On the modelling of solid state reactions.Synthesis of YAG

There is a model of yttrium aluminium garnet (YAG) synthesis presented in this article. The developed model is based on nonlinear reaction–diffusion partial differential equations. The solution was carried out numerically using finite difference techniques. We got dependability curves for diffusion and reaction rates and offered possible method to localize values of diffusion and reaction rate constants precisely enough.AMS subject classification: 35K57, 65M06     

Ionic transport phenomenon across sol–gel derived organic–inorganic composite mono-valent cation selective membranes

Organic–inorganic composite mono-valent cation selective membranes (MCSMs) were prepared by sol–gel under acidic conditions, in which sulfonic acid groups were introduced at the inorganic segment. Studies on physicochemical and electrochemical properties revealed their excellent mechanical, thermal, and oxidative stabilities, high conductivity, ion-exchange capacity, permselectivity for mono-valent cations, ionic diffusion and water transport number. These properties suggested the suitability of MCSMs, especially Si-65%, for electro-separation of Na⁺ from Ca²⁺, Mg²⁺, and Fe³⁺. The effect of electrolyte solution on the characteristics of the current–voltage (i–v) curve in MCSM was studied based on the concentration polarization. Electro-transport of different ions in terms of plateau length and concentration profiles for different ions in the solution phase, diffusion boundary layer and membrane phase were presented. Information obtained from i–v curve analysis were validated by electrodialysis (ED) experiments for individual or mixed electrolyte solutions. Electro-transport efficiency and separation factor of different ions for MCSM and Nafion117 (N117) membranes were compared, which suggested suitability of MCSMs for separating cations.     

Chronoammetric Determination of the Lithium Transfer Rate in Carbon Electrodes

The diffusion processes, which proceed in an Li _x C₆ electrode under potentiostatic conditions (when a potential step is applied), are considered. The passive film, which continuously exists on the surface of the electrode, has a pronounced effect on the current–time plot and quantitative diffusion parameters, which are determined chronoammetrically. An analytical solution of the diffusion problem is obtained for small deviations from equilibrium. Experimental current–time plots for thin lithium–carbon electrodes are well described by the theoretical equations; simultaneously, the passive-layer resistance, the diffusion coefficient for lithium in carbon, and the derivative of the electrode potential with respect to its composition, , are determined.     

Computer simulation of the steady state currents at enzyme doped carbon paste electrodes

The plate-gap model of porous enzyme doped electrode has been proposed and analyzed. It was suggested that reaction diffusion conditions in pores of bulk electrode resemble particular conditions in thin gap between parallel conducting plates. The model is based on the diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetic of the enzymatic reaction inside gap. Steady state current was calculated for the wide range of given parameters and substrate concentrations. All dependences of current on substrate concentration were approximated by hyperbolas in order to obtain “apparent” parameters (maximal currents and apparent Michaelis constants) of modelled biosensors. Simple approximate relationships between given and apparent parameters were derived. The applicability of theoretical plate-gap model was tested for the case of carbon paste electrodes which were doped with PQQ – dependent glucose dehydrogenase. It was found, that soluble glucose dehydrogenase based biosensors exhibit characteristic features of the theoretical plate-gap biosensors.     

Electrodeposition of Lu on W and Al electrodes: Electrochemical formation of Lu–Al alloys and oxoacidity reactions of Lu(III) in the eutectic LiCl–KCl

The electrodeposition of lutetium on inert electrodes and the formation of lutetium–aluminium alloys were investigated in the eutectic LiCl–KCl in the temperature range 673–823 K. On a tungsten electrode, the electroreduction of Lu(III) proceeds in a single step and electrocrystalization plays an important role. Experimental current–time transients are in good agreement with theoretical models based on either instantaneous or progressive nucleation with three dimensional growth of the nuclei, depending on the working temperature. The diffusion coefficient of Lu(III) was determined by chronopotentiometry by applying the Sand equation. The activation energy for diffusion was found to be 31.5 ± 1.3 kJ mol⁻¹. Al₃Lu and mixtures of Al₃Lu and Al₂Lu, characterized by XRD analysis and SEM, were obtained from the LiCl–KCl melt containing Lu(III) by potentiostatic electrolysis using an Al electrode. The activity of Lu and the standard Gibbs energies of formation for Al₃Lu were estimated from open-circuit chronopotentiometric measurements. The E–pO²⁻(potential–oxoacidity) diagram for Lu–O stable compounds in LiCl–KCl at 723 K has been constructed by combining theoretical and experimental data. In this way, the apparent standard potential for the Lu(III)/Lu system has been determined by potentiometry. Potentiometric titrations of Lu(III) solutions with oxide donors, using a yttria stabilized zirconia membrane electrode “YSZME” as a pO²⁻ indicator electrode, have shown the stability of LuOCl and Lu₂O₃ in the melt and their solubility products have been determined at 723 K.     

Some comments on diffusion in ternary systems

The diffusion coefficients in the ternary system NaCl (0.3 m)–NH₄Cl (0.3 m)–H₂O at 25° C have been measured. Some aspects of the diffusion equations for ternary systems are discussed within the range of applicability of the Gouy technique and based on the gravitational stability of free diffusion layers.     

LC Determination of Mono-Substituted Phenols in Water Using Liquid–Liquid–Liquid Phase Microextraction

A simple liquid–liquid–liquid microextraction device of new design was used to pre-concentrate phenols from water samples before liquid chromatographic (LC) analysis. Extraction was induced by the pH difference inside and outside an organic phase located at the interface. The pH of the donor phase outside the organic phase was adjusted to 1 with HCl whereas the acceptor phase was a basic solution at pH 13. On stirring neutral phenols were extracted into the organic solvent then back-extracted into 1 μL of basic acceptor solution suspended from the tip of a micro syringe. The acceptor phase was then withdrawn into the micro syringe and injected directly into the LC. The technique uses a low-cost disposable extraction ‘device’ and is very convenient to operate. Up to 230-fold enrichment of analytes could be achieved. This procedure could also serve as a sample clean-up step because neutral and basic compounds were not extracted into the acceptor phase. The RSD (n = 5) was better than 6.2% and the linear calibration range was from 1 to 1000 µg–L⁻¹ with r ² ≥ 0.992.Optimization of experimental conditions (rate of stirring, ionic strength of the sample solution, concentration of reagents, time of extraction, and organic solvent volume) were also examined. The method was applied to the determination of phenols in tap and well waters.Revised: 14 February and 29 March 2005     

Steady-state Ion Transport through a Three-Layered Membrane System: A Mathematical Model Allowing for Violation of the Electroneutrality Condition

A relatively simple mathematical model based on the Poisson equation is considered. The model is intended for modeling transport through multilayered ion-exchange membranes operating at overlimiting currents. The boundary-value problem is solved by a numerical method of parallel shooting and by an approximate method based on the assumption that the charge density is distributed quasi-uniformly. Concentration profiles in diffusion layers and membranes, current–voltage curves, and dependences of effective transport numbers on the current density are examined.     

The Charging of a Dielectric Fluid during Its Flow Near a Plane Metal Plate

The problem of the charging of a dielectric fluid during its streamline flow near a plane metal plate is solved. An electric potential is specified at the plate. Simple dependences of the electric charge density and electric current on the problem parameters are obtained. The current–voltage characteristic of the plate is found.     

Viscosities and intradiffusion coefficients in the ternary system NaCl−MgCl2−H2O at 25°C

The intradiffusion coefficients of Na⁺, Cl^– ions and water and the tracerdiffusion coefficients of Ca²⁺ ion have been measured in the ternary system NaCl–MgCl₂–H₂O at 25°C. The intradiffusion coefficients of Mg²⁺ in this system have been estimated from the corresponding Ca²⁺ diffusion measurements. Viscosities were measured at the same solution concentrations as were used for the diffusion experiments. Intradiffusion and tracerdiffusion coefficients in a range of temperatures from 5 to 45°C are reported for standard sea-water which is a member of the above ternary set.     

Review and theoretical analysis of ac–av methods for the investigation of hydrogen insertion: Part II. Entry side impedance, transfer function and transfer impedance formalism

The formalism related to alternating current–voltage methods is reviewed, completed and unified for hydrogen insertion in metals and alloys, in relation to permeation cell membranes with potentiometric or potentiostatic detection of hydrogen and electrodes with impermeable boundary conditions. The electrochemical system representation in terms of an electrical dipole or quadripole is first given to introduce the impedance on the entry side, the transfer impedances and the potential and current density transfer functions through the membranes, which can be used experimentally to investigate hydrogen insertion. Next, the surface process is presented, taking the direct (one-step) insertion mechanism into consideration for the sake of simplicity. Based on the surface process and diffusion formalisms, theoretical expressions are derived for the entry side impedance, transfer functions and transfer impedances, depending on the electrode or membrane type and the boundary conditions.     

Study of the effect of the membrane composition on ion transfer across a supported liquid membrane

The rate of ion transfer across the supported liquid membrane (SLM) is studied in the rotating diffusion cell (RDC), varying the chemical composition of the SLM from net-cloth supported gel membranes to radiation-grafted polymer membranes. Steady-state current–voltage curves are measured as a function of the rotation rate, and values for the standard rate constant, k⁰, are determined for a series of tetraalkylammonium cations from the analysis of the initial slopes and the diffusion limiting currents. The analysis gives values for k⁰ of the order of 10⁻²–10⁻⁴ cm s⁻¹, which is in rather good agreement with the values found in the literature for this type of the system. As controlled delivery of ionic drugs can be achieved by control of the electric current, whereby the SLM acts as a drug reservoir, the study is extended to the release of the anti-Alzheimer drug Tacrine, where ion-exchange fibers are embedded in the membrane as the drug carrier. Our previous transient experiments are also discussed, and it is suggested that their interpretation is seriously hampered by the non-uniform potential distribution, which brings about high capacitive currents.     

Simple and selective method for determination of iodide in pharmaceutical products by flow injection analysis using the iodine–starch reaction

This work exploited the well-known iodine–starch reaction for development of a simple flow-injection (FI) method for determination of iodide in pharmaceutical samples. Iodide in an injected zone was oxidized to iodine. A gas diffusion unit enables selective permeation of iodine through a hydrophobic membrane. Detection was made very selective for elemental iodine by employing formation of the I₃ ^––starch complex. The detection limit (3S/N) of the system was 1 mg I L^–1. For a liquid patent medicine used for asthma treatment we suggested modification of the system. Direct injection of this sample, which contains a particularly high concentration level of iodide (ca. 9000 mg I L^–1), can be achieved by coupling a dialysis unit to the FI system. This has increased the working range to 6000–10,000 mg I L^–1 without employing complicated nanoliter injection.     

Low pressure vapor–liquid equilibrium in ethanol + congener mixtures using the Wong–Sandler mixing rule

Phase equilibrium in binary ethanol mixtures found in alcoholic beverage production has been analyzed using a cubic equation of state (EoS) and suitable mixing and combining rules. The main objective of the study is the accurate modeling of the congener concentration in the vapor phase (substances different from ethanol), considered to be an important enological parameter in the alcohol industry. The Peng–Robinson (PR) equation of state has been used and the Wong–Sandler (WS) mixing rules, that include a model for the excess Gibbs free energy, have been incorporated into the equation of state constants. In the Wong–Sandler mixing rules the van Laar (VL) model for the excess Gibbs energy has been used. This combination of equations of state, mixing rules and combining rules are commonly applied to high pressure phase equilibrium and have not yet been treated in a systematic way to complex low pressure ethanol mixtures as done in this work. Nine binary ethanol + congener mixtures have been considered for analysis. Comparison with available literature data is done and the accuracy of the calculations is discussed, concluding that the model used is accurate enough for engineering applications.     

Spatially Dependent Kinetics of Electrons and Excited Atoms in the Column Plasma of a He–Xe dc Discharge

The radially varying kinetics of electrons and excited atoms in the cylindrical axially homogeneous positive column of a dc glow discharge in a gas mixture of helium and 2% xenon was studied. The experimental investigations comprise the radially resolved measurements of the isotropic part of the electron velocity distribution function (EVDF) using a single-probe technique and of the densities of atoms in the lower excited states by using a laser diode absorption method. The theoretical investigations are based on the solution of the space-dependent kinetic equation for the EVDF and the balance equations of excited gas atoms. Besides a strict solution, various simplified treatments of the electron kinetics as the conventional homogeneous approach and the nonlocal approach have been applied. The electron kinetic behavior in the helium–xenon column plasma changes remarkably with increasing helium gas pressure from a distinctly nonlocal behavior at a low pressure of 100 Pa to a nearly local behavior at a medium pressure of 600 Pa.     

Analytic calculation of phase diagrams for solutions containing colloids or globular proteins

Second-order Barker–Henderson perturbation theory gives phase diagrams for colloid and protein solutions that include stable and metastable fluid–fluid, solid–fluid, and solid–solid phases. The potential of mean force is described by a hard-sphere interacting with a Yukawa potential. Calculations for different ranges of attraction show that, as expected, fluid–fluid coexistence becomes metastable when the potential becomes short-ranged. For a very short-ranged Yukawa potential, the phase diagram shows isostructural solid–solid equilibria with a critical point. To test more simplified models, phase diagrams from second-order Barker–Henderson perturbation theory are compared with those from the random-phase approximation for the fluid phase and the van der Waals theory for the solid phase; this comparison shows significantly different phase diagrams. Moreover, with a potential of mean force with primary and secondary minima, calculations using second-order perturbation theory identify conditions where colloidal and protein solutions can present two fluid–fluid regions, each with a critical point; however, the higher-density fluid–fluid region is likely to be metastable. The analytic calculations described here may be useful for interpretation of experimental phase diagrams and for guiding design of separation processes.     

Laser-based characterization of a flame-assisted plasma

A well-characterized flame-assisted plasma was developed to understand the role of flow nonuniformities and plasma/wall interactions in plasma devices for use in validation of laser-based Doppler shift spectroscopic methods. A hydrogen/oxygen capillary diffusion flame burner was used as a plasma source, with barium seeded into the reactants to provide a source of ions and electrons. For analysis the plasma was assumed to be a stationary, partially ionized, collision dominated, thermal plasma consisting of barium ions, electrons, and neutrals between two parallel-plate electrodes. The plasma was examined in terms of the continuum equations for ions and electrons, together with Poisson's equation to predict spatial profiles of electron and positive ion density and potential as functions of applied potential. First an analytic solution based on constant plasma properties and negligible difusion was introduced. The model was then extended by including effects of diffusion and variable plasma properties. Experimentally, current/voltage characteristics of the plasma were measured conventionally, relative ion concentration and temperature were measured with laser-induced fluorescence, and local potential distribution was measured using an electrostatic probe. The diffusionless theory predicted well the bulk behavior of the plasma, but not the correct spatial distributions of ion concentration and potential. The extended model produced a more satisfactory fit to the data. At conditions of 1.4 equivalence ratio, 70 torn pressure, 300 ppm seed concentration, and 100–400 V applied potentials, electric fields of the order of 10², 10³ V/cm were observed near the powered electrode, and of few tens of V/cm in the hulk of tire plasma. The field strength in the sheath ensures the operation of the Doppler shift diagnostics, once the recommendations tor LIF signal detectability are fulfilled.     

Electrochemical reactivity at redox-molecule-based nanoelectrode ensembles

A model describing electrochemical reactivity at nanoelectrode ensembles consisting of redox-molecule-based active sites immobilized on otherwise passivated electrode surfaces is presented. A mathematical treatment in terms of hemispherical diffusion of redox-active solutes to a layer of independent molecule-based nanoelectrode sites is shown to be equivalent to one in terms of a bimolecular diffusion-limited reaction between a layer of immobilized redox molecules and a reservoir of redox-active solutes. This equivalence derives from the fact that in both cases the mass-transfer problem is essentially that of hemispherical diffusion. The model is further developed to consider rate limitation by both the bimolecular redox reaction between the active-site molecule and redox molecules in solution and the heterogeneous redox reaction between the electrode and the active-site molecule. Analytical expressions are derived for the current–voltage relation corresponding to catalyzed electron transfer at an ensemble of redox-molecule-based nanoelectrode sites, and the expressions are used to interpret preliminary data for ultrasensitive electrochemical detection in flow streams via an electrochemical amplification process that is thought to involve redox mediation by individual analyte molecules adsorbed onto monolayer-coated electrodes.     

Exact solution of Schrödinger equation with deformed ring-shaped potential

Exact solution of the Schrödinger equation with deformed ring-shaped potential is obtained in the parabolic and spherical coordinates. The Nikiforov–Uvarov method is used in the solution. Eigenfunctions and corresponding energy eigenvalues are calculated analytically. The agreement of our results is good.AMS Subject Classification: 03.65.–w, 12.39.Jh, 21.10.–k     

Dielectric Studies of Glycine–Ethylene Glycol–Water Solutions Using Time Domain Reflectometry

Time domain reflectometry (TDR) has been used for dielectric relaxation measurements on the glycine–ethylene glycol–water ternary system (TDR) at 25, 30, 35, and 40°C in the frequency range from 10 MHz to 10 GHz. Glycine–ethylene glycol–water solutions are prepared with different concentrations of ethylene glycol (0, 5, 10, 15, 20, and 30%) and also for different glycine molar concentrations (0, 0.2, 0.4, 0.6, 0.8, and 1 M). The dielectric relaxation parameters are measured for aqueous glycine solutions also to compare the results with those for the glycine–ethylene glycol–water ternary system. For all the solutions considered, only one relaxation peak was observed in this frequency range. The complex permittivity spectra for the aqueous glycine solutions can be well described by the Cole–Davidson expression, whereas that for the ternary system can be well described by the Havriliak–Negami expression. The logarithm of the relaxation time log() shows a nonlinear relation with the glycine molar concentration that implies a change in the relaxation mechanism with glycine concentration. The dielectric strength increases with an increase in glycine molar concentration, whereas it decreases with an increase in ethylene glycol concentration.