Minimum Weight Design for Structural Eigenvalue Problems by Optimal Control Theory*, †

The application of optimal control theory to minimum weight design of continuous one-dimensional structural elements subject to eigenvalue constraints is discussed. If not only the value of an eigenvalue is prescribed but also its position in the sequence of the ordered eigenvalues—for example, the critical buckling load of a column—the corresponding optimal control problem is shown to include necessarily all eigenvalues. Considering the unspecified eigenvalues as free parameters, necessary conditions for minimum weight design are derived. These conditions are compared with those obtained by use of variational methods. Attention is focused on the special case of multimodal solutions.     

Mössbauer- and EPR-Snapshots of an Enzymatic Reaction: The Cytochrome P450 Reaction Cycle

Hyperfine Interactions - In this communication we present a complimentary Mössbauer- and EPR-study of the time dependance of the reaction of substrate free P450cam with peracetic acid within a...     

Atomic‐Scale Observation of the Metal–Promoter Interaction in Rh‐Based Syngas‐Upgrading Catalysts

The direct conversion of syngas to ethanol, typically using promoted Rh catalysts, is a cornerstone reaction in CO₂ utilization and hydrogen storage technologies. A rational catalyst development requires a detailed structural understanding of the activated catalyst and the role of promoters in driving chemoselectivity. Herein, we report a comprehensive atomic‐scale study of metal–promoter interactions in silica‐supported Rh, Rh–Mn, and Rh–Mn–Fe catalysts by aberration‐corrected (AC) TEM. While the catalytic reaction leads to the formation of a Rh carbide phase in the Rh–Mn/SiO₂ catalyst, the addition of Fe results in the formation of bimetallic Rh–Fe alloys, which further improves the selectivity and prevents the carbide formation. In all promoted catalysts, Mn is present as an oxide decorating the metal particles. Based on the atomic insight obtained, structural and electronic modifications induced by promoters are revealed and a basis for refined theoretical models is provided.     

Monitoring in situ catalytically active states of Ru catalysts for different methanol oxidation pathways

One of the prerequisites for the detailed understanding of heterogeneous catalysis is the identification of the dynamic response of the catalyst surface under variable reaction conditions. The present study of methanol oxidation on different model Ru pre-catalysts, performed approaching the realistic catalytic reaction conditions, provides direct evidence of the significant effect of reactants' chemical potentials and temperature on the catalyst surface composition and the corresponding catalytic activity and selectivity. The experiments were carried out for three regimes of oxygen potentials in the 10(-1) mbar pressure range, combining in situ analysis of the catalyst surface by synchrotron-based photoelectron core level spectroscopy with simultaneous monitoring of the products released in the gas phase by mass spectroscopy. Metallic Ru with adsorbed oxygen and transient 'surface oxide', RuO(x), with varying x have been identified as the catalytically active states under specific reaction conditions, favouring partial or full oxidation pathways. It has been shown that the composition of catalytically active steady states, exhibiting different activity and selectivity, evolves under the reaction conditions, independent of the crystallographic orientation and the initial pre-catalyst chemical state, metallic Ru or RuO(2).     

In situ XPS study of Pd(1 1 1) oxidation. Part 1: 2D oxide formation in 10 mbar O2

The oxidation of the Pd(1 1 1) surface was studied by in situ XPS during heating and cooling in 3 × 10⁻³ mbar O₂. A number of adsorbed/dissolved oxygen species were identified by in situ XPS, such as the two dimensional surface oxide (Pd₅O₄), the supersaturated O_ads layer, dissolved oxygen and the R 12.2° surface structure.Exposure of the Pd(1 1 1) single crystal to 3 × 10⁻³ mbar O₂ at 425 K led to formation of the 2D oxide phase, which was in equilibrium with a supersaturated O_ads layer. The supersaturated O_ads layer was characterized by the O 1s core level peak at 530.37 eV. The 2D oxide, Pd₅O₄, was characterized by two O 1s components at 528.92 eV and 529.52 eV and by two oxygen-induced Pd 3d_5/2 components at 335.5 eV and 336.24 eV. During heating in 3 × 10⁻³ mbar O₂ the supersaturated O_ads layer disappeared whereas the fraction of the surface covered with the 2D oxide grew. The surface was completely covered with the 2D oxide between 600 K and 655 K. Depth profiling by photon energy variation confirmed the surface nature of the 2D oxide. The 2D oxide decomposed completely above 717 K. Diffusion of oxygen in the palladium bulk occurred at these temperatures. A substantial oxygen signal assigned to the dissolved species was detected even at 923 K. The dissolved oxygen was characterised by the O 1s core level peak at 528.98 eV. The “bulk” nature of the dissolved oxygen species was verified by depth profiling.During cooling in 3 × 10⁻³ mbar O₂, the oxidised Pd²⁺ species appeared at 788 K whereas the 2D oxide decomposed at 717 K during heating. The surface oxidised states exhibited an inverse hysteresis. The oxidised palladium state observed during cooling was assigned to a new oxide phase, probably the R 12.2° structure.     

Microstructural impact of anodic coatings on the electrochemical chlorine evolution reaction

Sol-gel Ru(0.3)Sn(0.7)O(2) electrode coatings with crack-free and mud-crack surface morphology deposited onto a Ti-substrate are prepared for a comparative investigation of the microstructural effect on the electrochemical activity for Cl(2) production and the Cl(2) bubble evolution behaviour. For comparison, a state-of-the-art mud-crack commercial Ru(0.3)Ti(0.7)O(2) coating is used. The compact coating is potentially durable over a long term compared to the mud-crack coating due to the reduced penetration of the electrolyte. Ti L-edge X-ray absorption spectroscopy confirms that a TiO(x) interlayer is formed between the mud-crack Ru(0.3)Sn(0.7)O(2) coating and the underlying Ti-substrate due to the attack of the electrolyte. Meanwhile, the compact coating shows enhanced activity in comparison to the commercial coating, benefiting from the nanoparticle-nanoporosity architecture. The dependence of the overall electrode polarization behaviour on the local activity and the bubble evolution behaviour for the Ru(0.3)Sn(0.7)O(2) coatings with different surface microstructure are evaluated by means of scanning electrochemical microscopy and microscopic bubble imaging.