How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue     

Static micromixers based on large-scale industrial mixer geometry

Mixing liquids at the micro-scale is difficult because the low Reynolds numbers in microchannels and in microreactors prohibit the use of conventional mixing techniques based on mechanical actuators and induce turbulence. Static mixers can be used to solve this mixing problem. This paper presents micromixers with geometries very close to conventional large-scale static mixers used in the chemical and food-processing industry. Two kinds of geometries have been studied. The first type is composed of a series of stationary rigid elements that form intersecting channels to split, rearrange and combine component streams. The second type is composed of a series of short helix elements arranged in pairs, each pair comprised of a right-handed and left-handed element arranged alternately in a pipe. Micromixers of both types have been designed by CAD and manufactured with the integral microstereolithography process, a new microfabrication technique that allows the manufacturing of complex three-dimensional objects in polymers. The realized mixers have been tested experimentally. Numerical simulations of these micromixers using the computational fluid dynamics (CFD) program FLUENT are used to evaluate the mixing efficiency. With a low pressure drop and good mixing efficiency these truly three-dimensional micromixers can be used for mixing of reactants or liquids containing cells in many microTAS applications.     

Enantioselective Diels-Alder reactions with N-hydroxy-N-phenylacrylamide

[reaction: see text] The use of hydroxamic acids as templates for Lewis acid catalyzed enantioselective Diels-Alder reactions has been examined. A very simple chiral Lewis acid, prepared by mixing optically pure binaphthol with 3 equiv of trimethylaluminum, catalyzes the [4 + 2] cycloaddition of N-hydroxy-N-phenylacrylamide with cyclopentadiene at 0 degrees C in high yield (>96%) and with a fairly good level of enantioselectivity (91% ee). Facile conversion of the products to the corresponding alcohols or aldehydes makes the hydroxamic acid intermediates particularly useful.     

Selective, controllable, and reversible aggregation of polystyrene latex microspheres via DNA hybridization

The directed three-dimensional self-assembly of microstructures and nanostructures through the selective hybridization of DNA is the focus of great interest toward the fabrication of new materials. Single-stranded DNA is covalently attached to polystyrene latex microspheres. Single-stranded DNA can function as a sequence-selective Velcro by only bonding to another strand of DNA that has a complementary sequence. The attachment of the DNA increases the charge stabilization of the microspheres and allows controllable aggregation of microspheres by hybridization of complementary DNA sequences. In a mixture of microspheres derivatized with different sequences of DNA, microspheres with complementary DNA form aggregates, while microspheres with noncomplementary sequences remain suspended. The process is reversible by heating, with a characteristic "aggregate dissociation temperature" that is predictably dependent on salt concentration, and the evolution of aggregate dissociation with temperature is observed with optical microscopy.     

Structure des savons alcalins

Summary This is a systematic X-ray diffraction study of the structure of the mesomorphic phases occurring with potassium soaps ranging from C₈ to C₂₂.Four types of structure have been identified. The first is lamellar with both polar groups and paraffin chains in the crystalline state. The second is also lamellar, but with both polar groups and paraffin chains in the liquid state. The third corresponds to the localization of indefinitely long ribbons on a two-dimensional oblique lattice; polar groups are crystalline and paraffin chains desorganized. The fourth corresponds to the localization of discs on a three-dimensionnalB-faces centered orthorhombic lattice; polar groups are crystalline and paraffin chains disorganized.The structural parameters and the polymorphism of the polar groups have been discussed.

---

Zusammenfassung Wir beschreiben hier eine systematische Röntgenstrahlendiffraktionsforschung der Struktur der mesomorphen Phasen von Kalium Seifen von C₈ bis C₂₂.Vier Strukturtypen wurden gefunden. Die erste Struktur ist lamellar; beides, die polaren Gruppen und die Paraffinketten sind kristallisiert. Die zweite Struktur ist auch lamellar; aber in diesem Falle sind beides, die polaren Gruppen und Paraffinketten geschmolzen. Die dritte Struktur entspricht einer Lokalisation von Seifenbändern in einem zweidimensionalen monoklinen Gitter; die polaren Gruppen sind kristallisiert und die Paraffinketten geschmolzen. Die vierte Struktur entspricht einer Lokalisation von Seifenscheiben in einemB-flächenzentrierten orthorhombischen Raumgitter; die Polargruppen sind kristallisiert und die Paraffinketten geschmolzen.Wir haben aus den experimentellen Resultaten einige Schlußfolgerungen gezogen.

     

Crystallographic evidence of hexacoordination at phosphorus via intramolecular coordination of donor groups on phosphane and phosphane sulphide

The X-ray structure analysis of bis(8-dimethylamino-l-naphthyl)phenylphosphane (3) and of the corresponding sulphide 4 has revealed hexacoordination at phosphorus in both cases, the N … P separations being less than the sum of the van der Waal radii. Furthermore, in both cases the overall geometry corresponds to a distorted bicapped tetrahedron. The optimum geometry calculated for 4 via the program developed by Autodesk (MM + method) suggests that the structure of the molecule is a function not only of steric requirements but also of electronic effects.     

EPR study of ceria–silica and ceria–alumina catalysts: Localization of superoxide radical anions

Oxygen adsorption experiments were performed on evacuated and prereduced CeO₂/SiO₂ and CeO₂/Al₂O₃ catalysts with and without platinum. Considerable amounts of the superoxide radical ions were stabilized on all the samples. Signal parameters suggest Ce⁴⁺–O₂⁻ positioning for all detectable superoxide species. Physisorbed oxygen broadens O₂⁻ signal beyond detection for all the alumina-based samples, while the same procedure for all the silica-based samples did not change signal shape of O₂⁻ species. Detectable O₂⁻ species are localized in the bulk of ceria and the nature of support (silica or alumina) determines the number of oxygen vacancies and the rate of electron transfer. XRD data suggest that for alumina-based samples small and/or thin islands of ceria dominate, while comparatively large ceria particles are stabilized on the surface of silica-based samples with the same ceria content. Average size of ceria crystallites is still not determining factor and cannot account for the observed differences. Higher concentrations of paramagnetic species may be stabilized on alumina-based samples and thus, sensor-like behavior towards gaseous oxygen at room temperature was detected for them—oxygen admission reversibly changes superoxide lineshape. For silica samples, only minor changes of O₂⁻ lineshapes were typical upon the change of the partial pressure of oxygen at ambient and low temperatures. Addition of platinum has little effect on parameters of the O₂⁻ signal, except an enhancement of the superoxide decay in the reducing media. Possible site for O₂⁻ stabilization inside the lattice of CeO₂ was proposed and relevance of the observed effects to the redox catalysis discussed.     

Combining alkali metals and zinc to harness heterometallic cooperativity in cyclic ester ring-opening polymerisation

Heterometallic cooperativity is an emerging strategy to elevate polymerisation catalyst performance. Here, we report the first heterotrimetallic Na/Zn₂ and K/Zn₂ complexes supported by a ProPhenol ligand, which deliver “best of both” in cyclic ester ring-opening polymerisation, combining the outstanding activity (Na/K) and good control (Zn₂) of homometallic analogues. Detailed NMR studies and density-functional theory calculations suggest that the Na/Zn₂ and K/Zn₂ complexes retain their heterometallic structures in the solution-state. To the best of our knowledge, the K/Zn₂ analogue is the most active heterometallic catalyst reported for rac-lactide polymerisation (k_obs = 1.7 × 10⁻² s⁻¹), giving activities five times faster than the Na/Zn₂ complex. These versatile catalysts also display outstanding performance in ε-caprolatone and δ-valerolactone ring-opening polymerisation. These studies provide underpinning methodologies for future heterometallic polymerisation catalyst design, both in cyclic ester polymerisation and other ring-opening (co)polymerisation reactions.

Cooperative heterotrimetallic Na/Zn₂ and K/Zn₂ complexes combine the excellent activities and control of the homometallic analogues, giving “best of both” in cyclic ester ring-opening polymerisation.