Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

Synthesis and Conformational Switching of Partially and Differentially Bridged Resorcin[4]arenes Bearing Fluorescent Dye Labels. Preliminary Communication

We report the synthesis of modified Cram‐type cavitands bearing one or two fluorescent labels for single‐molecule spectroscopic studies of vase? kite conformational switching (Scheme 3). Syntheses were performed by stepwise bridging of the four couples of neighboring H‐bonded OH groups of resorcin[4]arene bowls (Schemes 2 and 3). The new substitution patterns enable the construction of a large variety of future functional architectures. ¹H‐NMR Investigations showed that the new partially and differentially bridged cavitands feature temperature‐ and pH‐triggered vase? kite conformational isomerism similar to symmetrical cavitands with four identical quinoxaline bridges (Table). It was discovered that vase? kite switching of cavitands is strongly solvent‐dependent.     

Unraveling the crystallization mechanism of CoAPO-5 molecular sieves under hydrothermal conditions

The hydrothermal crystallization of CoAPO-5 molecular sieves has been studied using time-resolved in-situ SAXS/WAXS, UV-vis, Raman, and XAS. Data collected during heating to 180 degrees C allowed the observation of different steps occurring during the transformation of the amorphous gel into a crystalline material from a macroscopic and atomic perspective. Raman spectroscopy detected the initial formation of Al-O-P bonds, whereas SAXS showed that these gel particles had a broad size distribution ranging from ca. 7 to 20 nm before crystallization began. WAXS showed that this crystallization was sharp and occurred at around 160 degrees C. Analysis of the crystallization kinetics suggested a one-dimensional growth process. XAS showed that Co(2+) transformed via a two-stage process during heating involving (i) a gradual transformation of octahedral coordination into tetrahedral coordination before the appearance of Bragg peaks corresponding to AFI, suggesting progressive incorporation of Co(2+) into the poorly ordered Al-O-P network up to ca. 150 degrees C, and (ii) a rapid transformation of remaining octahedral Co(2+) at the onset of crystallization. Co(2+) was observed to retard crystallization of AFI but provided valuable information regarding the synthesis process by acting as an internal probe. A three-stage, one-dimensional crystallization mechanism is proposed: (i) an initial reaction between aluminum and phosphate units forming a primary amorphous phase, (ii) progressive condensation of linear Al-O-P chains forming a poorly ordered structure separated by template molecules up to ca. 155 degrees C, and (iii) rapid internal reorganization of the aluminophosphate network leading to crystallization of the AFI crystal structure.     

Mechanistic study into the direct epoxidation of propene over gold/titania catalysts

The epoxidation of propene over gold/titania based catalysts was investigated using different techniques. Infrared spectroscopic information showed that one key step in the reaction mechanism is a reaction catalyzed by gold between titania surface groups and propene. In this reaction step, a bidentate propoxy species is formed on titania. This species adsorbs strongly on the catalyst, and it is the same species which is formed when propene oxide adsorbs on titania. Gravimetrical adsorption experiments and catalytic tests show that product adsorption and desorption are important factors determining the catalytic activity and the catalyst stability. By combining the information from different techniques, a kinetic mechanism is proposed.     

Origin of enantioselection in chiral alcohol oxidation catalyzed by Pd[(-)-sparteine]Cl2

A kinetic investigation into the origin of enantioselectivity for the Pd[(-)-sparteine]Cl(2)-catalyzed aerobic oxidative kinetic resolution (OKR) is reported. A mechanism to account for a newly discovered chloride dissociation from Pd[(-)-sparteine]Cl(2) prior to alcohol binding is proposed. The mechanism includes (1) chloride dissociation from Pd[(-)-sparteine]Cl(2) to form cationic Pd(-)-sparteine]Cl, (2) alcohol binding, (3) deprotonation of Pd-bound alcohol to form a Pd-alkoxide, and (4) beta-hydride elimination of Pd-alkoxide to form ketone product and a Pd-hydride. Utilizing the addition of (-)-sparteine HCl to control the [Cl(-)] and [H(+)] and the resulting derived rate law, the key microscopic kinetic and thermodynamic constants were extracted for each enantiomer of sec-phenethyl alcohol. These constants allow for the successful simulation of the oxidation rate in the presence of exogenous (-)-sparteine HCl. A rate law for oxidation of the racemic alcohol was derived that allows for the successful prediction of the experimentally measured k(rel) values when using the extracted constants. Besides a factor of 10 difference between the relative rates of beta-hydride elimination for the enantiomers, the main enhancement in enantiodetermination results from a concentration effect of (-)-sparteine HCl and the relative rates of reprotonation of the diastereomeric Pd-alkoxides.