and reactants, the type of solvent as well as the temperature. The use of high water concentrations and post-synthetic calcination at 600 °C results in silica particles that can be considered as nonporous with respect to the size of the active molecules to be immobilized. The effect of reaction temperature on size distribution is identified. Low polydispersity is achieved by performing the reaction in a temperature range in which a change in temperature has only a weak or no effect on the final particle diameter. Upon optimization of the sol–gel process, the shape of the particles is still spherical. The agreement between experimental and geometric data is within the expected precision of the characterization techniques.     

EFFECT OF SURFACE ENERGY ON DISLOCATION-INDUCED FIELD IN HALF-SPACE WITH APPLICATION TO THIN FILM-SUBSTRATE SYSTEMS

In this work the elastic field of an edge dislocation in a half-space with the effect of surface energy has been obtained. The elastic field is then used to study the image force on the dislocation, the critical thickness for dislocation generation in epitaxial thin films with strain mismatch and the yielding strength of thin films on substrates. The results show that the image forces on the dislocation deviate from the conventional solutions when the distance of the dislocation from the free surface is smaller than several times of the characteristic length. Also due to the effect of surface energy, the critical thickness for dislocation generation is smaller than that predicted by the conventional elastic solutions and the extent of the deviation depends on the magnitude of mismatch strain. In contrast, the effect of surface energy on the yielding strength for many practical thin films can be neglected except for some soft ones where the characteristic length is comparable to the thickness.     

Symmetry and Resonance in Periodic FPU Chains

The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This “Birkhoff–Gustavson normal form” retains the symmetries of the original system and we show that in most cases this allows us to view the periodic FPU Hamiltonian as a perturbation of a nondegenerate Liouville integrable Hamiltonian. According to the KAM theorem this proves the existence of many invariant tori on which motion is quasiperiodic. Experiments confirm this qualitative behaviour. We note that one can not expect this in lower-order resonant Hamiltonian systems. So the periodic FPU chain is an exception and its special features are caused by a combination of special resonances and symmetries. Received: 25 July 2000 / Accepted: 20 December 2000     

Application of the R-functions method to the solution of elliptic PDEs (Poster Presentation)

In the current work, the basics of the theory of R-functions have been presented. Applications of this theory were shown on two model problems – Poisson equation and biharmonic equation – in complex two-dimensional domains both with homogeneous Dirichlet boundary conditions. The solution is performed in conjunction with the Bubnov-Galerkin method. As the basis for approximation tensor products of monomials were taken. The convergence study includes the comparison of current results with the standard finite element solution and the dependence of the number of coordinate functions on the relative error in the maximum-norm. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inverse error propagation and model identification for coupled dynamic problems with application to electromagnetic metal forming

The purpose of this work is the development and application of strategies to identify material model parameters for metals at high strain-rates using data obtained from high-speed electromagnetic metal forming. To this end, a staggered algorithm for the finite-element-based numerical solution of the coupled electromagnetic-mechanical boundary-value problem has been developed based on mixed Eulerian–Lagrangian multigrid methods. On this basis, the parameter determination together with a sensitivity analysis and error estimation are carried out. After verifying the validity of this approach using synthetic data sets, it is applied to the identification of material parameters using experimental results from electromagnetic tube forming.     

Characterization of municipal solid waste incineration (MSWI) bottom ash by scanning electron microscopy and quantitative energy dispersive X-ray microanalysis (SEM/EDX)

Scanning electron microscopy (SEM) with energy-dispersive X-ray microanalysis (EDX) is frequently used for morphological and qualitative chemical characterization of different materials. The applicability of this method for phase identification, is, however, often underestimated. The application of SEM/EDX for the characterization of different phases in fresh and altered municipal-waste incinerator bottom-ash samples with high lateral resolution is presented. Polished thin sections were prepared from the samples, but fresh fracture surfaces were also used. The EDX analyses were performed by using the correction procedures of a conventional standardless ZAF correction, a peak-to-background ZAF correction, and a correction method for light-element analysis. Because of their highly reactive properties the bottom-ash SEM samples require a special method of preparation. The method facilitates nondestructive preparation of the sensitive bottom-ash alteration phases (e.g. cement phases, hydroxides, salts) and their microstructures. Received: 18 August 2000 / Revised: 8 November 2000 / Accepted: 12 November 2000     

On the modelling of anisotropic elastic and inelastic material behaviour at large deformation

The purpose of this work is the formulation and discussion of an approach to the modelling of anisotropic elastic and inelastic material behaviour at large deformation. This is done in the framework of a thermodynamic, internal-variable-based formulation for such a behaviour. In particular, the formulation pursued here is based on a model for plastic or inelastic deformation as a transformation of local reference configuration for each material element. This represents a slight generalization of its modelling as an elastic material isomorphism pursued in earlier work, allowing one in particular to incorporate the effects of isotropic continuum damage directly into the formulation. As for the remaining deformation- and stress-like internal variables of the formulation, these are modelled in a fashion formally analogous to so-called structure tensors. On this basis, it is shown in particular that, while neither the Mandel nor back stress is generally so, the stress measure thermodynamically conjugate to the plastic “velocity gradient”, containing the difference of these two stress measures, is always symmetric with respect to the Euclidean metric, i.e., even in the case of classical or induced anisotropic elastic or inelastic material behaviour. Further, in the context of the assumption that the intermediate configuration is materially uniform, it is shown that the stress measure thermodynamically conjugate to the plastic velocity gradient is directly related to the Eshelby stress. Finally, the approach is applied to the formulation of metal plasticity with isotropic kinematic hardening.     

A dual approach to primal degeneracy

The Revised Primal Simplex algorithm, in its simplest form, has no defence against degeneracy. Various forms of the perturbation method are usually effective, but most offer no guarantee of avoiding all degeneracy, and can lead to numerical difficulties. This paper presents a method that avoids cycling and circling by taking a dual approach.The degenerate subproblem consists of all the original variables, but only the degenerate transformed constraints. The current primal objective, which may be mixed, is used. This subproblem may be solved using the dual simplex algorithm, starting from the current dual infeasible solution, and with a zero dual objective. If the dual algorithm terminates optimally then the whole problem is optimal (subject to primal feasibility). Otherwise the final solution provides a non-basic direction which improves the value of the mixed primal objective and moves away from the degenerate vertex. A purification algorithm then renders the solution basic and further improves the mixed objective.     

Nonlinear optical properties of organic dye dimer-monomer systems

An analysis is provided for the discussion of nonlinear optical properties of aggregated dye systems. The intensity-dependent transmission of fluorescein solutions excited by nanosecond dye laser pulses is shown to fit a monomer-dimer equilibrium shifted towards monomer formation by excitation. The implications for spatial light modulation and other nonlinear optical applications are discussed.