Fries rearrangement of aryl formates: a mechanistic study by means of 1H, 2H, and 11B NMR spectroscopy and DFT calculations

1H, 2H, and 11B NMR spectroscopy has been used to study the mechanism of the Fries rearrangement of aryl formates promoted by boron trichloride by monitoring both the substrate and the Lewis acid. DFT calculations were employed to investigate the energetics of several reaction paths and to calculate NMR chemical shifts of key intermediates and products. After the formation of a 1:1 substrate-Lewis acid adduct, the rearrangement proceeds in two steps, beginning with the cleavage of the ester bond and the release of formyl chloride in situ, which, in turn, acts as a formylating agent, introducing an aldehydic functionality into the aromatic ring. The high regioselectivity (only the ortho product is obtained) is also accounted for by the proposed intermolecular, Lewis acid-assisted mechanism.     

Stable isotope deltas: tiny, yet robust signatures in nature

Although most of them are relatively small, stable isotope deltas of naturally occurring substances are robust and enable workers in anthropology, atmospheric sciences, biology, chemistry, environmental sciences, food and drug authentication, forensic science, geochemistry, geology, oceanography, and paleoclimatology to study a variety of topics. Two fundamental processes explain the stable isotope deltas measured in most terrestrial systems: isotopic fractionation and isotope mixing. Isotopic fractionation is the result of equilibrium or kinetic physicochemical processes that fractionate isotopes because of small differences in physical or chemical properties of molecular species having different isotopes. It is shown that the mixing of radioactive and stable isotope end members can be modelled to provide information on many natural processes, including (14)C abundances in the modern atmosphere and the stable hydrogen and oxygen isotopic compositions of the oceans during glacial and interglacial times. The calculation of mixing fractions using isotope balance equations with isotope deltas can be substantially in error when substances with high concentrations of heavy isotopes (e.g. (13)C, (2)H, and (18)O ) are mixed. In such cases, calculations using mole fractions are preferred as they produce accurate mixing fractions. Isotope deltas are dimensionless quantities. In the International System of Units (SI), these quantities have the unit 1 and the usual list of prefixes is not applicable. To overcome traditional limitations with expressing orders of magnitude differences in isotope deltas, we propose the term urey (symbol Ur), after Harold C. Urey, for the unit 1. In such a manner, an isotope delta value expressed traditionally as-25 per mil can be written as-25?mUr (or-2.5?cUr or-0.25?dUr; the use of any SI prefix is possible). Likewise, very small isotopic differences often expressed in per meg 'units' are easily included (e.g. either+0.015?‰ or+15 per meg can be written as+15?μUr.     

Multiscale analysis and simulation of a reaction–diffusion problem with transmission conditions

This paper considers a transmission problem for partial differential equations obtained in the recent paper [M. Neuss-Radu, W. Jäger, Effective transmission conditions for reaction-diffusion processes in domains separated by an interface, SIAM J. Math. Anal. 39 (2007) 687–720] as the effective system modeling a reaction–diffusion process in two domains separated by a membrane. For the analysis of this problem an appropriate function space, which includes the coupling conditions for the concentrations on the interface, is introduced. The transmission conditions for the flux are included in the variational formulation with respect to this function space.The solution of the transmission problem is approximated by using the Galerkin method. Numerically the problem is reduced to a system of ordinary differential equations, where the coupling of the micro- and macro-variables leads to a special structure, distinguishing the variables relevant for the transmission. Results of numerical simulations are illustrating the effect of the microscopic process in the membrane on the macroscopic reaction–diffusion process in the bulk domains.     

Parabolic problems with the Preisach hysteresis operator in boundary conditions

Parabolic initial boundary-value problems coupled (via the boundary condition) with ordinary differential equations whose right-hand side contains the Preisach hysteresis operator are considered. In particular, these problems model thermocontrol processes in chemical reactors, climate-control systems, biological cells, etc. For the Preisach operator with and without time delay, solvability, periodicity of solutions, and global B-attractors are studied.     

Solution of porous medium type systems by linear approximation schemes

Summary The convergence of semi-discrete and discrete linear approximation schemes is analysed for nonlinear degenerate parabolic systems of porous medium type. The enthalpy formulation and variational technique are used. The semi-discretization used reduces the original parabolic P.D.E. to linear elliptic P.D.E. The algebraic correction arising from nonlinearities is treated by Newton-like iterations in finite steps. Some numerical experiments are discussed and compared with the analytical solutions.Supported by the Alexander von Humboldt-Foundation in 1989, and by SFB 123, University Heidelberg     

Couette Flows over a Rough Boundary and Drag Reduction

 We consider the Couette flow between two plates. The lower plate is fixed and has periodically placed riblets of the characteristic size ɛ on it. In the limit ɛ → 0 we find the effective Couette-Navier flow as an O(ɛ ² ) approximation for the effective mass flow and an O(ɛ ² )L ¹ -approximation for the velocity. In the effective solution the effect of roughness enters through the Navier slip condition with the matrix coefficient in front of the effective shear stress, calculated using a boundary layer problem. Furthermore, an O(ɛ ² ) approximation for the tangential drag force is found. In all estimates explicit dependence on the kinematic viscosity ν, the velocity of the upper plate and the distance between the plates L ₃ is kept. Also the uniqueness of the solution is expressed through a non-linear algebraic condition linking and L ₃ . Then the result is applied to the viscous sub-layers around immersed bodies, strictly containing the surface riblets. It is found that for the riblets of the characteristic size ɛ, being of the order smaller or equal to , the approximation obtained for the tangential drag could be applied. We compare ɛ and for realistic data and our results lead to the conclusion that the riblets reduce significantly tangential drag, which may explain their presence on the skin of Nektons. Received: 14 December 2001 / Accepted: 1 August 2002 Published online: 7 November 2002