“Cautious” utility maximization and iterated weak dominance

This paper examines the implications of assuming that rational players in a two-player noncooperative game maximize expected utility using cautious beliefs; i.e., beliefs that give positive probability to all rational strategies of the other players. The result is a solution concept that captures some of the flavor of but is not equivalent to the iterated elimination of weakly dominated strategies. The solution concept yields attractive results for some games, but suffers from nonexistence problems in other games. We interpret the nonexistence problems as showing that it is logically inconsistent to assume that rational players analyze all games on the basis of cautious expected utility maximization.We would like to thank Pierpaolo Battigalli, two anonymous referees, and an editor for helpful comments. Tilman Börgers gratefully acknowledges financial assistance from the Schweizerischer Nationalfonds.     

Utilization of ion exchangers in analytical chemistry XXVI : Application of the ion-exchange method to solutions containing oxidants

The free acid form of a cation-exchange resin of the sulfonated hydrocarbon type (Dowex 50) can be used for a quantitative liberation of the corresponding acids from salt solutions containing oxidants that are reduced by phenolic resins. Positive results have been obtained with solutions containing bromate, iodate, periodate, molybdate, and chromate. With permanganate a partial reduction occurs which prevents the application of the ion-exchange method for quantitative separation of solutions containing permanganate.     

Reevaluation of bandgap and free exciton binding energy of GaP

Very sensitive measurements on the spectral behaviour of the free-to-bound excitation σ_pl^°(hν) from the valence band to the deep 0 donor in GaP at low temperatures are presented. Evaluation of the threshold energy for the electronic transition, together with the known value of the 0 binding energy, provides a simple and accurate way to determine the indirect bandgap E_g of GaP. Our new value is E_g = 2.3525 ± 0.003 eV at 1.5 K, which gives an exciton binding energy E_x = 24 ± 3 meV, considerably larger than previously used values. These data also imply an upward revision of acceptor binding energies in GaP with 10 ± 2 meV.     

The nature of bond critical points in dinuclear copper(I) complexes

Closed-shell contacts between two copper(I) ions are expected to be repulsive. However, such contacts are quite frequent and are well documented. Crystallographic characterization of such contacts in unsupported and bridged multinuclear copper(I) complexes has repeatedly invited debates on the existence of cuprophilicity. Recent developments in the application of Bader's theory of atoms-in-molecules (AIM) to systems in which weak hydrogen bonds are involved suggests that the copper(I)-copper(I) contacts would benefit from a similar analysis. Thus the nature of electron-density distributions in copper(I) dimers that are unsupported, and those that are bridged, have been examined. A comparison of complexes that are dimers of symmetrical monomers and those that are dimers of two copper(I) monomers with different coordination spheres has also been made. AIM analysis shows that a bond critical point (BCP) between two Cu atoms is present in most cases. The nature of the BCP in terms of the electron density, ρ, and its Laplacian is quite similar to the nature of critical points observed in hydrogen bonds in the same systems. The ρ is inversely correlated to Cu-Cu distance. It is higher in asymmetrical systems than what is observed in corresponding symmetrical systems. By examining the ratio of the local electron potential-energy density (V(c)) to the kinetic energy density (G(c)), |V(c)|/G(c) at the critical point suggests that these interactions are not perfectly ionic but have some shared nature. Thus an analysis of critical points by using AIM theory points to the presence of an attractive metallophilic interaction similar to other well-documented weak interactions like hydrogen bonding.     

Nanocomposites of TiO 2 and Siloxane Copolymers as Environmentally Safe Flame-Retardant Materials †

Composites of titanium dioxide (TiO₂) nanoparticles and biocatalytically synthesized dimethylsiloxane copolyamides were prepared, and their thermal and flame-retardant properties were investigated. The flammability properties such as heat release capacity and total heat release were measured from microscale cumbustion calorimetry (MCC). The thermal degradation temperatures, char yields, and the heat-release capacities of these nanocomposites were significantly improved over the pure polymers. The heat-release capacities of the siloxane copolymer nanocomposites with 20wt% of TiO₂ were found to be 167 and 129 J/g K, which is a 35% less than the pure polymers (260 and 194 J/g K, respectively). The SEM/EDAX surface-analysis studies on nanocomposite films and their char revealed that nanocrystalline-TiO₂ plays an important role in forming carbonaceous silicate char on the surface as a protective layer.     

Predicting the solubility of xenon in n-hexane and n-perfluorohexane: a simulation and theoretical study

The solubility of xenon in n-hexane and n-perfluorohexane has been studied using both molecular simulation and a version of the SAFT approach (SAFT-VR). The calculations were performed close to the saturation line of each solvent, between 200 K and 450 K, which exceeds the smaller temperature range where experimental data are available in the literature. Molecular dynamics simulations, associated with Widom's test particle insertion method, were used to calculate the residual chemical potential of xenon in n-hexane and n-perfluorohexane and the corresponding Henry's law coefficients. The simulation results overestimate the solubility of xenon in both solvents when simple geometric combining rules are used, but are in good agreement if a binary interaction parameter is included. With the SAFT-VR approach we are able to reproduce the experimental solubility for xenon in n-hexane, using simple Lorentz-Berthelot rules to describe the unlike interaction. In the case of n-perfluorohexane as a solvent, a binary interaction parameter was introduced, taken from previous work on (xe + C₂F₆) mixtures. Overall, good agreement is obtained between the simulation, theoretical and experimental data.     

Catalytic cyclopropanation of olefins using copper(I) diphosphinoamines

Catalytic cyclopropanation reactions of olefins with ethyl diazoacetate were carried out using copper(I) diphosphinoamine (PPh₂)₂N(R) (R = ⁱPr, H, Ph and –CH₂–C₆H₄–CHCH₂) complexes at 40 °C in chloroform. High yields of the cyclopropanes were obtained in all cases. The rate of the reaction was influenced by the nuclearity of the complex and the binding mode of the ligand which was either bridging or chelating. Comparison of isostructural complexes shows that the rate follows the order R = ⁱPr > H > Ph, where R is the substituent on the N. However, cyclopropane formation versus dimerization of the carbene, and trans to cis ratios of cyclopropane was similar in all cases. The nearly identical selectivity for different products formed was indicative of a common catalytic intermediate. A labile “copper–olefin” complex which does not involve the phosphine or the counterion is the most likely candidate. The differences in the reaction rates for different complexes are attributed to differences in the concentration of the catalytically active species which are in equilibrium with the catalytically inactive copper–phosphinoamine complex. To test the hypothesis a diphosphinoamine polymer complexed to copper(I) was used as a heterogeneous catalyst. Leaching of copper(I) and deactivation of the catalyst confirmed the proposed mechanism.