Search results for "Equilibrium"
showing 10 items of 1021 documents
Theory of the growth mode for a thin metallic film on an insulating substrate
2002
We have developed a novel theory predicting the growth mode of a thin metallic film on an insulating substrate. This combines ab initio electronic structure calculations for several ordered metal/insulator interfaces (varying both coverage and substrate lattice constant), with a thermodynamic approach based on microscopic calculations. We illustrate this approach for Ag film deposited on MgO(0 0 1) substrate. Ab initio calculations predict high mobility of adsorbed silver atoms on the perfect magnesia surface even at low temperatures. Our theoretical analysis clearly demonstrates that the growth of metallic islands is predominant at the initial stage of silver deposition, which agrees with …
Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital
2012
Abstract This paper develops a method for proving the existence of competitive equilibrium in a distorted/non-optimal one-sector economy–a discrete time variant of the Romer model–without conditions on the equilibrium value of the marginal product of capital. Existence is obtained under weaker conditions than in Le Van et al. (2002) . Moreover, we provide an existence result for an economy with a regressive tax studied in Santos (2002) . The proofs rely on ideas of Becker and Boyd (1997) .
Equilibrium between Hydroxycycloalkanones and Oxabicycloalkanols
2009
Guido Kramer, Annette Oehlhof, and Herbert Meier Institute of Organic Chemistry, University of Mainz, Duesbergweg 10 – 14, 55099 Mainz, Germany Reprint requests to Prof. Dr. H. Meier. Fax: +49-(0)6131-3925396. E-mail: hmeier@mail.uni-mainz.de Z. Naturforsch. 2009, 64b, 847 – 850; received April 8, 2009 Hydroxycycloalkanones 1 of medium ring size (8 – 10) exist in a transannular tautomeric equilibrium with the corresponding oxabicycloalkan-1-ols 2, which represent hemiacetals. Normally, the bicyclic structures 2 predominate in solution although their portion decreases with increasing solvent polarity. A correlation of the Gibbs reaction enthalpies ∆G (1→2) with the solvent parameters ET (30)…
Intramolecular proton transfer of serine in aqueous solution. Mechanism and energetics
2000
Serine amino acid in aqueous solution is theoretically studied at the B3PW91/6-31+G** level using a dielectric continuum solvent model. Neutral and zwitterionic structures in the gas phase and in solution are described and the proton-transfer mechanism is discussed. A neutral conformation in which the carboxyl hydrogen atom is already oriented toward the amino group seems to be the absolute energy minimum in the gas phase and the most stable neutral form in solution. The absolute energy minimum in solution is a zwitterionic form. The energy barrier for proton transfer is predicted to be very small, in particular when zero-point-energy contributions are added. Our calculations allow the dyna…
Untersuchung des Solvatationsgleichgewichts im ternären system Tetrachlormethan/Polymethylmethacrylat/Benzol durch kernmagnetische relaxation
1971
Im ternaren System CCl4/Polymethacrylate(PMMA)/Benzol tritt praferentielle Solvatation auf, Benzol ist in der Solvathulle des Polymeren angereichert. Es genugt eine Solvatationsgleichgewichtskonstante, um die praferentielle Solvatation bei variablen Konzentrationsverhaltnissen zu beschreiben. Gemessen wurde die Kernmagnetische Relaxationszeit T1 von Benzol in Abhangigkeit von der Polymerkonzentration. Der Vergleich mit analogen Messungen im System C6D6/PMMA/C6H6 ergibt fur die Solvatationsgleichgewichtskonstante K = (c32 · c10)/(c12 · c30) = 2,5 ± 0,5. Hierbei bedeuten: c10 die CCl4-Konzentrationen im „freien” Losungsmittel, c30 die Benzolkonzentrationen im „freien” Losungsmittel, c12 und c…
The kinetics of anionic polymerization of styrene in 1,2-dimethoxiethane
2007
Kinetic measurements in a flow apparatus in combination with conductance measurements, permit the determination of the two equilibrium constants Kes and Kdiss* and the three propagation rate constants k(±)c, k(±)s and k(−) as a function of temperature. The great differences in the polymerization rate in various solvents are mainly caused by their influence on the equilibrium constants. The influence of the solvent on the rate constants is not greater than in other chemical reactions.
NMR relaxation and solvation equilibrium in the ternary system CCl4-polymethylmethacrylate-benzene
2007
In the ternary system CCl4-PMMA-benzene, benzene is preferentially adsorbed in the solvation shell of the polymer. One solvation equilibrium constant allows a satisfactory description of the preferential solvation for a large range of solvent compositions. The nuclear magnetic relaxation time T1 of benzene protons was measured for different values of the polymer concentration. The measurements are compared with analogous measurements in the system C6D6-PMMA-C6H6 where no preferential solvation is to be expected. For the system CCl4-PMMA-benzene the resulting dimensionless solvation equilibrium constant is K = c32c10/c12c30 = 2.5 ± 0.5 where c10 is the CCl4 concentration in the “free” solven…
Application of conductometric and pH metric measurements in determining the kinetics and equilibrium parameters of the heterophasic ion exchange: Met…
2019
The application possibilities of conductometric and pH metric measurements in the description of the process of heterophasic ion exchange have been analysed, between metal cation (Zn, Cu) - proton, which occurs according to the formula, M+ + HR ⇄ H+ + MR, where R is an anion permanently bound in the sorbent. Kinetic models of the pseudo-first and pseudo-second order reactions, as well as the Langmuir isotherm model which describes the process equilibrium, have been used in mathematical presentations. It was confirmed that conductometric and pH metric measurements are equally effective in the assessment of such processes' parameters, in comparison with the expensive method of determining met…
Self-organization and nanostructural control in thin film heterojunctions.
2013
In spite of more than two-decades of studies of molecular self-assembly, the achievement of low cost, easy-to-implement and multi-parameter bottom-up approaches to address the supramolecular morphology in three-dimensional (3D) systems is still missing. In the particular case of molecular thin films, the 3D nanoscale morphology and function are crucial for both fundamental and applied research. Here we show how it is possible to tune the 3D film structure (domain size, branching, etc.) of thin film heterojunctions with nanoscale accuracy together with the modulation of their optoelectronic properties by employing an easy two-step approach. At first we prepared multi-planar heterojunctions w…
Stackelberg equilibrium with many leaders and followers. The case of zero fixed costs
2017
Abstract I study a version of the Stackelberg game with many identical firms in which leaders and followers use a continuous cost function with no fixed cost. Using lattice theoretical methods I provide a set of conditions that guarantee that the game has an equilibrium in pure strategies. With convex costs the model shows the same properties as a quasi-competitive Cournot model. The same happens with concave costs, but only when the number of followers is small. When this number is large the leaders preempt entry. I study the comparative statics and the limit behavior of the equilibrium and I show how the main determinants of market structure interact. More competition between the leaders …