Two families of mixed finite elements for second order elliptic problems

Summary Two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. Error estimates inL ² () andH ^–5 () are derived for these elements. A hybrid version of the mixed method is also considered, and some superconvergence phenomena are discussed.     

The second order optical potential for theπd system at the threshold

The second order optical potential for thed system is derived in the framework of the Watson formalism and applied to the calculation of the 1s-state energy shift of the atom and thed scattering lengtha _d . The results are in good agreement with those of the Faddeev type calculations.The authors wish to thank V. B. Belyaev, R. Mach, M. G. Sapozhnikov and R. A. Eramzhyan for stimulating discussions and helpful advice.     

Die elektrische Zerstäubung von Silicium in Aceton

Zusammenfassung Die Bildung kolloider L?sungen durch Hochspannungskurzschlu\funken zwischen kleinen Siliciumstücken in Aceton unter sauerstoffreiem Stickstoff wird untersucht: sowohl die Ver?nderungen der Siliciumoberfl?chen durch das kurzzeitige Schmelzen und Verdampfen des Siliciums, als auch die chemischen Eigenschaften der in L?sung befindlichen Kolloide. Das Interesse war nicht, wie bei der Svedbergschen Kolloidzerst?ubung, auf die Methode zur Herstellung kolloider Metalle, in diesem Falle kolloiden Siliciums, gerichtet, sondern auf die chemische Umsetzung des Siliciums unter den gegebenen extremen Temperaturbedingungen mit dem Aceton zu kolloiden Siliciumverbindungen. Durch fraktioniertes Zentrifugieren und Eindampfen der Restl?sung ist die kolloide L?sung der Siliciumverbindungen in 3 Anteile zerlegt worden: Ein braunes Pulver, schwarze Flocken und ein dem Silikagel ?hnliches Gel. Die 3 Substanzen enthielten alle Si, O, C und H in Form einer anorganischen Si-O-haltigen Komponente und einer unges?ttigten Kohlenwasserstoffkomponente. Je gr?\er der Anteil der organischen Komponente ist, desto kleiner und l?slicher sind die Kolloidteilchen in Aceton. Die Struktur der Gelteilchen ist sehr labil und geht unter Verglimmen in eine stabilere aber nicht kristalline über. Dieser Vorgang findet beim Erw?rmen, auch unter vollkommenem Ausschlu\ von Sauerstoff, statt. Das Gel l?st sich in Laugen und flockt wieder mit S?uren. Das ganze Verhalten, einschlie\lich der analytischen Befunde, l?\t darauf schlie\en, da\ die hier erhaltene kolloide L?sung, aber auch das Svedbergsche Siliciumsol nicht kolloides elementares Silicium enthalten, sondern Kolloidteilchen, die silikonharzartigen Charakter besitzen. Hans Kautsky Jun. Diss. (Marburg 1954). Mein Vater, Prof. Dr. Hans Kautsky, regte mich zu dieser Arbeit an und gab mir wertvolle Ratschl?ge; ich danke ihm herzlich dafür. Herrn Dr. E. Hellner vom mineralogischen Institut der Philipps-Universit?t Marburg/Lahn, der die R?ntgenuntersuchungen unserer Substanzen vorgenommen hat, sei an dieser Stelle auch vielmals gedankt. Zu besonderem Dank bin ich der Deutschen Forschungsgemeinschaft für die apparative Unterstützung der Arbeit verpflichtet, der Firma Rosenthal-Isolatoren Gesellschaft m. b. H., Selb, für die kostenlose überlassung der Kondensatorbatterie.     

An NMR study of methanol diffusion in polymer electrolyte fuel cell membranes

Methanol diffusion in two polymer electrolyte membranes, Nafion 117 and BPSH 40 (a 40% disulfonated wholly aromatic polyarylene ether sulfone), was measured using a modified pulsed field gradient NMR method. This method allowed for the diffusion coefficient of methanol within the membrane to be determined while immersed in a methanol solution of known concentration. A second set of gradient pulses suppressed the signal from the solvent in solution, thus allowing the methanol within the membrane to be monitored unambiguously. Over a methanol concentration range of 0.5–8 M, methanol diffusion coefficients in Nafion 117 were found to increase from 2.9 × 10⁻⁶ to 4.0 × 10⁻⁶ cm² s⁻¹. For BPSH 40, the diffusion coefficient dropped significantly over the same concentration range, from 7.7 × 10⁻⁶ to 2.5 × 10⁻⁶cm² s⁻¹. The difference in diffusion behavior is largely related to the amount of solvent sorbed by the membranes. Increasing the methanol concentration results in an increase in solvent uptake for Nafion 117, while BPSH 40 actually excludes the solvent at higher concentrations. In contrast, diffusion of methanol measured via permeability measurements (assuming a partition coefficient of 1) was lower (1.3 × 10⁻⁶ and 6.4 × 10⁻⁷ cm² s⁻¹ for Nafion 117 and BPSH 40 respectively) and showed no concentration dependence. The differences observed between the two techniques are related to the length scale over which diffusion is monitored and the partition coefficient, or solubility, of methanol in the membranes as a function of concentration. For the permeability measurements, this length is equal to the thickness of the membrane (178 and 132 μm for Nafion 117 and BPSH 40 respectively) whereas the NMR method observes diffusion over a length of approximately 4–8 μm. Regardless of the measurement technique, BPSH 40 is a greater barrier to methanol permeability at high methanol concentrations.     

Solubility of benzil in binary alkane + dibutyl ether solvent mixtures. Comparison of predictive expressions derived from the nearly ideal binary solvent model

Experimental solubilities are reported for benzil dissolved in six binary mixtures containing dibutyl ether with hexane, heptane, octane, cyclohexane, methylcyclohexane, and 2,2,4-trimethylpentane at 25°C. Results of these measurements are compared to the predictions of equations developed previously for solubility in systems of nonspecific interactions. The most successful equation in terms of goodness of fit involved a volume fraction average of the excess Gibbs energies relative to the Flory-Huggins model, and predicted the experimental solubilities in the six systems studied to within an overall average absolute deviation of 3.4% and with a maximum deviation of 6.0%.     

Die Brechung von Wasser-in-Erdöl-Emulsionen mit dem Demulgator Dispersal BO im Zusammenhange mit der Veränderung der Wechselwirkungskräfte zwischen den Wassertröpfchen

Zusammenfassung Es wurde in Modellversuchen die Koaleszenz von zwei Wassertr?pfchen in Erd?l mit und ohne Zusatz des Demulgators untersucht. Gleichzeitig wurde die Geschwindigkeit der Ann?herung der Tr?pfchen registrierend gemessen und aus den Ergebnissen die Wechsel-wirkungskr?fte berechnet. Es konnte gezeigt werden, da? die Absto?ungskr?fte zwischen den Teilchen mit steigender Menge des Demulgators abnehmen, bis schlie?lich Anziehungskr?ftevan der Waalsscher Natur überwiegen, so da? eine Zerst?rung der Emulsion eintritt. Die gro?e Best?ndigkeit der Wasser-Erd?lemulsionen ist auf die mechanische Festigkeit der Adsorptionsschichten an der Phasengrenze zurückzuführen.     

LONG-LIVED AFTERGLOW OF PHOTOSYNTHETIC PIGMENTS IN SOLUTION: PHOTOCHEMILUMINESCENCE

Abstract —Our recent research on photochemiluminescence (PCL) of pigments in solutions is reviewed. PCL was observed in the course of photooxidation by oxygen of chlorophyll a , bacteriochlorophyll, protochlorophyll, their analogs, synthetic dyes and aromatic hydrocarbons. The PCL of chlorophyll was studied in detail. It depends on oxygen concentration, intensity of exciting light, pH, nature of pigments, solvents etc. The thermochemiluminescence was observed after illumination of liquid and solid pigment solutions at low temperature (down to - 170C). The excitation spectra of PCL coincide with the pigment absorption spectra. The PCL emission spectra in most cases differ from those of pigment fluorescence. Electron acceptors, electron donors, radical inhibitors and β-carotene quench PCL. The quenching efficiency of electron acceptors is similar to their action on the chlorophyll triplet state. The quenching effect of radical inhibitors and β-carotene correlates with their activity in reaction with singlet oxygen. The effect of quenchers on the chlorophyll fluorescence, photobleaching and pigment sensitized oxygenation was studied. Analysis of experimental data allowed the assumption that chemiluminescence accompanies the decomposition of labile pigment peroxides. The accumulation of peroxides is probably due to the reaction in the complex of pigment and singlet oxygen, formed as a result of energy transfer from photoexcited (triplet) pigment molecules to oxygen. The terminal chemiluminescence emission proceeds from the singlet excited states of molecules of pigments and products of their oxidation.     

On the structure of histidine and its role in enzyme active sites

A structural refinement is proposed for the mechanistic details of the action of the serine proteases. The proposal involves ring flipping of the imidazole function of the histidine side chain as a vehicle for proton transfer. The geometric feasibility of this motion is established by molecular graphics analysis of the crystal structure of-chymotrypsin. It is suggested that the shape of histidine is as important as its pK _a for its function at the active sites of enzymes.     

Thermochemical excess properties of multicomponent systems: Representation and estimation from binary mixing data

A general equation for the estimation of thermodynamic excess properties of multicomponent systems from observed excess properties of the various binary combinations of the components has been developed, based on a simple model of the multicomponent system. This estimation takes the form $$\Delta \bar Z_{12...N}^{ex} = \sum\limits_{i = 1}^N {\sum\limits_{j > i}^N {(X_i + X_j )(f_i + f_j )(\Delta \bar Z_{ij}^{ex} )^* } } $$ in which \((\Delta \bar Z_{ij}^{ex} )^* \) is the molar excess property (enthalpy, entropy, volume, free energy, etc.), of the binary system with components at the same molar ratio as in the multicomponent system, and f_i, f_j are weighted mole fractions using weighting factors based on the excess properties of the binary systems. The important features of this equation are: it is applicable to a broad range of thermodynamic properties, its application to both integral and differential mixing properties is independent of the manner in which the binary mixing data is represented (Redlich-Kister equation, Wilson equation, etc.), and it provides reasonably accurate predictions ranging from quite good for simple systems of nonspecific interactions to only fair for associated solutions. This equation is recommended as a point-of-departure for mathematical representation of experimental data for multicomponent systems.     

Microchips as Controlled Drug-Delivery Devices

Controlled-release systems are common in a number of product areas, including foods, cosmetics, pesticides, and paper. Microencapsulated systems, for example, are used for the release of flavors and vitamins in foods, fragrances in perfumes, and inks in carbonless copy paper. Controlled-release systems for drug delivery first appeared in the 1960s and 1970s. In the past three decades, the number and variety of controlled release systems for drug-delivery applications has increased dramatically. Many of these use polymers having particular physical or chemical characteristics such as biodegradability, biocompatibility, or responsiveness to pH or temperature changes. However, recent advances in the field of microfabrication have created the possibility of a new class of controlled-release systems for drug delivery, namely, that of small, programmable devices. Their small size, potential for integration with microelectronics, and ability to store and release chemicals on demand could make controlled-release microchips useful in a number of areas, including medical diagnostics, analytical chemistry, chemical detection, industrial process monitoring and control, combinatorial chemistry, microbiology, and fragrance delivery. More importantly, drug-delivery microchips resulting from this convergence of controlled release and microfabrication technologies may provide new treatment options to clinicians in their fight against disease.