Self-Diffusion of Co2+ Ions in CoBr2, CoI2 and Electrolyte-Diffusion of ZnSO4 in Agar Gel Medium

Self-diffusion of Co²⁺ ions in CoBr₂ and CoI₂ is reported in the concentration range of 10^–5 to 0.25M in 1% agar gel at 25 °C. The deviations observed between the experimental and theoretical values of diffusion coefficients are explained by considering different types of interactions occurring in the ion-gel water system. The applicability of the transition state theory to the diffusion of ZnSO₄ in agar gel medium is tested by varying the temperature as well as the gel concentration at high concentration of the electrolyte. The activation energy E and D ₀ value decrease with increasing gel concentration in agreement with the theory.     

Tracer diffusion of Co2+ ions in some transition metal sulphates in agar gel

Tracer diffusion of Co²⁺ ions is studied in agar gel medium in the presence of some transition metal sulphates using the zone diffusion technique. A comparison between the experimental and theoretical values of diffusion coefficients computed on the basis of Onsager's theory shows a divergence between them. These deviations are explained on the basis of various effects in the iongel-water system.     

Tracer and self-diffusion of rosebengal sodium131I in 1% agar gel medium

Tracer and self-diffusion coefficients for Rosebengal labelled with¹³¹I are determined in agar gel medium at different temperatures and the activation energies for the two processes are determined by zone diffusion technique. The slight difference in tracer and self-diffusion values observed is small enough to be consistent with Hertz's recent theory of linear response of tracer diffusion coefficients in electrolyte and non-electrolyte systems.     

Diffusion of Cesium Ions in Agar Gel Containing Alkali Metal Bromides

The present paper gives an account of different aspects of the tracer diffusion of Cs⁺ ions in alkali metal bromides. We have measured the diffusion coefficients, D, of cesium ions in 1% agar gel medium at 25 ^∘C using a zone-diffusion technique over a concentration range of 5 × 10⁻⁵ to 0.1 mol,dm⁻³. The values of the diffusion coefficients were found to deviate from theory, which are explained on the basis of different types of interactions occurring in the ion-gel-water system. The study is also focused on the effect of alkali metal bromides on the obstruction effect and activation energy for the tracer-diffusion of cesium ions in agar gel medium. It is observed that both parameters, extent of obstruction, ∝, and activation energy, E, decrease with increasing charge density of the cation of the supporting electrolyte. The influence of these trends is explained on the basis of competitive hydration between the ions and agar molecules, and the relative distortion in the water structure that is brought about by these different ions and agar molecules.     

Tracer-diffusion of cobalt ions in sodium and potassium nitrates in agar gel

Tracer-diffusion of Co²⁺ ions is studied in agar gel in the presence of sodium and potassium nitrates at 25°C. The diffusion coefficient values at various electrolyte concentrations are compared with the corresponding theoretical values computed on the basis of Onsager's theory. The deviations from the theory are attributed to the various co-occurring effects in the diffusion medium. The activation energy for the process of diffusion of Co²⁺ ions in presence of above electrolytes is also reported.     

Binary diffusion coefficients of phenolic compounds in subcritical water using a chromatographic peak broadening technique

Infinite dilution diffusion coefficients of certain phenolic compounds were measured as a function of temperature in water slightly acidified with formic acid using the Taylor dispersion method. The diffusion coefficients calculated using the chromatographic peak broadening technique were found to increase exponentially with an increase in the temperature. The diffusion coefficients of the selected phenolic compounds did not vary as a function of their molecular weights and the diffusion coefficients of the phenolic compounds increased as a function of temperature (from 2.16 × 10⁻¹⁰ m² s⁻¹ at 298 K to 5.79 × 10⁻¹⁰ m² s⁻¹ at 413 K for malvidin-3,5-diglucoside). However, for some phenolic compounds such as gallic acid monohydrate, quercetin-3-β-d-glucoside, protocatechuic acid and (−)-epicatechin, there were difficulties in making measurements above temperatures of 352 K, 372 K, 392 K and 413 K, respectively, due to thermal degradation of the phenolic compounds in water above these temperatures. The experimentally measured diffusion coefficients of the phenolic compounds were correlated as a function of temperature and solvent viscosity and were compared with those predicted using theoretical models. The validity of the Stokes-Einstein diffusion model in predicting the diffusion coefficients of the phenolic compounds in hot pressurized water was also evaluated.     

Diffusion current at microdisk electrodes—application to accurate measurement of diffusion coefficients

Stationary electrodes (platinum and glassy carbon) were used for accurate measurement of diffusion coefficients. The theoretical diffusion current-time profile was calculated by digital simulation, by means of which the diffusion coefficient and the product of the charge number of electrode reaction n and the reactant concentration c^o were determined simultaneously from a single chronoamperogram. The feasibility of the method was demonstrated by measuring the diffusion coefficients of Tl(I) ions. When the nc^o value agreed with the corresponding known value, the diffusion coefficients were in good agreement with the standard values determined by the thin-walled hanging mercury drop electrode method. The diffusion coefficient of hexacyanoferrate(III) ions in 1 mol dm^?3 KCl at, 25°C was also determined.     

Combined sorption/transport of sodium dodecyl sulfate and hydrochloric acid in a blend of cellulose acetate butyrate with cellulose acetate hydrogen phthalate

The transport of hydrochloric acid (0.001-0.1 M) and sodium dodecyl sulfate (0.001-0.1 M) has been measured through a membrane consisting of a blend of cellulose acetate butyrate and cellulose acetate hydrogen phthalate. The cellulose derivative blend is suggested to suffer an alteration in the degree of hydrophobicity when in equilibrium with sodium dodecyl sulfate (SDS) through hemimicelle formation. An increase in surface hydrophobicity of the blend when in equilibrium with SDS solution was observed by fluorescence measurements using the vibronic bands of the probe pyrene, as well as by water desorption kinetics; a decrease of the effective diffusion coefficients from 1.2 × 10⁻¹¹ m² s⁻¹ in the absence of SDS to approximately 2 × 10⁻¹³ m² s⁻¹ in its presence was found. The value obtained for the mutual diffusion coefficient of HCl in the concentration range 0.001-0.1 M (D=4.2×10⁻¹⁴ m² s⁻¹) shows also that the membrane presents hydrophobic features. The flux of SDS in the blend membrane at different pH values shows two distinct permeation rates depending on the cmc. However, from the calculation of permeability coefficients at SDS concentrations below the cmc a clear decrease in P is found, whilst, at concentrations above the cmc the permeability coefficients are nearly constant, only showing a slightly increase. The diffusion coefficients of SDS in the blend increase over the whole SDS concentration range analysed and show an effective diffusion coefficient 2-3 orders of magnitude below the diffusion coefficients of SDS in aqueous solutions. This fact suggests that the only diffusing species are SDS unimers. The presence of HCl in the SDS bulk solution has the effect of increasing the permeability and diffusion coefficients. Mutual analysis of permeation and diffusion coefficients and sorption isotherms shows that, on decreasing the pH, the interactions between SDS and the polymer network decrease. This is also reflected in a clear decrease of the hydrophobic interactions between the diffusing and polymeric species, provoked by a decrease in the unimer-unimer association.     

Influence of some amino acids on the dynamic swelling behavior of radiation-induced acrylamide hydrogel

The influence of some amino acids—alanine, glycine, valine, glutamine, histidine, phenylalanine, and tryptophan—on the swelling behavior of acrylamide (AAm) hydrogel prepared by γ-radiation was investigated. Swelling experiments of AAm hydrogel were made in the universal buffer solutions and the amino acid solutions at certain pHs at 37°C. These selected pH values were pK₁, pK₂ and isoelectric point (pI) values such as ionization of α-carboxyl groups, ionization of α-amino groups, and the pIs of the amino acids, respectively. The swelling of AAm hydrogel increased when pH values of solutions were increased. The value of equilibrium swelling of AAm hydrogel in the solution of universal buffer was 880% at pH 10.0, whereas it was 670% at pH 2.0. The values of equilibrium swelling of AAm hydrogel in amino acid solutions were between 830 and 965% at pH 10.0, whereas they were between 635 and 775% at pH 2.0. The rate constant of swelling, initial swelling rate, theoretical maximum swelling, diffusional exponent, network parameter, and diffusion coefficient were calculated by swelling kinetics. Diffusions of the amino acid solutions into the hydrogel were generally found as non-Fickian in character. The diffusion coefficients of the hydrogel were between 0.91 × 10⁻⁶ and 2.41 × 10⁻⁶ cm²/s.     

Tracer-diffusion of Zn2+ ions in cobalt sulphate

Tracer-diffusion of Zn²⁺ ions in the presence of CoSO₄ is studied at 25°C in 1% agar gel over a concentration range of 10^–5 to 0.25M using a zone-diffusion technique. The deviations observed between experimental and theoretical values of diffusion coefficients are explained by considering different types of interactions occurring in the ion-gel-water system. Further, study of the obstruction, effect in the diffusion of Zn²⁺ ions at different concentrations of CoSO₄ reveals that the -value decreases with increasing concentration of the electrolyte. This observation is accounted on the basis of competitive hydration between ions and agar molecules.     

Ternary diffusion coefficients of diethanolamine and N-methyldiethanolamine in aqueous solutions containing diethanolamine and N-methyldiethanolamine

Ternary diffusion coefficients of diethanolamine (DEA) and N-methyldiethanolamine (MDEA) in aqueous solutions containing DEA and MDEA using the Taylor dispersion technique have been measured for temperatures (303.2, 313.2, and 323.2 K). The systems studied were aqueous solutions containing total amine concentrations of 2.5 and 4.0 kmol m⁻³, each having four different amine molar ratios. The density and viscosity of the blended amine solutions were also measured. The mutual diffusion coefficients of aqueous DEA and aqueous MDEA solutions were also reported. The main diffusion coefficients (D₁₁ and D₂₂) and the cross-diffusion coefficients (D₁₂ and D₂₁) were reported as function of temperature and concentration of alkanolamines. The limiting conditions for the main diffusion coefficients and the cross-diffusion coefficients were discussed at first, and a comparison between the ratios of the cross-diffusion coefficients to the main diffusion coefficients for DEA and MDEA was made. The dependence of the main diffusion coefficients on the viscosity of solutions was also investigated.     

Turing pattern formation in anisotropic medium

Diffusion of reacting species in chemical and biochemical systems in anisotropic medium is markedly different from those occurring in isotropic medium, therefore approximating diffusion coefficients as constants may not be desirable as this has dynamical consequences. This paper is devoted to the analytical and numerical investigation of the development of spatial patterns in such systems. To this end we consider a general reaction–diffusion system with concentration-dependent diffusion and formulate a scheme to derive the general form of envelope equation for such systems. The theory is applied to the chlorite–iodide–malonic acid system, a standard paradigm for activator–inhibitor mechanism, to derive the instability condition in terms of the anisotropy parameters (\(\kappa _{i}, i = u, v\) that impart concentration-dependence to the diffusion coefficients) and identify the supercritical and subcritical Turing regions in the bifurcation diagram. The theoretical predictions are in good agreement with the numerical simulations.     

Electrolyte diffusion of ZnCl2 and self-diffusion of Cd2+ ions in agar gel medium at different temperatures

The values of activation energy required for the diffusion of ZnCl₂ and for Cd²⁺ ions in Cd/Ac/₂ are reported in agar gel medium at 5×10^–5 and 0.001M concentration, respectively. These values are compared with the previously reported values in the same systems at different concentrations. The decrease in activation energy with concentration of electrolyte is in agreement with the Wang's model.     

Molecular Modeling to Estimate the Diffusion Coefficients of Drugs and Other Small Molecules

Diffusion is a spontaneous process and one of the physicochemical phenomena responsible for molecular transport, the rate of which is governed mainly by the diffusion coefficient; however, few coefficients are available because the measurement of diffusion rates is not straightforward. The translational diffusion coefficient is related by the Stokes–Einstein equation to the approximate radius of the diffusing molecule. Therefore, the stable conformations of small molecules were first calculated by molecular modeling. A simple radius r_s and an effective radius r_e were then proposed and estimated using the stable conformers with the van der Waals radii of atoms. The diffusion coefficients were finally calculated with the Stokes–Einstein equation. The results showed that, for the molecules with strong hydration ability, the diffusion coefficients are best given by r_e and for other compounds, r_s provided the best coefficients, with a reasonably small deviation of ~0.3 × 10⁻⁶ cm²/s from the experimental data. This demonstrates the effectiveness of the theoretical estimation approach, suggesting that diffusion coefficients have potential use as an additional molecular property in drug screening.     

Diffusion in polyacrylate aqueous systems at 25°C. Role of reference frame choice in interpreting diffusion coefficient data

Diffusion coefficients have been measured for the binary systems sodium polyacrylate-water and polyacrylic acid-water at 25°C as a function of concentration. Diffusion coefficients have been also measured for the ternary system sodium chloride-sodium polyacrylate-water at constant NaCl concentration and varying polyacrylate concentration. The experimental results have been compared with some limit expressions, available in literature, for the four D _ik diffusion coefficients of systems containing two electrolytes with a common ion. The ternary system shows strong interaction between flows: as the polyelectrolyte concentration, C₂, approaches zero, the main diffusion coefficient D₂₂ and the cross coefficient D₂₁ approach zero, while the cross coefficient D₁₂ reach quite high values. The water motion during the diffusion process is also discussed.     

Study of mass transfer in a dynamic hollow‐fibre liquid phase microextraction system

The extraction characteristics of a dynamic hollow‐fibre liquid phase microextraction system were investigated by studying the mass transfer and diffusion rates of dinitrophenols from plasma samples over the liquid membrane (dihexylether). The measured diffusion coefficients were compared with theoretical values calculated from Stokes diameters. The diffusion mechanism was simulated by computer and the most polar compounds, 2,4‐dinitrophenol and 4,6‐o‐dinitrocresol, had associated diffusion coefficients that were close to the calculated theoretical values. 2‐sec‐Butyl‐4,6 dinitrophenol and 2‐tert‐butyl‐4,6‐dinitrophenol, the compounds with the highest log P values, were retained by the polypropylene membrane, which reduced the experimentally observed diffusion rates to about half of the theoretical values. The retention was most likely due to dispersive forces interacting with the pore inner walls. Extraction was linearly correlated with time for all compounds and the repeatability was high (RSDs 7–11%), even for the shortest extraction times. Method LOD as the amount injected ranged between 0.3 and 3.1 ng for an extraction cycle of 213 s.     

Sublimation and Diffusion Kinetics of 2,4,6-Trinitrotoluene (TNT) Single Crystals by Atomic Force Microscopy (AFM)

In this article, we report the in-situ nanoscale experimental measurement of sublimation rates, activation energy of sublimation, and diffusion coefficients of 2,4,6-trinitrotoluene (TNT) single crystals in air using atomic force microscopy (AFM). The crystals were prepared by slow evaporation at 5 °C using acetone-dissolved TNT. The mass loss was calculated by monitoring the shrinkage of the surface area of layered islands formed on the surface of the TNT crystals due to sublimation upon isothermal heating at temperatures below the melting point. The results suggest the sublimation process occurs via two-dimensional detachment of TNT molecules from the non-prominent facets on the crystal surface which imitates the nucleation and crystal growth process. Sublimation rates are one order of magnitude smaller than previously reported values. However, the calculated activation energy (112.15 ± 3.2 kJ/mol) and temperature-dependent sublimation rates agree well with the reported values for TNT thin films and microcrystals determined by UV-vis absorbance spectroscopy and quartz crystal microscopy (QCM) (90–141 kJ/mol). The average diffusion coefficient is (4.35 × 10^–6 m²/s) which is within the range of the reported theoretical values with an average of 5.59 × 10^–6 m²/s, and about 25% less than that determined using thermogravimetric analysis for powder TNT.     

Atom diffusion in furnaces — models and measurements

Experimental as well as the theoretical approach to estimate diffusion coefficients for several analyte elements with different behavior in graphite furnaces, lead, gold, indium and chromium, were investigated. ‘Close’ graphite furnaces of two designs differing in the size of end apertures and the diameter of the injection port were used. The furnaces were fast heated at rates of approximately 10 000 K s⁻¹. The peak absorbance of all studied analytes was independent of geometry, suggesting that the separation of atomization and removal was attained. Residence times of the analytes in the two different furnaces were determined from absorbance tail shapes. In the case of gold, the influence of temperature in the range between 1800 and 2200 K on the residence time in both furnaces was also found. The residence times measured in the two different furnaces under otherwise identical conditions, made possible to select the accurate model of diffusional removal from several possible models. The knowledge of the accurate model allowed the estimate of experimental diffusion coefficients. They were thus compared with those semiempirically calculated from kinetic theory of gases, extended to allow for the intermolecular forces. The accuracy of these calculations is limited since the input data (critical temperatures, boiling temperature or melting temperature, molal volumes at the critical, boiling and melting points, metallic crystallographic radii and dissociation constants of metal dimers) are not known with adequate accuracy. The comparison of ‘theoretical’ and ‘experimental’ values of diffusion coefficients makes possible to assess value of using individual sources of input data for the semiempirical calculations.     

Diffusion in three and four component microemulsions containing nonionic surfactant studied by pulsed field gradient nuclear magnetic resonance and quasi-elastic light scattering

Diffusion studies were performed with various methods to obtain some insight into the structure and the dynamical processes of three and four component microemulsions containing p-nonylphenol ethylene oxide adducts which were mixtures of highly branched p-nonyl isomers with well defined distributions of the ethylene oxide chain length.Diffusion coefficients were determined by pulsed field gradient and pulsed field gradient Fourier transform¹ H NMR as well as by quasi-elastic light scattering.The combined application of pulsed field gradient NMR and quasi-elastic light scattering gives information about the critical behaviour of the systems whereas pulsed field gradient Fourier transform NMR allows the determination of the diffusion coefficients of the individual constituents.The results suggest that the very complex three and four component microemulsions studied undergo critical concentration fluctuations in a large temperature region from about 15 °C below the lower critical solution temperatures. The deduced critical exponents are in good agreement with theoretical predictions. The aggregates in the three and four component microemulsions show differences in the self diffusion behaviour of their constituents.     

Activity coefficients and diffusion coefficients of dilute aqueous solutions of lithium,sodium, and potassium hydroxides

A simplified version of Harned's conductimetric technique has been used to measure binary diffusion coefficients of aqueous lithium, sodium, and potassium hydroxides at 25°C from 0.002 to 0.14 mol-dm^–3. Because of the large difference in mobility between OH^– and the cations, the electrophoretic effect tends to reduce the rate of diffusion of the alkali metal hydroxides; the largest effect is observed for LiOH solutions. The measured diffusion coefficients are in excellent agreement with predictions of the Onsager-Fuoss theory of ion transport. Precise activity coefficients determined from the diffusion measurements are compared with activity coefficients obtained previously by emf methods.