Mechanism and kinetics of the catalytic CO-H2 reaction: An approach by chemical transients and surface relaxation spectroscopy

The aim of this paper is to demonstrate the importance of providing time-resolved information in catalysis research. Two truly in situ methods will be presented and compared for their merits and drawbacks: chemical transient kinetics (CTK) and pulsed field desorption mass spectrometry (PFDMS). The presentation will be given by way of example choosing the syngas (CO/H2) reaction over cobalt-based catalysts as a catalytic process. Despite numerous efforts in the past, the mechanism of this reaction is still under debate. In CTK the reaction is studied on a metal-supported catalyst under flow conditions in a pressure range extending from atmospheric pressure down to 100 Pa. Sudden changes in the partial pressures of the reactants then allow following the relaxation to either steady-state conditions ("transients") or cleanoff ("back transients"). In PFDMS short field pulses of several volts per nanometer are applied to a model catalyst which resembles a single metal particle grain (a "tip"). These pulses intervene during the ongoing reaction under flow conditions at pressures ranging from 10(-1) to 10(-5) Pa and cause field desorption of adsorbed species. This method is particularly suited to detect reaction intermediates in a time-dependent manner since the repetition frequency of the pulses can be systematically varied. It is shown that both methods lead to complementary results. While CTK allows conclusions on the mechanism of CO hydrogenation by following the time-dependent formation of hydrocarbon species, PFDMS provides insight into the initial steps leading to adsorbed CxHy species. A quantitative assessment of the CTK data allows the demonstration that the catalyst under working conditions is in an oxidized rather than metallic state. The initial steps to oxidation are also traced by PFDMS. Most importantly, however, CTK results allow formulation of a reaction mechanism that is common for both hydrocarbon and oxygenate formation and is based on the occurrence of a formate-type species as the most abundant surface intermediate.     

A Counter-Example to the Theorem of Hiemer and Snurnikov

A planar polygonal billiard $\mathcal{P}$ is said to have the finite blocking property if for every pair (O, A) of points in $\mathcal{P}$ there exists a finite number of “blocking” points B ₁,...,B _n such that every billiard trajectory from O to A meets one of the B _i 's. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.     

Phoebegrandine C, a novel proaporphine-tryptamine dimer, from Phoebe grandis (Nees) Merr

A novel proaporphine-tryptamine dimer alkaloid, named phoebegrandine C 1, was isolated from the leaves of Phoebe grandis (Nees) Merr. Its structural elucidation was carried out using spectroscopic techniques, notably 2D NMR.     

Variable-range hopping and quantum creep in one dimension

We study the quantum nonlinear response to an applied electric field E of a one-dimensional pinned charge-density wave or Luttinger liquid in the presence of disorder. From an explicit construction of low-lying metastable states and of bounce instanton solutions between them, we demonstrate quantum creep v=e(-c/E(1/2)) as well as a sharp crossover at E=E(*) towards a linear response form consistent with variable-range hopping arguments, but dependent only on electronic degrees of freedom.     

Excavations in molecular crystals

Single crystals built from porous molecular networks can react with agents that penetrate the crystals, cleave fragments from the network, and thereby increase the volume available for guests, all without loss of crystallinity.     

A difluorosulfide as a Freon-free source of phosphonodifluoromethyl carbanion

The synthesis of difluoromethylphosphonates is becoming difficult due to environmental protective laws restricting the use of HCFCs and CFCs as starting chemicals. To circumvent this limitation, we report the preparation of a thioether as a new source of the lithiodifluoromethylphosphonate. This methodology avoiding the use of HCFCs involves a selective fluorination of sulfide followed by a thiaphilic addition of an organometallic reagent, which offers an alternative route to obtain phosphonodifluoromethyl carbanion. A contrasted reactivity, due to a medium effect, was also noted which allows addition of a wide range of electrophiles including nitroalkenes and DMF to thioethers.     

Molecular tectonics. Use of the hydrogen bonding of boronic acids to direct supramolecular construction

Tetraboronic acids 1 and 2 have four -B(OH)(2) groups oriented tetrahedrally by cores derived from tetraphenylmethane and tetraphenylsilane. Crystallization produces isostructural diamondoid networks held together by hydrogen bonding of the -B(OH)(2) groups, in accord with the tendency of simple arylboronic acids to form cyclic hydrogen-bonded dimers in the solid state. Five-fold interpenetration of the networks is observed, but 60% and 64% of the volumes of crystals of tetraboronic acids 1 and 2, respectively, remain available for the inclusion of disordered guests. Guests occupy two types of interconnected channels aligned with the a and b axes; those in crystals of tetraphenylmethane 1 measure approximately 5.9 x 5.9 A(2) and 5.2 x 8.6 A(2) in cross section at the narrowest points, whereas those in crystals of tetraphenylsilane 2 are approximately 6.4 x 6.4 A(2) and 6.4 x 9.0 A(2). These channels provide access to the interior and permit guests to be exchanged quantitatively without loss of crystallinity. Because the Si-C bonds at the core of tetraboronic acid 2 are longer (1.889(3) A) than the C-C bonds at the core of tetraboronic acid 1 (1.519(6) A), the resulting network is expanded rationally. By associating to form robust isostructural networks with predictable architectures and properties of porosity, compounds 1 and 2 underscore the usefulness of molecular tectonics as a strategy for making ordered materials.     

Size minimization and approximating problems

We consider Plateau type variational problems related to the size minimization of rectifiable currents. We realize the limit of a size minimizing sequence as a stationary varifold and a minimal set. Other examples of functionals to be minimized include the integral over the underlying carrying set of a power q of the multiplicity function, with .Because minimizing sequences may have unbounded mass we make use of a more general object called a rectifiable scan for describing the limit. This concept is motivated by the possibility of recovering a flat chain from a sufficiently large collection of its slices. In case the given boundary is smooth and compact, the limiting scan has finite mass and corresponds to a rectifiable current.Received: 11 February 2002, Accepted: 16 June 2002, Published online: 17 December 2002Mathematics Subject Classification (2000): 49Q15, 28A75Thierry De Pauw: The research of the first author was supported by a Marie Curie fellowship of the European Community program Human Potential under contract HMPF-CT-2001-01235Robert Hardt: The research of the second author was partially supported by NSF grant DMS-0072486