Synthesis of α, ω perfluoropolyether iodides

Perfluoropolyether (PFPE) diacyl halides of formula XCOCF₂O[(CF₂O)_n(CF₂CF₂O)_m]_pCF₂COX, with X = Cl, F and molecular weight (MW) 400-4000 g mol⁻¹ are smoothly converted in high yields to the corresponding α, ω diiodides in the absence of solvent, employing KI or LiI at 210 °C with extrusion of CO. During the reactions, β-elimination of COF₂ from the terminal difluoromethylene oxide units (CF₂O, C₁ unit) occurs to some extent until a tetrafluoroethylene oxide unit (OCF₂CF₂, C₂ unit) is encountered yielding a OCF₂CF₂I terminus. This considerably alters the MW distribution of the final diiodide especially for low MW PFPEs. Operating in supercritical conditions of CO (scCO) or both scCO and CO₂ (scCO₂) on low (<600 g mol⁻¹) MW diacyl halides, lowers β-elimination from 95 to 52 mol% if KI is used or from 43 to 30 mol% if LiI is used. With higher MW (>600 g mol⁻¹) β-elimination is lowered from 15 to <1 mol% in scCO conditions employing KI.     

Sample capacity in open tubular and micro-packed columns for GC

Equations have been derived from which the maximum sample size which may be loaded on a column without significantly affecting the performance may be calculated. It is shown that micro-packed columns can handle a sample which is as much as forty times larger than that which can be loaded onto wall-coated open tubular columns with comparable conditions.     

Cyclic esters of aliphatic diacids with pyrocatechol and hydroquinone

Cyclic esters of adipic acid, suberic acid and sebacic acid were prepared by reaction of the acid dichlorides and pyrocatechol or hydroquinone in benzene under high dilution conditions. While only the cyclic dimers could be obtained from hydroquinone, pyrocatechol formed cyclic monomers as well as cyclic dimers (and also a cyclic dimer with succinic acid). The structure of all compounds was confirmed by¹H-NMR- and mass spectra. The crystal structures of the pyrocatechol esters were determined by single crystal X-ray analysis.

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Cyclische Ester aliphatischer Dicarbonsäuren mit Brenzcatechin und Hydrochinon

Zusammenfassung Es wurden cyclische Ester von Adipinsäure, Korksäure und Sebacinsäure durch Reaktion der entsprechenden Säure-Dichloride mit Brenzcatechin oder Hydrochinon bei hoher Verdünnung hergestellt. Während mit Hydrochinon lediglich die cyclischen Dimeren erhalten werden konnten, wurden mit Brenzcatechin sowohl cyclische Monomere als auch cyclische Dimere erhalten (ebenfalls das cyclische Dimer mit Bernsteinsäure). Die Strukturen wurden mittels¹H-NMR und Massenspektren gesichert. Die Kristallstrukturen der Brenzcatechin-Ester wurden mittels Röntgenstrukturanalyse bestimmt.

     

Solubility Behavior in Ternary Water-Salt Systems under Sub- and Supercritical Conditions

Summary.  Two main types of binary systems with distinctive solubility behavior under sub- and supercritical conditions were used to subdivide ternary water-salt systems into three classes. Characteristic features of solubility behavior and phase equilibria in ternary water-salt systems of each class at temperatures above 200°C are discussed on the basis of available experimental data and some conclusions obtained as a result of theoretical derivation of fluid and complete phase diagrams. Corresponding author. E-mail: Valyashko@IGIC.RAS.RU Received September 25, 2002; accepted (revised) November 28, 2002 Published online April 24, 2003 RID="a" ID="a" Dedicated to Prof. Dr. H. Gamsjaeger on the occasion of his 70^th birthday anniversary     

Optimum performance of capillary GC columns as a function of tube diameter and film thickness under various operating conditions. Computer program for calculation of H-ū curves and minimum analysis times

The Golay-Giddings and Poiseuille equations are used to derive equations for the calculation of the maximum plate number and minimum time conditions for given columns at fixed, but selectable, outlet pressures. In addition, expressions are presented for the determination of minimum analysis times for separation problems requiring given plate numbers. In this instance, the optimum column length can be calculated as a function of outlet pressure. A Basic computer program, incorporating the equations for the various optima, together with the H-ū curves, is described. Input variables are either column length or desired plate number, column diameter, film thickness, capacity ratio of the solute, column outlet pressure, seperation temperature, and carrier gas. The carrier gas viscosity is automatically calculated in the case of hydrogen, helium, or nitrogen. For these gases, and if the solute is a n-alkane, the diffusivity of the solute in the mobile phase is calculated. In this case, the carbon number of the solute is needed in the computation. For high molecular weight polydimethylsilicone phases (e.g. SE-30), the program can approximate the diffusivity of n-alkanes in the stationary phase at the given temperature as a function of the carbon number. Of course, manually entered values of viscosity and diffusion coefficients can be included in the calculations.     

Influence of quaternary onium salts,crown ethers and cryptands on olefin epoxidations promoted by HOCl/ClO− in the Presence of Mn(III)-tetrakis(2,6-dichlorophenyl)porphyrin chloride

Reaction rates of alkene epoxidations, promoted by aqueous NaOCl and catalyzed by Mn(III)-tetrakis(2,6-dichlorophenyl)porphyrin chloride1 (P) in the presence of a lipophilic axial ligand (L) (e.g.N-hexylimidazole) and carried out under H₂O/CH₂Cl₂ two phase conditions at 0°C, are strongly enhanced by lowering the pH of the aqueous phase from 12.7 to 9.5. Under these conditions, a further relevant increase in the reaction rates can be achieved by adding phase-transfer catalysts (PT), e.g. quaternary ammonium salt 3, lipophilic crown ether4 or cryptand5, provided that the amount of L is very small (L/P=1 for very reactive alkenes, e.g. cyclooctene, and 10 for poorly reactive ones, e.g. 1-dodecene). In the case of cyclooctene epoxidation, the use of 0.006–0.03 mol. equiv. of PT completes the reaction in 1–10 min., the initial rates being up to 600 turnovers/min. with (2.2.2,C₁₀) cryptand. In the absence of the axial ligand, the quaternary ammonium salt3 and cryptand5 show an inhibitory effect. Such an effect is due to the formation of the poorly reactive Mn(P)CI species, by Cl– extraction to the organic phase. However, dibenzo crown ether 4 does not show this effect. In the presence of 4, and with L/P =1, the 1-dodecene epoxidation reaches 94% in 1 min. The unique behavior of crown ethers can be explained by their ineffectiveness in extracting alkali chlorides, providing a very low concentration of Cl– in the organic phase and thus avoiding the Mn(III)-porphyrin deactivation.This paper is dedicated to the memory of the late Dr C. J. Pedersen.     

An open optimization problem in statistical quality control

We ask the experts in global optimization if there is an efficient solution to an optimization problem in acceptance sampling: Here, one often has incomplete prior information about the quality of incoming lots. Given a cost model, a decision rule for the inspection of a lot may then be designed that minimizes the maximum loss compatible with the available information. The resulting minimax problem is sometimes hard to solve, as the loss functions may have several local maxima which vary in an unpredictable way with the parameters of the decision rule.     

Metastable systems driven by colored noise: The stationary state

The influence of the Bardeen-Herring back-jump correlations on the Fermi-Dirac statistics of the one-dimensional nonhomogeneous fermionic lattice gas is studied by the Monte Carlo simulation technique and semianalytically. The resulting distribution is obtained, exhibiting increased population of the lower levels in comparison to the Fermi-Dirac statistics.     

Convexlike and concavelike conditions in alternative,minimax, and minimization theorems

Convexlike and concavelike conditions are of interest for extensions of the Von Neumann minimax theorem. Since the beginning of the 80's, these conditions also play a certain role in deriving generalized alternative theorems of the Gordan, Motzkin, and Farkas type and Lagrange multiplier results for constrained minimization problems.In this paper, we study various known convexlike conditions for vector-valued functions on a set and investigate convexlike and concavelike conditions for real-valued functions on a product setC×D, where we are mainly interested in the relationships between these conditions. At the end of the paper, we point out several conclusions from our results for the above-mentioned mathematical fields.The author is indebted to Dr. R. Reemtsen and Dr. V. Jeyakumar for their helpful comments during the preparations of this paper.     

Value function and optimality conditions for semilinear control problems

This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx(t)=Ax(t) + f(t, x(t), u(t)), u(t) U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.Work (partially) supported by the Research Project Equazioni di evoluzione e applicazioni fisicomatematiche (M.U.R.S.T.-Italy).