Adsorption of iodide ions on the Cd(0001) single crystal plane in methanol

The adsorption of I⁻ ions on the Cd(0001) single crystal plane from solutions in methanol has been investigated by impedance measurement method. The ionic charge due to the specific adsorption has been obtained using the mixed-electrolyte method for both electrode charge and electrode potential as the independent electrical variables. The Gibbs energy of adsorption of ions has been calculated using the different modifications of the virial adsorption isotherm. It was found that under comparable conditions, the results obtained at constant electrode potential and at constant electrode charge are coincident and the adsorption of I⁻ anion increases in the sequence of solvents: water < methanol, ethanol, and metals: Cd < Bi. The electrosorption valency has been calculated. It was found that on the Cd(0001) plane the electrosorption valency of I⁻ anions has a constant value that is similar for methanol and ethanol and also for these solvents on Bi single crystal planes.     

Calculation of core-level electron spectra of ionic liquids

On the example of 40 ion pairs (5 cations times 8 anions), this study demonstrates how the core-level binding energy values can be calculated and used to plot theoretical spectra at low computational cost using density functional theory methods. Three approaches for obtaining the binding energy values are based on delta Kohn–Sham (ΔKS) calculations, 1s KS orbital energies, and atomic charges. The ΔKS results show reasonable agreement with the available experimental X-ray photoelectron data. The 1s KS orbital energies correlate well with the ΔKS results. Atomic charge correlation with ΔKS is improved by accounting for the charges of neighboring atoms. Assignment of binding energies to atoms and the applicability of the mentioned methods to model systems of ionic liquids are discussed.     

Electrochemical properties of nanoporous carbon electrodes in various nonaqueous electrolytes

Electrical double layer and electrochemical characteristics at the nanoporous carbon|acetonitrile interface with additions of Et₄NBF₄, Et₃MeNBF₄, EtMe₃NBF₄, LiClO₄, and LiBF₄ have been studied by cyclic voltammetry and impedance spectroscopy methods. A value of zero charge potential, dependent on the structure of the cations as well as on the composition of the anions, the region of ideal polarizability, and other characteristics has been established. Analysis of the complex plane plots shows that the nanoporous carbon|acetonitrile+0.1 M electrolyte (Et₄NBF₄, Et₃MeNBF₄, or EtMe₃NBF₄) interface can be simulated by the equivalent circuit, in which the two parallel conduction parts in the solid and liquid phases are interconnected by the double layer capacitance in parallel with the complex admittance of the hindered reaction of the charge transfer process or of the partial charge transfer (i.e. adsorption stage limited) process. The values of the characteristic frequency depend on the electrolyte composition and on the electrode potential, i.e. on the nature of the ions adsorbed at the surface of the nanoporous carbon electrode. In the region of moderate a.c. frequencies, the modified Randles-like equivalent circuit has been used for simulation of the complex plane plots. In the region of negative surface charge densities, the intercalation process of Li⁺ ions from LiClO₄ and LiBF₄ solutions into the surface film is possible and these data can be simulated using the modified Ho et al. model or Meyer et al. model. Electronic Publication     

Mechanism of the reaction of acetylene with Grignard reagents

Kinetics of the reaction between acetylene and phenylmagnesium bromide were investigated in diethyl ether in the presence of small additions of triethylamine and without a catalyst. The mechanistic scheme suggested by Grignard et al. was supplemented with the reaction of bromomagnesiumacetylene with the Grignard reagent. The rate constants for individual reactions were determined. Triethylamine catalyzes the reactions to different extents, the conversions of bromomagnesiumacetylene being the most susceptible to the catalysis. The possible ways of the action of the catalyst were discussed and the importance of nucleophilic assistance was stressed.     

A discrete collocation method for Fredholm integro-differential equations with weakly singular kernels

A fully discrete version of a piecewise polynomial collocation method is constructed to solve initial or boundary value problems of linear Fredholm integro-differential equations with weakly singular kernels. Using an integral equation reformulation and special graded grids, optimal global convergence estimates are derived. For special values of parameters an improvement of the convergence rate of elaborated numerical schemes is established. Some of our theoretical results are illustrated by numerical experiments.     

On the convergence of spline collocation methods for solving fractional differential equations

In the first part of this paper we study the regularity properties of solutions of initial value problems of linear multi-term fractional differential equations. We then use these results in the convergence analysis of a polynomial spline collocation method for solving such problems numerically. Using an integral equation reformulation and special non-uniform grids, global convergence estimates are derived. From these estimates it follows that the method has a rapid convergence if we use suitable nonuniform grids and the nodes of the composite Gaussian quadrature formulas as collocation points. Theoretical results are verified by some numerical examples.     

Electrochemical impedance study of hydrogen evolution on Bi(001) electrode in the HClO4 aqueous solutions

Electrochemical impedance spectroscopy has been applied for investigation of the hydrogen evolution kinetics at the electrochemically polished Bi(001) plane, and the complicated reaction mechanism (slow adsorption and charge-transfer steps) has been established. The charge-transfer resistance and adsorption capacitance values depend noticeably on the electrode potential applied. The adsorption resistance is maximal in the region of electrode potential E _min = −0.65 V vs. (Hg|Hg₂Cl₂|4 M KCl), where the minimal values of constant phase element (CPE) coefficient Q have been calculated. The fractional exponent α _CPE values of the CPE close to unity (α _CPE ≥ 0.94 and weakly dependent on the electrode potential and pH of solution () have been obtained, indicating the weak deviation of Bi(001)|HClO₄ + H₂O interface from the ideally flat capacitive electrode. Q differs only very slightly from double-layer capacitance C _dl values in the whole region of potentials and , investigated.