Real-space study of the growth of magnesium on ruthenium

The growth of magnesium on ruthenium has been studied by low-energy electron microscopy (LEEM) and scanning tunneling microscopy (STM). In LEEM, a layer-by-layer growth is observed except in the first monolayer, where the completion of the first layer in inferred by a clear peak in electron reflectivity. Desorption from the films is readily observable at 400 K. Real-space STM and low-energy electron diffraction confirm that sub-monolayer coverage presents a moir\'e pattern with a 1.2 nm periodicity, which evolves with further Mg deposition by compressing the Mg layer to a 2.2 nm periodicity. Layer-by-layer growth is followed in LEEM up to 10 ML. On films several ML thick a substantial density of stacking faults are observed by dark-field imaging on large terraces of the substrate, while screw dislocations appear in the stepped areas. The latter are suggested to result from the mismatch in heights of the Mg and Ru steps. Quantum size effect oscillations in the reflected LEEM intensity are observed as a function of thickness, indicating an abrupt Mg/Ru interface.Comment: 21 pages, 10 figure

Some considerations on the fundamentals of chemical kinetics: steady state, quasi-equilibrium, and transition state theory

The elementary reaction sequence A ↔ I → P is the simplest mechanism for which the steady-state and quasi-equilibrium kinetic approximations can be applied. The exact integrated solutions for this chemical system allow inferring the conditions that must fulfil the rate constants for the different approximations to hold. A graphical approach showing the behavior of the exact and approximate intermediate concentrations might help to clarify the use of these methods in the teaching of chemical kinetics. Finally, the previously acquired ideas on the approximate kinetic methods lead to the proposal that activated complexes in steady state rather than in quasi-equilibrium with the reactants might be a closer to reality alternative in the mathematical development of Transition State Theory (TST), leading to an expression for the rate constant of an elementary irreversible reaction that differs only in the factor 1-k (k being the transmission coefficient) with respect to that given by conventional TST, and to an expression for the equilibrium constant of an elementary reversible reaction more compatible with that predicted by chemical thermodynamics

Two Rate constant kinetic model for the chromium(III)-EDTA complexation reaction by numerical simulations

The complexation reaction of Cr(III) ion in the presence of a large excess of EDTA does not follow a pseudo-first-order kinetics as sometimes suggested. There are two causes for the deviation from this simple behavior: the involvement of a long-lived intermediate, precluding the application of the steady-state approximation, and the autoinhibition provoked by the release of hydrogen ions from the organic ligand to the medium as the final Cr(III)-EDTA violet complex is formed. Numerical simulations have allowed obtaining for each kinetic experiment the values of two rate constants, k1 (corresponding to the formation of the long-lived intermediate from the reactants) and k2 (corresponding to the formation of the final complex product from the long-lived intermediate), as well as the number of hydrogens liberated per molecule of final complex product formed (Hkin). The results indicate that k1 is associated to a fast step (Ea = 87 ± 4 kJ mol-1) and k2 to a slow step (Ea = 120 ± 2 kJ mol-1), whereas the number of hydrogen ions lies within the range 0 < Hkin < 2 in all the kinetic runs. A mechanism in accordance with the experimental data has been proposed

Oxidation of hexacyanoferrate(II) ion by hydrogen peroxide: evidence of free radical intermediacy

The redox reaction between hexacyanoferrate(II) ion as the reducing agent and hydrogen peroxide as the oxidizing one, in slightly acid (pH 4.36-6.65) aqueous solutions containing phosphate ions, has been studied by means of an UV-Vis spectrophotometer monitoring the formation of Fe(III) at 420 nm. The initial hydrolysis of the Fe(II)-cyanide complex reactant to yield a pentacyanoaquaferrate(II) intermediate, as well as a decrease in the solution pH (acid catalysis), had both a positive effect on the reaction rate, whereas an increase in the concentrations of Fe(III), phosphate and chloride ions, and d-mannitol had a negative effect (inhibition). A computer program, specifically designed for this purpose, allowed arriving at a complex eight-coefficient experimental rate law by application of the initial rate method, accounting for the dependences of the reaction rate on the concentrations of Fe(II), H2O2 and Fe(III). The reaction was characterized by a low value of the apparent activation energy (28.9 ± 2.7 kJ mol−1). Finally, a multi-step reaction mechanism, involving the participation of a penta-coordinated Fe(II) complex, and hydroxyl, superoxide and other free radicals as intermediates, has been proposed. This mechanism was supported by the available experimental information and confirmed by numerical simulations performed via the fourth order Runge-Kutta integration method

Ligand sequential replacement on chromium(III)-aqua complexes by L-alanine and other biological amino acids: a kinetic perspective

The ligand sequential replacement on chromium(III)-aqua complexes by L-alanine in slightly acidic aqueous solutions (pH range: 3.55-5.61) has been kinetically followed by means of UV-Vis spectrophotometry. A two rate constant model has been applied to fit the absorbance-time data, corresponding to the formation (k1) and decay (k2) of an intermediate not reactive enough to be in steady state (long-lived intermediate). The kinetic orders of the amino acid were fractional (0.40 ± 0.03 for k1 and 0.40 ± 0.02 for k2). The two steps showed base catalysis, and the activation energies were 60 ± 3 (for k1) and 83 ± 6 (for k2) kJ mol-1. The rate constants for the coordination of the first L-alanine ligand followed the sequence CrOH2+ < Cr(OH)2+ < Cr(OH)3, Cr3+ being almost inactive. This suggests that the increase in the reaction rate with increasing pH was caused by the enhancement of the lability of the Cr(III)-aqua bonds induced by the presence of hydroxo ligands. The activation parameters for a series of ligand substitution on Cr(III)-aqua complexes by organic molecules yielded a statistically significant enthalpy-entropy linear plot with an isokinetic temperature of 296 ± 21 K

Three rate-constant kinetic model for permanganate reactions autocatalyzed by colloidal manganese dioxide: the oxidation of L-phenylalanine

The reduction of permanganate ion to MnO2 Mn2O3 soluble colloidal mixed oxide by L-phenylalanine in aqueous phosphate-buffered neutral solutions has been followed by a spectrophotometric method, monitoring the decay of permanganate ion at 525 nm and the formation of the colloidal oxide at 420 nm. The reaction is autocatalyzed by the manganese product and three rate constants have been required to fit the experimental absorbance-time kinetic data. The reaction shows base catalysis and the values of the activation parameters at different pHs have been determined. A mechanism including both the non-autocatalytic and the autocatalytic reaction pathways, and in agreement with the available experimental data, has been proposed. Some key features of this mechanism are the following: (i) of the two predominant forms of the amino acid, the anionic form exhibits a stronger reducing power than the zwitterionic form; (ii) the non-autocatalytic reaction pathway starts with the transfer of the hydrogen atom in the position of the amino acid to permanganate ion; and (iii) the autocatalytic reaction pathway involves the reduction of Mn(IV) to Mn(II) by the amino acid and the posterior re-oxidation of Mn(II) to Mn(IV) by permanganate ion

Oxidation of hexcacyanoferrate(II) ion by hydrogen peroxide: inhibition by polyalcohols and related compounds

The oxidation of hexacyanoferrate(ll) ion by a large excess of hydrogen peroxide, in slightly acidic aqueous media containing potassium dihydrogen phosphate (pH 5.10 ± 0.05), was followed by monitoring the increase of absorbance at 420 nm as the colorless Fe(ll) complex gradually evolved into the yellow Fe(lll) complex. The reaction was inhibited by OH-containing organic compounds, either alcohols or carbohydrates, and two different inhibition pathways were observed, an iron(III)-independent pathway (rate constant k1) and an iron(III)-mediated pathway (rate constant k2). A BASIC-language computer program was developed in order to use the fourth-order Runge-Kutta integration method to obtain the concentrations of the Fe(ll)-inhibitor complex and the Fe(lll) reaction product. Rate constant k1, whose value is determined by that of the initial rate, decreased slightly as the concentration of alcohol / carbohydrate increased, and a mechanism involving the formation of hydroxyl radicals in a Fenton-like reaction and its posterior scavenging by the organic antioxidant additive has been proposed. Of the 8 inhibiting agents that were tried, the most potent antioxidant under the experimental conditions of this study was D-mannitol. Rate constant k2, whose value is a measurement of the deviation from a pseudo-first order behavior provoked by the inhibiting agent, increased notably as the concentration of the latter increased, and a mechanism involving the complexation of the Fe(lll) product by the organic inhibitor and its posterior outer-sphere one electron reduction from hexacyanoferrate(ll) ion has also been proposed. This might result in a blockage of the regeneration of pentacyanoaquaferrate(ll) ion, an intermediate believed to be essential for the redox reaction to take place

Enthalpy-entropy compensation effect in chemical kinetics and experimental errors: a numerical simulation approach

Many kinetic studies concerning homologous reaction series report the existence of an activation enthalpy-entropy linear correlation (compensation plot), its slope being the temperature at which all the members of the series have the same rate constant (isokinetic temperature). Unfortunately, it has been demonstrated by statistical methods that the experimental errors associated with the activation enthalpy and entropy are mutually interdependent. Therefore, the possibility that some of those correlations might be caused by accidental errors has been explored by numerical simulations. As a result of this study, a computer program has been developed to evaluate the probability that experimental errors might lead to a linear compensation plot parting from an initial randomly scattered set of activation parameters (p-test). Application of this program to kinetic data for 100 homologous reaction series extracted from bibliographic sources has allowed concluding that most of the reported compensation plots can hardly be explained by the accumulation of experimental errors, thus requiring the existence of a previously existing, physically meaningful correlation

Kinetics of the chromium(III)/L-glutamic acid complexation reaction: formation, decay, and uv-vis spectrum of a long-lived intermediate

The kinetics of the aqueous reaction of Cr(III) with either L-glutamic acid or sodium hydrogen L-glutamate at pH 2.46-5.87 have been followed by means of absorbance readings. The rate of formation of the reaction products showed acceleration-deceleration periods, caused by the accumulation and posterior decay of an intermediate in nonnegligible concentration. A double-exponential integrated rate law allowed obtaining two rate constants for each absorbance-time experimental series, associated with the appearance (k1) and decay (k2) of the long-lived intermediate. An increase of the initial concentrations of either hydrogen L-glutamate (apparent kinetic orders < 1) or hydroxide (kinetic orders = 1) ions resulted in an increase of both k1 and k2, but addition of an inert electrolyte (KNO3) resulted in opposite effects on k1 (decrease) and k2 (increase). The experimental activation energies were 83 ± 10 (for k1) and 95 ± 5 (for k2) kJ mol−1. The electronic spectrum of the low reactivity detected intermediate resembled more closely to that of the blue/green reactant than that of the violet reaction product. The low number of protons set free by the complexating hydrogen L-glutamate ligand seems to suggest that some polymerization of the coordinated amino acid (to form a di- or tripeptide) might take place. The available experimental data indicate that the coordination of the organic ligand must be preceded by the breakdown of a strong Cr(III)-H2O chemical bond in the slow steps of the mechanism

Differences in Measuring Market Risk in Four Subsectors of the Digital Economy

This paper defends the wisdom of not considering the Digital Economy to be one homogeneous sector. Our hypothesis is that it is best to consider it the result of adding four different subsectors. We test whether indeed the economic and financial performance of a portfolio of listed companies in each of the four subsectors presents relevant differences. We use the value at risk measure to estimate market risk of the four subsectors of the digital economy. The riskiest subsector is Mobile/Internet Contents & Services followed by SW&IT Services and Application Software. On the contrary, the Telecom sector is by far the safest one. These results support the hypothesis that the Digital Economy is not a homogeneous sector