Why is cis/trans stereoinversion with Li+(THF)4 migration across the phenyl ring of α-lithiostyrene accelerated by two ortho-methyl groups?

Common wisdom might anticipate that two methyl groups placed on a molecular migration route should act as an impediment. However, the “conducted tour” migration of Li⁺(THF)₄ across the aryl ring (“π-route”) during the cis/trans stereoinversion of α-arylvinyllithiums had been found to occur with practically equal velocities in the presence of either one or two ortho-alkyl substituents. We now report that the omission of both ortho-methyl groups retards the stereoinversion process. In order to arrive at an answer to the title question, we investigate the aggregation equilibria and microsolvation states of ortho, ortho′-unsubstituted α-lithiostyrenes by means of approved secondary NMR criteria. Beyond such necessary knowledge about the ground-state properties, we provide kinetic evidence showing that the retarded cis/trans stereoinversion of α-lithiostyrene proceeds by the pseudomonomolecular, ionic mechanism with Li⁺(THF)₄ migration.     

Steady flow of a viscous incompressible fluid in an unbounded «funnel-shaped» domain

In this paper we consider a domain which is tube-like at one exit to infinity and the halfspace at the other side. We prove existence of steady motions for the Navier-Stokes problem and for the case in which the fluid is moving through a porous medium at rest filling . In both cases the proof holds for arbitrary fluxes. We describe the asymptotic behaviour of the solutions in the halfspace for both problems.     

A reaction-diffusion equation for a cyclic system with three components

The one-dimensional reaction-diffusion equations for the process (D) $$A + B \to 2A,B + C \to 2B,C + A \to 2C$$ are extended to include the counteracting reactions (R) $$A + 2B \to 3B,B + 2C \to 3C,C + 2A \to 3A$$ which have a reaction rate α relative to the direct process (D). This process can be seen as a three-component version of the reaction which is described by the Fisher-Kolmogorov equation. The fixed points of the equations are studied as a function of α. It is shown that the equations admit solutions which consist of a series of traveling fronts. Other solutions exist which are traveling periodic waves. A very remarkable fact is that for these waves exact expressions can be constructed.     

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Analytical and Bioanalytical Chemistry -     

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Analytical and Bioanalytical Chemistry -