On the application of open circuit relaxation spectroelectrochemistry to the diagnosis and evaluation of the kinetics of succeeding second order chemical reactions

The spectroelectrochemical technique of open circuit relaxation (OCR) has found limited application in the kinetic characterization of systems wherein the electrogenated absorbing species is consumed in a second or higher order reaction. This limited usage arises from the inapplicability of conventional homogeneous kinetic data analysis techniques to the absorbance-time transients observed in the OCR experiment. Treatment of such transients by conventional kinetic expressions (e.g., 1/A vs. t for second order reactions) results in non-linear plots which neither serve as diagnostic criteria for the assignment of kinetic order nor provide meaningful rate constants. This paper presents an empirical method for the treatment of spectroelectrochemical OCR data arising from post-electron transfer kinetic processes which exhibit second order dependence on the concentration of the electrogenerated absorbing species. This procedure, which takes into account the inhomogeneous distribution of the reactant species, affords reduced data plots which not only are linear, hence diagnostic of kinetic order, but also provide a valid measure of the bimolecular rate parameters characteristic of this type of dynamic system. The procedure has been applied to the treatment of OCR data for the reaction of 9,10-diphenylanthracene cation radical with 4-cyanopyridine in acetonitrile. Excellent agreement between the resulting kinetic parameters and those obtained using stopped-flow techniques has been demonstrated.     

Energy bands in the presence of an external force field—II Anomalous velocities

The theory of field-modified energy bands is extended to include the effect of weak scattering forces on the energy band structure. The modified current operator is found to contain terms giving anomalous currents of a type previously treated by and (Phys. Rev. 95, 1154 (1954) in connection with electrical conduction in ferromagnets. The physical meaning of these currents is discussed, and they are shown to be analogous to spin-dependent currents in Dirac's theory of the electron. They may be regarded formally as resulting from a non-commutability of the components of the coördinates. It is shown that such currents, proportional to the acceleration, are caused by every accelerating mechanism, including scattering mechanisms. A classical transport theory including the anomalous currents is derived, valid for scattering mechanisms for which the momentum transfer per collision is small, and a very simple problem carried through by way of example. A formal theory including the anomalous transport currents is given for the general case of arbitrary scattering mechanism and overlapping bands. Finally, a critique is given of some recent theories of the spontaneous Hall effect in ferromagnetics.     

Conformational analysis of tetraarylethanes

NMR evidence establishes that both diastereomers of 1,2-diphenyl-1,2-bis(4-pyridyl)ethane (2), identified by optical resolution of the racemic form, exist predominantly in the anti conformation. Furthermore, empirical force field calculations show that the gauche conformer of 1,1,2,2-tetrakis(2,6-dimethylphenyl)ethane (3) is less stable by ca. 10 $\text{kcal}\text{mol}$ than the anti structure. It thus appears that neither polar effects nor steric congestion are effective in reversing the marked preference of 1,1,2,2-tetraphenylethane (1) and other unclamped tetraarylethanes for an anti ground state. In contrast, as predicted by empirical force field calculations and confirmed by X-ray and NMR evidence, the ground state structure of 9,9'-bifluorenyl (4) is gauche. The conformational behavior of 1–4 is discussed in terms of the intramolecular aryl ring stacking in clamped and unclamped tetraarylethanes.     

On convergence determining and separating classes of functions

Herein, we generalize and extend some standard results on the separation and convergence of probability measures. We use homeomorphism-based methods and work on incomplete metric spaces, Skorokhod spaces, Lusin spaces or general topological spaces. Our contributions are twofold: we dramatically simplify the proofs of several basic results in weak convergence theory and, concurrently, extend these results to apply more immediately in a number of settings, including on Lusin spaces.     

Gewichtsbestimmung

Ohne Zusammenfassung