The surface potential of a spherical colloid particle: functional theoretical approach

By using the iterative method in functional analysis, the potential of the electrical double layer of a spherical colloid particle, which is represented by the so-called Poisson-Boltzmann (PB) equation, has been solved analytically under general potential conditions. With the help of the diagram method in mathematics, the surface potential of the particle has been defined from the second iterative solution. The influence of the parameters included in the solutions on the surface potential has been studied. The results show that the surface potential of the particle increases as the temperature of the system, the aggregation number, and the concentration of ions increase, but decreases with an increase in the dielectric constant and the valence of the ions. The corresponding space charge density also has been illustrated in this work.     

Study on the Radius of an Electrical Spherical Micelle： Functional Theoretical Approach

For the purpose of eliminating restriction, the Poisson-Bokzmann (PB) equation, which represents the potential of the electrical double layer of spherical miceUes, can be solved analytically only under the lower potential condition, a kind of iterative method in functional analysis theory has been used. The radius of the spherical particle can be obtained from the diagram of the second iterative solution of the potential versus the distance from the center of the particle. The influences of the concentration of the ions, the charge number of ions, the aggregation number of the particle, the dielectric constant of solvent and the temperature of system on the radius also have been studied.     

Kinetic aspects of the ion-exchange reactions of Cs<Superscript>+</Superscript>, Na<Superscript>+</Superscript>, Sr<Superscript>2+</Superscript>and Eu<Superscript>2+</Superscript> ions on the H<Superscript>+</Superscript> form of chromium hexacyanoferrate(II)

Summary This paper reports the radiochemical study of the ion-exchange of Cs⁺, Na⁺, Sr²⁺ and Eu³⁺ ions with H⁺ by chromium hexacyanoferrate(II) which was prepared in a granular form using a gel method. The slow steps which determine the rate of exchange of these ions are directly proportional to the particle diameter and this is confirmed from the linearity test of Bt vs. t plots at different particle diameters. Boyed’s equation and Reichenberg’s tables were used for evaluating all the kinetic parameters. The results reveal that the effective particle radii are unchanged for both chromium hexacyanoferrate(II) dried at 60 and 120 °C. The obtained data were analyzed using McKay plots and Arrhenius equation and the kinetic and thermodynamic parameters, e.g., effective diffusion coefficient, activation energies and entropies of activation have been evaluated. The mobility of these ions inside the particles of chromium hexacyanoferrate(II) decrease in the order of Eu³⁺>Sr²⁺>Na⁺⊃Cs⁺.     

The hard-sphere model for linear and regular star polybutadienes

The dilute solution properties of linear, 18-arm, and 270-arm star polybutadienes have been studied in a theta solvent and in a good solvent. Values of the radius of gyration R_G, the second virial coefficient A₂, the intrinsic viscosity [η], and the diffusion coefficient D₀ have been measured for each polymer. The ratios R_T/R_G, R_V/R_G, and R_H/R_G for each type of polymer are used to compare the four dilute solution properties. R_T is termed the “thermodynamic radius.” It is the radius of the hard sphere with the same excluded volume as the polymer coil. R_T is calculated from A₂ by R_T = (3A₂M₂/16ηN_A)^1/3. R_V and R_H are equivalent hard spheres defined for the intrinsic viscosity and translational diffusion coefficient, respectively. R_T/R_G, R_V/R_G, and R_H/R_G increase from about 0.7 for linear polymer coils as the number of arms in the star increases. Values of the ratios for the 18-arm stars are less than the value for the hard-sphere, but the values of the ratios of the 270-arm stars are equal to the hard-sphere limit within experimental error.     

Osmotic and activity coefficients in the binary solutions of 1-butyl-3-methylimidazolium chloride and bromide in methanol or ethanol at T = 298.15 K from isopiestic measurements

Osmotic coefficients of the binary solutions of two room-temperature ionic liquids (1-butyl-3-methylimidazolium chloride and bromide) in methanol and ethanol have been measured at T = 298.15 K by the isopiestic method. The experimental osmotic coefficient data have been correlated using a forth-order polynomial in terms of (molality)^0.5, with both, ion interaction model of Pitzer and electrolyte non-random two liquid (e-NRTL) model of Chen. The values of vapor pressures of above-mentioned solutions have been calculated from the osmotic coefficients. The model parameters fitted to the experimental osmotic coefficients have been used for prediction of the mean ionic activity coefficients of those ionic liquids in methanol and ethanol.     

Sorption characteristics of an economical sorbent material used for removal radioisotopes of cesium and europium

Application study for the evaluation of sorption characteristics of sawdust as an economical sorbent material used for decontamination of radioisotopes cesium and europium from aqueous solution has been carried out in the present work. In this respect, sawdust (untreated and treated by HNO₃) has been prepared from the commercial processing of wood for furniture production. Pore properties of the activated carbon such as BET surface area, pore volume, pore size distribution, and pore diameter were characterized by N₂ adsorption and DFT software. Radiotracer method onto sawdust from aqueous solutions was studied in a batch technique with respect to pH, contact time, temperature. The kinetics of adsorption of Eu³⁺ and Cs⁺ have been discussed using five kinetic models namely, pseudo-first-order model, pseudo-second-order model, Elovich equation, intraparticle diffusion model, and modified Freundlich equation that have been tested in order to analysis the experimental data. Kinetic parameters and correlation coefficients were determined. It was shown that the second-order kinetic equation could describe the sorption kinetics for two metal ions. The metal uptake process was found to be controlled by intraparticle diffusion. Thermodynamic parameters, such as ΔH, ΔG and ΔS, have been calculated by using the thermodynamic equilibrium coefficient obtained at different temperatures. The obtained results indicated that endothermic nature of sorption process for both ^152+154Eu and ¹³⁴Cs onto sawdust.     

A new algorithm for solving large inhomogeneous linear system of algebraic equations

An algorithm based on a small matrix approach to the solution of a system of inhomogeneous linear algebraic equations is developed and tested in this short communication. The solution is assumed to lie in an initial subspace and the dimension of the subspace is augmented iteratively by adding the component of the correction vector obtained from the Jacobi scheme on the coefficient matrix A (A^TA, if the matrix A is nondefinite) that is orthogonal to the subspace. If the dimension of the subspace becomes inconveniently large, the iterative scheme can be restarted. The scheme is applicable to both symmetric and nonsymmetric matrices. The small matrix is symmetric (nonsymmetric), if the coefficient matrix is symmetric (nonsymmetric). The scheme has rapid convergence even for large nonsymmetric sparse systems.     

泛函数迭代法求解反胶束内双电层电势

用泛函数分析理论中的迭代法求解了反胶束内关于双电层势的Poisson- Boltzmann（PB）方程，导出了泛电位下的第一、二次迭代的解析表达式。与 Debye-Huckel（DH）线性近似及计算机的数值解进行对比表明，迭代解不仅在低电 位条件下能与两者相符合，而且在高电位下与数值解在相吻合。     

Solvatochromic parameters for binary mixtures of an ionic liquid with various protic molecular solvents

Abstract  

Solvatochromic parameters (E _T ^N, normalized polarity parameter; π*, dipolarity/polarizability; β, hydrogen-bond acceptor basicity; α, hydrogen-bond donor acidity) have been determined for binary mixtures of propan-2-ol, propan-1-ol, ethanol, methanol and water with recently synthesized ionic liquid (IL; 2-hydroxyethylammonium formate) at 25 °C. In all solutions except aqueous solution, E _T ^N values of the media increase abruptly with the ILs mole fraction and then increase gradually to the value of pure IL. A synergistic behavior is observed for the α parameter in all solutions. The behavior of π* and β are nearly ideal for all solutions except for solutions of methanol with the IL. The applicability of nearly ideal combined binary solvent/Redlich–Kister equation was proved for the correlation of various solvatochromic parameters with solvent composition. The correlation between the calculated and the experimental values of various parameters was in accordance with this model. Solute–solvent and solvent–solvent interactions were applied to interpret the results.     

Diffusion of protons in silica hydrogel

The effect of preparation pH of silica hydrogel on the effective diffusion coefficient of protons in silica hydrogel (D _e , m²/s), on surface area of silica gel (S, m²/s) and on particle size of silica gel (D _p , mm) was studied. Silica hydrosols were obtained by adding water glass to sulfuric acid. The effective diffusion coefficient of proton in silica hydrogel was determined by the method of diffusion from silica hydrogel plane sheet to a stirred solution of a limited volume. A numerical solution was obtained for the diffusion equation using the Regula Falsi method. Regression analyses of experimental data were conducted.Diffusion of protons in silica hydrogel is a complicated process due to a decelerating effect of the porous structure of silica hydrogel and to the accelerating effects of slow ions such as Na⁺ and surface diffusion. The effective diffusion coefficient increased with surface area of silica gel, indicating the diffusion of protons on the surface of the silica particles.     

Solvatochromic parameters for binary mixtures of an ionic liquid with various protic molecular solvents

Abstract  Solvatochromic parameters (E _T ^N, normalized polarity parameter; π*, dipolarity/polarizability; β, hydrogen-bond acceptor basicity; α, hydrogen-bond donor acidity) have been determined for binary mixtures of propan-2-ol, propan-1-ol, ethanol, methanol and water with recently synthesized ionic liquid (IL; 2-hydroxyethylammonium formate) at 25 °C. In all solutions except aqueous solution, E _T ^N values of the media increase abruptly with the ILs mole fraction and then increase gradually to the value of pure IL. A synergistic behavior is observed for the α parameter in all solutions. The behavior of π* and β are nearly ideal for all solutions except for solutions of methanol with the IL. The applicability of nearly ideal combined binary solvent/Redlich–Kister equation was proved for the correlation of various solvatochromic parameters with solvent composition. The correlation between the calculated and the experimental values of various parameters was in accordance with this model. Solute–solvent and solvent–solvent interactions were applied to interpret the results. Graphical Abstract  Predicted values of solvatochromic parameters (SP) (E _T ^N, normalized polarity parameter; π*, dipolarity/polarizability; β, hydrogen-bond acceptor basicity; α, hydrogen-bond donor acidity) from the correlation equations versus its experimental values for binary mixtures of 2-hydroxyethylammonium formate with water, methanol, ethanol, propan-1-ol and propan-2-ol.      

Analysis of a polydisperse system using small-angle X-ray scattering

The small-angle X-ray data from a polydisperse solution of sodium silicate have been measured in the concentration range 3.6–169 mg/cm³ using aKratky camera. The following values of the particle parameters were obtained: the average radius of gyration =7.5 nm, the average particle weight =900 000, the average volume =671 nm³, and the average particle surface area =717 nm².From the above parameters and the apparent specific volume, analysed to be 0.422 cm³/g, the water content of the silicate particles was determined to be 3% (by weight).From small-angle X-ray measurements, performed on solutions exposed to a hydrodynamic field, it is indicated that at least the larger particles in the solution have a relatively symmetric shape. Based on this observation it was assumed that the particles in solution are spherical, and particle size distribution functions were calculated using a least-squares program. It was found that the distribution cannot be described by a simple function, such as aGaussian function; instead, the distribution follows a histogram with three local maxima.Dedicated to Prof. Dr. Dr.Otto Kratky, Graz, on the occasion of his 80th birthday.     

Surface characterization and thermodynamics of adsorption of Sr2+, Ce3+, Sm3+, Gd3+, Th4+, UO 2 2+ on activated charcoal from aqueous solution

Surface parameters of the activated charcoal were measured using precise instrumental techniques for dehydration, carbon content, trace metals impurities, anions, bulk, tap and true densities, surface area, pore volume, porosity and average particle diameter. The adsorption of Sr²⁺, Ce³⁺, Sm³⁺, Gd³⁺, Th⁴⁺ and UO ₂ ²⁺ ions on activated charcoal from aqueous solution was studied as a function of temperature. Thermodynamic parameters such as HH ⁰ and S ⁰ were calculated from the slopes and intercepts of the linear variation of lnK ₁ vs. 1/T, whereK ₃ is obtained from Langmuir equation. The results show endothermic heats of adsorption, but negative free energy values indicate that the adsorption process of metal ions on activated charcoal is favored at high temperature. The value of isosteric heat of adsorption, calculated from the Clausius-Clapeyron equation, shows that the surface of the activated charcoal is heterogeneous with respect to activity. A wavelength dispersive x-ray fluorescence spectrometer was used for measuring the concentration of metal ions.     

Adsorption and thermodynamic behavior of uranium(VI) on <Emphasis Type="Italic">Ulva sp</Emphasis>.-Na bentonite composite adsorbent

Summary The algae-clay composite adsorbent was tested for its ability to recover U(VI) from diluted aqueous solutions. Macro marine algae (Ulva sp.) and clay (Na bentonite) were used to prepare composite adsorbent. The ability of the composite adsorbent to adsorp uranium(VI) from aqueous solution has been studied at different optimized conditions of pH, concentration of U(VI), temperature, contact time. Parameters of desorption were also investigated to recover the adsorbed uranium. The adsorption patterns of uranium on the composite adsorbent followed the Freundlich and Dubinin-Radushkevich isotherms. The thermodynamic parameters such as the enthalpy ΔH, entropy ΔS and Gibbs free energy ΔG were calculated from the slope and intercept of lnK_d vs. 1/T plots. The results suggested that the Ulva sp.-Na bentonite composite adsorbent is suitable as sorbent material for recovery and biosorption/adsorption of uranium ions from aqueous solutions.     

Transport processes in the sorption of colored ions by peat particles

A three-step model has been proposed for the adsorption of Astrazone Blue dye (Basic Blue 69) on peat. The initial rate of uptake of dye ions due to physical adsorption and chemisorption (ion exchange) has been correlated using a surface mass transfer coefficient. These coefficients have been determined and expressed in the dimensionless mass transfer form, Sh/Sc^0.33, as a function of agitation, initial dye concentration, peat particle size range, dye solution temperature, and mass of peat.     

Mixed Ligand Complexes of Chromium (III) Ethylenediamine Tartrate: A Polarographic Study

Polarographic techniques have been used to investigate the complexing behaviour of chromium (III)-ethylenediamine-tartrate in aqueous solution. These complexes are reduced irreversibly at the dropping mercury electrode. The stability constants have been calculated by the method of Sundaresan and Sundaram. The values of the kinetic parameters; standard rate constant (K_s), transfer coefficient (α) and activation energy (Q) have also been calculated in each case.     

Crystal field calculation of g values and zero-field splitting for high spin ferric complexes of rhombic character

For high spin ferric ions in rhombic symmetry, we have used a crystal field model to relate term splittings of the ⁴ T ₁, ² T ₂ and ⁴ T ₂ excited states to zerofield split energies and g values of the ⁶ A ₁ term. In this model five crystal field parameters were used, namely, one cubic parameter, two tetragonal parameters and second and fourth order rhombic parameters. In tetragonal symmetry with only three crystal field parameters, a simpler model including only the ⁴ T ₁ and ² T ₂ excited states is adequate to relate term energies to g values and zero-field split energies. However, we have demonstrated the importance of the ⁴ T ₂ state in rhombic crystalline fields. No higher lying terms other than ⁴ T ₂ can influence the ⁴ T ₁ term directly through the tetragonal or rhombic crystal field, Furthermore, we show that the fourth order rhombic crystal field parameter is a key parameter because the rhombic splitting of the dominant low lying ⁴ T ₁ term of high spin ferric complexes depends to first order on the fourth order crystal field potential. We have performed a computer diagonalization of the spin-orbit, electrostatic and crystal field perturbation matrix, and calculated g values and zero-field splittings in seventeen high spin ferric mixed crystalline species of varying rhombicities and for metmyoglobin and cytochrome P-450. The high spin and spin-mixed regions are developed completely to yield the crystal field term energies, zero-field splittings and basis functions together with g values.     

The thermodynamic properties of solutions of sodium chloride,water, and 1-propanol

The temperature-concentration dependences of the activity coefficient of NaCl in aqueous solutions of 1-propanol at 298 and 318 K, solution ionic strength up to 3m, and alcohol contents of 10–40 wt % were determined by the method of electromotive forces with ion-selective electrodes. The results were used to estimate interaction parameters in the Pitzer model. The Darken method was used to calculate the integral Gibbs energy of solutions.     

Ionic contribution to the complex dielectric constant of a polymer under dc bias

A diffusion equation for the distribution of ionic impurities in a polymer under a dc field has been solved analytically for the conditions that neither injection nor absorption of impurity ions takes place at either electrode and that the ions do not interact. By using the solution of the diffusion equation, an ionic contribution to the complex dielectric constant is calculated. The most important results are as follows. (1) At high temperatures and low frequencies, the dielectric loss factor of the polymer decreases exponentially with the time elapsed after the application of the dc bias. (2) The dielectric constant is not greatly affected by the bias. (3) The ionic contribution to the loss factor in the absence of the dc bias is represented as ?_i^″ = 4πνDq²/ωkT, where ν is the density of mobile ions, D the diffusion coefficient, q the charge of an ion, ω the angular frequency, k the Boltzmann constant, and T the absolute temperature. (4) A method is presented for distinguishing between the apparent activation energy for diffusion and that for generation of mobile ions.     

Thermal membrane potential across cation-exchange membranes for various halide solutions

Thermal membrane potential across cation-exchange membranes was measured for various halide solutions. Linear relationships between thermal membrane potential () and temperature difference (T) were observed, and the temperature coefficient of thermal membrane potential (/T) decreases with increase in the molality of the external solution as predicted by a theory reported. When counterions of membranes are hydrogen ions, the sign of the coefficients turns into minus near 0.01 mol/kg of the external solution for all membranes, although the coefficients are always positive for all the other forms. The dependence of the coefficients on the molality of the external solutions sometimes deviated slightly from the theory. This deviation is attributed to some change in water content of the membranes. A reproducible method of measuring water content of membranes was applied to discuss the change in the state of the membranes.