A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

A model of adsorption at liquid-solid interface involving association in the bulk phase

A model of monolayer adsorption of binary liquid mixtures on homogeneous and heterogeneous solid surfaces involving association of one component in the bulk phase is discussed. Suitable model calculations, illustrating association and heterogeneity effects, have been performed according to an equation derived for adsorption excess. This equation has been examined by using the experimental data of adsorption of alcohols from benzene andn-heptane on silica gel.

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Adsorptionsmodell für die Grenzfläche Feststoff-Flüssigkeit unter Berücksichtigung der Assoziation in der Flüssigkeitsphase

Zusammenfassung Es wird ein Adsorptionsmodell binärer, flüssiger Mischungen an homogenen und heterogenen Oberflächen von Feststoffen unter Beachtung der Assoziation eines der Bestandteile in der Flüssigkeitsphase diskutiert. Mit der aus dem Oberflächenüberschuß abgeleiteten Gleichung wurden entsprechende Modellberechnungen durchgeführt, die die mit Assoziation und Heterogenität verbundenen Effekte illustrieren. Die Gleichung wurde für die experimentellen Daten der Alkoholadsorption aus Benzol undn-Heptan an Kieselgel überprüft.

     

Partial molal heat capacities of aqueous tetraalkylammonium bromides as functions of temperature

Enthalpies of solution have been measured from 5 to 85°C for aqueous tetraethyl- and tetrapropylammonium bromides, and the integral heat method is employed to evaluate for these electrolytes over a wide temperature range. Data taken from the literature have been used to evaluate for aqueous Bu₄NBr over a similar temperature range. These data, along with similar data for Me₄NBr, previously reported, have been used to evaluate absolute ionic heat capacities. While the absolute values agree only qualitatively with two other methods of division, the temperature dependences of the three methods essentially agree up to 65°C. Heat capacities due to structural effects on the solvent, obtained by subtracting the inherent heat capacities of the ions, are extraordinarily positive for all four tetraalkylammonium ions and have negative temperature coefficients, indicating that all four ions, including the tetramethylammonium ion, are structure-making ions.     

Microheterogeneity in aqueous-organic solutions: Heat capacities,volumes and expansibilities of some alcohols,aminoalcohol and tertiary amines in water

The heat capacities per unit volume and the densities of aqueous solutions of 2-propanol, neopentanol, tert-amylalcohol, 2-amino-2-methylpropanol, triethylamine and diethylmethylamine were measured, in many cases as a function of temperature, over the whole mole fraction or solubility range. Apparent and partial molal heat capacities, volumes and expansibilities were derived. The concentration dependence of these functions suggest the existence of transitions in some of these systems, in the water-rich region, qualitatively similar to micellization. The large relaxation contribution observed with some of the thermodynamic functions of hydrophobic alcohols and amines suggests a reinforcement of hydrophobic hydration due to strong hydrogen-bonding interactions of the polar groups with water.     

An application of the modified Poisson- Boltzmann equation in studies of osmotic properties of micellar solutions

The spherical cell model of colloidal solutions is applied in calculations of the osmotic pressure of micellar systems. The predictions of the nonlinear Poisson-Boltzmann equation (MPB) and of the Modified Poisson-Boltzmann equation (MPB) containing the leading terms of the fluctuation potential and the exclusion volume corrections to the mean potential acting on simple ions are compared with the results of recent computer simulations. Both PB and MPB seem satisfactory for solutions with monovalent counterions while the MPB is preferable for studies of the solutions containing divalent countenons.On leave from the University of Ljubljana, Ljubljana, Yugoslavia     

Vapor pressure,speciation, and chemical activities in highly concentrated sodium borate solutions at 277 and 317°C

The system H₂O-B₂O₃-Na₂O has been studied experimentally at 277 and 317°C. The activities of water and boric acid have been determined at mole ratios Na/B from 0 to 1.5, and total dissolved solids 3 to 80 weight percent. The activity of boric acid has been fitted to within experimental error using a speciation model with eight complex species. This model is consistent with the model previously published by Mesmer et al. The electrolyte properties of the liquid are modeled using the Pitzer-Simonson model of very concentrated electrolyte solutions. The calculated values of water activity agree with experiment, and the activity of NaOH and pOH have also been calculated. The potassium borate system also was briefly studied at 317°C, and is adequately described by a model with five complex species. The potassium borate liquid is more alkaline at K/B= 1 than a sodium borate liquid at the same mole ratio, but pOH in the two systems is the same at lower mole ratios.     

The phase diagram of KNO3-KClO3

The binary phase diagram of KNO₃-KClO₃ is studied by means of differential scanning calorimetry (DSC) and high-temperature X-ray diffraction. The limited solid solutions, K(NO₃)_1−x(ClO₃)_x (0<x<0.20) and K(NO₃)_1−x(ClO₃)_x (0.90<x<1.0), were formed in the KNO₃-based solid solutions and KClO₃-based solid solutions phase, respectively. For KNO₃-based solid solutions, KNO₃ ferroelectric phase can be stable from 423 to 223 K as a result of substituting of NO₃ by ClO₃-radicals. The temperatures for solidus and liquidus have been determined based on limited solid solutions. Two models, Henrian solution and regular solution theory for KNO₃-based (α) phase and KClO₃-based (β) phase, respectively, are employed to reproduce solidus and liquidus of the phase diagram. The results are in good agreement with the DSC data. The thermodynamic properties for α and β solid solutions have been derived from an optimization procedure using the experimental data. The calculated phase diagram and optimized thermodynamic parameters are thermodynamically self-consistent.     

6AZO-CONTAINING SELF-ASSEMBLY ULTRA-THIN FILMS AND THEIR PHOTOVOLTAIC PROPERTIES

A kind of azo-containing resin (Azo-R) was synthesized by a simple way through the coupling reaction of 2-nitro-N-methyldiphenylamine-4-diazoresin (NDR) with phenol, and a new covalentely attached multilayer film from Azo-R as H-donor and photosensitive diazoresin, diphenylamine-4-diazoresin (DR) as H-acceptor via H-bonding attraction by selfassembly technique has been fabricated. Following the decomposition of diazonium group of DR under exposure to UV light, the H-bonds between the layers of the film convert to covalent bonds and the film becomes very stable toward polar solvents or electrolyte aqueous solutions. Thus the UV-irradiated azo-containing films can be used to measure photocurrent in a conventional three-electrode photoelectrochemical cell using KCl as supporting electrolyte. It was confirmed that the azo-containing multilayer film is responsible for the photocurrent generation.     

On the properties of surfactant aqueous solutions

Summary From studies of aqueous solutions of dodecylammoniumnitrate an association mechanism has been proposed involving multiequilibrium. In the concentration range considered we can differentiate between two aspects: ranges of marked qualitative and quantitative changes and formation of differently structured surfactant species.

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Zusammenfassung Aus der Untersuchung wäßriger Lösungen von Dodecylammoniumnitrat würde ein Assoziationsmechanismus abgeleitet, welcher ein Multiequilibrium beinhaltet. Im untersuchten Konzentrationsbereich können zwei Bereiche unterschieden werden: Bereiche mit ausgeprägten qualitativen und quantitativen Änderungen und Bereiche mit der Bildung von verschieden strukturierten oberflächenaktiven Spezies.

     

Equations for calculation of the pH of buffer solutions containing sodium or potassium dihydrogen phosphate, sodium hydrogen phosphate, and sodium chloride at 25°C

Published thermodynamic data measured in aqueous mixtures of sodium or potassium dihydrogen phosphate with hydrogen phosphate and chloride at 25°C were used to test recently developed methods for calculation of the pH of phosphate buffer solutions. Equations for ionic activity coefficients are used in these methods. It is shown that all data used in the tests up to an ionic strength of about 0.5 mol-kg^-1 can be accurately predicted by the two methods recommended. In one of these methods, equations of the Hückel type are used for ionic activity coefficients and in the other equations of the Pitzer type. Several sets of phosphate buffer solutions are recommended,e.g., for calibrations of glass electrode cells. In the recommended sets, the pH of the buffer solutions can be calculated either by the Hückel or Pitzer method, and the pH predictions of these methods agree in most cases within 0.005 at least up to ionic strengths of about 0.2 mol-kg^-1. The pH values of the two primary pH standards endorsed by IUPAC based on aqueous mixtures of KH₂PO₄ and Na₂HPO₄,i.e., pH values of 6.865 and 7.413, can also be accurately predicted by the equations recommended in this study.