Analytical solution of nonlinear diffusion processes in modified electrode

The system of coupled nonlinear diffusion equations are solved analytically for the transport and kinetics of electrons and reactant in the layer of a modified electrode. Analytical expressions of concentrations of mediator and substrate are presented using Homotopy perturbation method. A simple expression of electrochemical rate constant K _ME⁺ is also obtained for all values of reaction parameters. The available limiting case results are compared with our results and are found to be in good agreement.     

On the nature of the first excited states of the uranyl ion

Results of calculations on the uranylion using the LCAO MO Hartree—Fock—Slater method including relativistic effects are reported. The highest occupied molecular orbital is calculated to be σ_u, consisting predominantly of U 5f character. The σ_u orbital is the HOMO partly because of “pushing-from-below” by the U 6p orbital, but also as a result of the change in potential of the U 5f electrons with the uranium core elections brought about by relativistic contraction of the core electrons. This effect also determines the character of the first virtual levels (δ_u and Φ_u, respectively) in equatorial ligand fields.     

Calculation of Combined Diffusion Coefficients from the Simplified Theory of Transport Properties

The aim of this study is to check if it is possible to use the combined diffusion coefficients introduced by Murphy at equilibrium in a two-temperature model (electron temperature T_e different from that of heavy species T_h), such as that defined by Devoto and Bonnefoi for transport properties. On the one hand, the two-temperature (2-T) theory of transport properties was established by Devoto and Bonnefoi by separating electrons and heavy species because of their mass difference. Their simplified theories allow the calculation of transport coefficients (except diffusion) out of thermal equilibrium, but it has to be noted that when T_e tends toward T_h, the results are those obtained with an equilibrium calculation. On the other hand, Murphy's combined diffusion coefficients describe the diffusive mixing of two nonreactive ionized gases at equilibrium. First, the exact combined diffusion coefficients of Murphy are calculated for an Ar–N₂ (50 wt.%) mixture at atmospheric pressure. Expressions of combined diffusion coefficients are then obtained by using the simplified theory of Bonnefoi at thermal equilibrium. The results of the calculation of combined diffusion coefficients from the simplified theory of transport properties, assuming Te=Th, are compared with those of Murphy at equilibrium. It is shown that large discrepancies occur as soon as the ionization degree is over 10%. These results prove that the simplified 2-T theory of transport coefficients cannot be used for the treatment of diffusion, probably because the mass flux of electrons is no longer constrained. Thus, a new theory of transport coefficients has to be developed, taking into account the coupling of electrons and heavy species.     

Synthesis,structures and magnetic properties of a series of polynuclear copper(II)‐lanthanide( III) complexes assembled with carboxylate and hydroxide ligands

Heterometallic copper(II)‐lanthanide(III) complexes have been made with a variety of exclusively O‐donor ligands including betaines (zwitterionic carboxylates) and chloroacetate, which are dinuclear CuLn, tetranuclear Cu₂Ln₂, pentanuclear C_u3Ln₂, and octadecanuclear C_u12 complexes. The results show that subtle changes in both the carboxylates and acidity of the reaction solution can cause drastic changes in the structures of the products. Magnetic studies exhibit that shielding of the Ln³⁺ 4f electrons by the outer shell electrons is very effective to preclude significant coupling interaction between the Ln³⁺ 4f electrons and Cu²⁺ 3d electrons in either a mono‐atomic hydroxide‐bridged, or a carboxylate‐bridged system.     

Ion induced ridge electrons and their diffraction in solid foil targets

We present detailed double differential distributions of electrons emitted downstream when 100 and 170 keV protons interact with thin carbon, gold and aluminuum foils and compare them to those obtained with protons and neutral hydrogen projectiles interacting with helium gas. The distributions obtained with the gas target show, besides the well known convoy electron peak produced by capture or loss of electrons into the continuum of the emerging ion, a narrow ridge that is aligned with the beam direction. This ridge, which is attributed to electrons moving in the two Coulomb center potential saddle determined by the target and projectile ions, also appears in the ion-solid electron distributions. A typical solid state effect consists in the appearance of two strong lateral humps which are explained as due to diffraction of the ridge electrons in the three dimensional lattice of the polycrystalline foil material. Contrarily the diffraction of convoy electrons is impeded by their strong correlation to the moving ions. In the case of the Aluminuun target the observed diffraction is typical for Al₂O₃. This indicates that the observed electrons originate from a thin polycrystalline oxyde layer close to the downstream surface of emission.     

Current functional theory for multi-electron configuration

The density functional theory (DFT) formalism is reformulated into a framework of currents so as to give the energy a parameter dependent behaviour, e.g., time. This “current” method is aimed at describing the transition of electrons from one orbital to another and especially from the ground state to an excited state and extended to the relativistic region in order to include magnetic fields which is relevant especially for heavy metallic compounds. The formalism leads to a set of coupled first order partial differential equations to describe the time evolution of atoms and molecules. The application of the method to ZnO and H₂O to calculate the occupation probabilities of the orbitals lead to the results that compare favorably with those obtained from DFT. Furthermore, evolution equations for electrons in both atoms and molecules can be derived. Applications to specific examples of small molecules (being metallo-oxides and water) are mentioned at the end.     

Dimensional Matching versus Induced‐Fit Distortions: Binding Affinities of Planar and Curved Polyaromatic Hydrocarbons with a Tetragold Metallorectangle

A tetragold(I) rectangle‐like metallocage containing two pyrene‐bis‐imidazolylidene ligands and two carbazolyl‐bis‐alkynyl linkers is used for the encapsulation of a series of polycyclic aromatic hydrocarbons (PAHs), including corannulene. The binding affinities obtained for the encapsulation of the planar PAHs guests in CD₂Cl₂ are found to exponentially increase with the number of π‐electrons of the guest (1.3 > logK >6.6). For the bowl‐shaped molecule of corannulene, the association constant is much lower than the expected one according to its number of electrons. The molecular structure of the host–guest complex formed with corannulene shows that the molecule of the guest is compressed, while the host is expanded, thus showing an interesting case of artificial mutual induced‐fit arrangement.     

Self-Consistent Analysis of a Helium Plasma in a Cylindrical Hollow Cathode

The helium plasma in a cylindrical, axially symmetric direct current hollow cathode discharge is theoretically investigated. A self-consistent hybrid method is used to describe the radial behaviour of the plasma components and the electric field around the axial centre of the discharge. The hybrid method includes the solution of an equation system consisting of Poissons equation and fluid equations for electrons, ions and excited helium atoms. Using the electric field and excited atom densities obtained in this system, the space-dependent transport and collision rate coefficients of the electrons are obtained by a kinetic treatment of the electrons. This treatment is based on a powerful multi-term method for solving the inhomogeneous Boltzmann equation in cylindrical coordinates. The theoretical results obtained for a discharge current of some mA and a pressure of few Torr are compared with available experimental ones.     

Reaction kinetics of hydrated electrons in a quaternary micro emulsion system: A pulse radiolysis study

The pulse-radiolysis technique has been employed to produce and study the kinetics of hydrated electrons (e_aq⁻) in a quaternary micro emulsion (Sodium Lauryl Sulfate (NaLS)/water/cyclohexane/1-pentanol) system. Two orders of magnitude higher life time (20 μs) of the e_aq⁻ has been obtained as compared to that in reverse micelles reported earlier. Several probes including a biomolecule have been used to determine the water pool concentrations and quenching constants (k_q). The observed yield and half life (t_1/2) of the hydrated electrons vary smoothly as the water droplet sizes are changed. The bimolecular rate constants for the reaction of e_aq⁻ with different solutes have been determined. It has been observed that the measured bimolecular rate constants for the reaction of hydrated electrons with different solutes are indicative of the solubilization sites, the water core sizes, and the surrounding environment. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet: 30: 699–705, 1998     

Fermionic and bosonic coupled channel calculations in momentum space for electron-positron pair creation in relativistic heavyy-ion collisions

Electron-positron pair creation in relativistic heavy ion collisions is non-perturbatively described by coupled channel equations in a coordinate system with equal constant, but opposite velocities of the ions. The basis states are obtained by discretizing the states of the free Dirac equation in the positive and negative continuum. With the standard (fermionic) coupled channel method the free pair production in Pb⁸²⁺ on Pb⁸²⁺ atE _1ab=10 GeV/nucleon is calculated. In order to treat multiple pair production with a reduced number of states we introduce a bosonic formalism for the electron-positron pairs in the framework of coupled channels including the rescattering of the electrons and positrons by the electromagnetic field of the ions. We apply this formalism to collisions of Pb⁸²⁺ on Pb⁸²⁺ atE _1ab=200 GeV/nucleon.     

Film thicknesses determined by X-ray photoelectron spectroscopy

The knowledge of the reduced thickness of overlayers in the thickness range up to 5 nm is a valuable contribution to quantitative analysis in XPS. A new method for its determination is described which can be applied to most of the commercially available instruments. The method considers influences like countrate statistics, surface roughness, thickness distribution, elastic electron scattering, divergence of the photoelectrons detected by the spectrometer and energy dependence of the inelastic mean free path of the electrons in matter. The reliability of the results is verified by XPS-measurements performed on SiO₂-layers on Si.Besides, the XPS-results obtained from Si₃N₄-layers on Si measured under different take-off angles demonstrate the applicability of this method for the investigation of film growth. A further aspect is given by the recognition of elastic electron scattering by a simplified expression no longer asking for Monte Carlo calculations.     

Influence of Pt promoter on the photo-oxidative degradation by visible-light plasmonic Pt-titania catalyst

Nanometer platinum-deposited titania particles were prepared through a soft chemical reduction method. The physico-chemical properties of the obtained products are analyzed by X-ray diffraction, UV-vis diffuse reflectance spectroscopy, and photoluminescence spectra. The as-prepared metal-TiO₂ nanohybrid was found to show excellent photocatalytic reactivity toward rhodamine-B decomposition. In the current case, chemical reduction of hydrogen hexachloroplatinate by glucose results in the intercalation of metallic platinum into the titania matrix. The deposited platinum atoms were featured by surface-plasmon resonance under visible-light excitation and electrons from platinum nanoparticles would transfer to the conduction band of titania and accelerate the formation O₂^*− to degrade dye molecule. As a consequence, platinum deposition onto TiO₂ surface is confirmed to yield a superior photocatalytic performance over the naked titania.     

Brownian dynamics simulations of the reactions of hydrated electrons with components of DNAs and a DNA double-helix

As a first step toward developing simulation models for studying the indirect mechanism of radiation damage to DNAs, we have carried out Brownian dynamics simulations to study the reactions of hydrated electrons with a 12-base-pair B-DNA, (dA)₁₂(dT)₁₂, and with bases, monodeoxynucleotides, and polydeoxynucleotides. We first studied in detail the sensitivity of diffusion reaction rate constants to different model and simulation parameters. Based on the sensitivity studies, a set of model and simulation parameters was obtained for the final production runs. The use of this set of parameters reduced the computational costs but delivered reasonably reliable results. The calculated reaction rate constants were in qualitative agreement with experiments. For the DNA double-helix, (dA)₁₂(dT)₁₂, the simulations demonstrated that hydrated electrons preferred to attack the two ends of the double-helix. Electrostatic interactions between the DNA and the hydrated electrons make the T strand more susceptible to attack than the A strand. The increased reactivity of the T strand due to electrostatic interactions results from the increased reactivity of the C6 sites of the thymine bases, at the expense of the reactivity of the C8 sites of the adenine bases. The reactivity of the relatively buried reactive sites of the adenine and thymine bases are less affected by electrostatic interactions. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 888–901, 1997     

An SCF study of P4O6 and P4O10

The electronic structures of the oxides P₄O₆ and P₄O₁₀ are calculated by the self-consistent molecular orbital method including all valence electrons and the 3d orbitals on phosphorus. It is found that the former molecule appears to be virtually non-polar whilst in the latter, the P-O (terminal) bonds are highly polar. The bond order matrix shows that the internal P-P bonding in the P₄ unit is not marked.     

Fulfilling the 2(N+1)2 Hirsch rule in smaller hollow fullerenes. Evaluation of long‐range magnetic behavior and NMR patterns of C28, , C24N4, and C28H4

The formation of different 32 π‐electron systems derived from a prominent small fullerene given by C₂₈, allows to evaluate several approaches ensuring an electronic shell closure in terms of the characteristic chemical shift anisotropy (CSA) and long‐range magnetic response properties for spherical aromatic compounds. Our results show that the inclusion of extra electrons and the doping of the cage, are able to sustain a long‐range shielding cone when an external field is oriented in a specific orientation. Such properties are inherent characteristics of spherical aromatic compounds, which are not obtained in the neutral C₂₈ fullerene, and in the exo‐bonded approach leading to C₂₈H₄. Thus, the doping of the cage is suggested as the most suitable approach to modify the overall count of electrons, leading to the expected response properties for further design of highly aromatic fullerenes.     

Applications of spectral-Representation model as a potential method for Cu clusters

We applied the spectral-representation technique developed by Katsuki and Huzinaga as a model potential in calculating the electronic structure of Cu clusters. The characteristics of this potential were closely investigated in Cu and Cu₂. For Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, we performed all-electron ab initio self-consistent field calculations and model-potential calculations where 3p, 3d, and 4s electrons, and 3d and 4s electrons are treated as valence electrons. The ionization potentials (IPs) given by the all-electron calculations were 6.26, 5.55, 4.52, 4.02, and 4.08 eV for Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, respectively. The IPs given by the model-potential calculations were 6.25, 5.56, 4.62, 4.09, and 4.23 eV for the 3p-, 3d-, and 4s-valence electrons, and 6.26, 5.68, 4.71, 4.07, and 4.19 eV for the 3d- and 4s-valence electrons. The IPs given by the model-potential calculations agree well with those of the all-electron calculations. We also performed model-potential calculations where only the 4s electrons were treated as valence electrons. The calculated IPs were 6.47, 5.98, 5.38, 4.63, and 4.88 eV for Cu, Cu₂, Cu₅, Cu₉, and Cu₁₃, respectively. These are ca. 0.8 eV higher than the IPs by the all-electron calculation for the larger clusters of Cu₅, Cu₉, and Cu₁₃. The higher IPs originate from the expulsion of the 3d electrons from the valence electrons. We also performed model-potential calculations with 4s electrons for Cu₇₄. The calculated IP is 4.61 eV, which is estimated to be 0.8 eV larger than that obtained by the all-electron calculation. The IPs with correlation corrections are 7.7, 7.4, 6.3, 5.8, 5.9, and 5.6 eV for Cu, Cu₂, Cu₅, Cu₉, Cu₁₃, and Cu₇₄, respectively. Experimental values are 7.73, 7.37, 6.30, 5.37, 5.67, and 5.26 eV. The agreement between the two is fairly good. The electron affinities are also discussed. © 1996 by John Wiley & Sons, Inc.     

Thermalization lengths of “subexcitation electrons” in water determined by photoinjection from metals into electrolyte solutions

Ranges of 0–4 eV electrons in aqueous electrolyte solutions have been measured using the technique of photoinjection. Variations of the method based on investigation of the dependence of the photoinduced charges on scavenger concentration, the intensity of incident light and time (in nanosecond scale) are used. The values of electron ranges in H₂O are found to amount to 80 Å and in D₂O—110 Å. The mechanism of thermalization of slow electrons in water is discussed. It is caused, mainly, by non-local losses associated with the excitation of the vibration-rotation matter spectrum. During thermalization the slow electrons are subject to numerous elastic scatterings whose cross-section is close to a gas-phase one.     

Correlation energies in the spin-density functional formalism

It has been shown recently that dynamical correlation effects can be adequately described by using an electron-gas expression for correlation between electrons of different spins. In this paper the method is applied to the calculation of excitation energies for the first- and second-row atoms and to the determination of ground-state properties for small polyatomic molecules, such as CH₂, CH₄, CH ₄ ⁺ , CH ₅ ⁺ . Additionally, deficiencies of the method for cases with few electrons and strongly varying electron density are investigated and an empirical correction to the electron-gas approximation is proposed. This correction is based on atomic data and gives an overall improvement for test molecules with two to four electrons.     

Preparation and Ultrafast Optical Characterization of Metal and Semiconductor Colloidal Nano-Particles

The ultrafast dynamics of photoinduced electrons in several metal and semiconductor colloidal nanoparticle systems are characterized using femtosecond laser spectroscopy. Various preparation methods are used and, in several cases, modified for making particles with long-term stability and narrow and controllable size distributions. The particle size and size distribution are determined using transmission electron microscopy and electronic absorption spectroscopy. For aqueous gold and silver colloids, spatial size confinement is found to cause substantially slower electronic relaxation due to reduction of non-equilibrium electron transport and weaker electron-phonon coupling. In gold colloids, photoejection of electrons into the liquid is observed, which is attributed to a two-photon enhanced ionization process. The effect of surfactant on the electron dynamics in CdS colloids is examined and found to be significant, substantiating the notion that electrons are dominantly trapped at the liquid-solid interface. In Ru³⁺-doped TiO₂ colloids, the electronic decay is found to be as fast as or even faster than in undoped TiO₂ and other semiconductor colloids such as CdS, suggesting that ion doping of large bandgap semiconductor colloids is not necessarily effective in lengthening the electron lifetime. In almost all cases studied, the majority of the photoinduced electrons are found to decay within a few tens of picoseconds due to non-radiative relaxation. The results are discussed in the context of the potential applications of metal and semiconductor nano-particles in areas including photocatalysis and photoelectrochemistry.