Limiting Diffusion Coefficients Research Articles

Diffusion coefficients of paracetamol in aqueous solutions

Binary mutual diffusion coefficients measured by the Taylor dispersion method, for aqueous solutions of paracetamol (PA) at concentrations from (0.001 to 0.050)mol·dm−3 at T=298.15K, are reported. From the Nernst–Hartley equation and our experimental results, the limiting diffusion coefficient of this drug and its thermodynamic factors are estimated, thereby contributing in this way to a better understanding of the structure of such systems and of their thermodynamic behaviour in aqueous solution at different concentrations.

Fundamental data: Solubility of nickel and oxygen and diffusivity of iron and oxygen in molten LBE

Experiments for determining nickel solubility limit and iron diffusion coefficient are presented and their results are discussed. Nickel solubility limit is determined by two methods: ex situ by solid sampling followed by ICP-AES analysis and in situ by Laser Induced Breakdown Spectroscopy and their results are compared. The iron diffusion coefficient is obtained using the technique of rotating specimen dissolution. Also a method to determine the oxygen solubility and diffusivity in LBE is developed and results at 460, 500 and 540 °C are presented. It is based on the following electrochemical cell: O 2 (reference mixture), Pt //YSZ//O 2 (LBE) which can work as an oxygen sensor or as a coulometric pump.

Limiting diffusion coefficients of ionic liquids in water and methanol: a combined experimental and molecular dynamics study

Mutual diffusion coefficients D(12) of the ionic liquids 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C(2)MIM][NTf(2)]) and [C(4)MIM][NTf(2)] in highly diluted solutions of water and methanol have been measured at different temperatures between 288 K and 313 K using the Taylor dispersion technique. Tracer diffusion coefficients of the two cations [C(2)MIM](+) and [C(4)MIM](+) as well as the anion [NTf(2)](-) in these solutions have been obtained by molecular dynamics (MD) simulations. For our simulations we used well established force fields for the solvents water and methanol and a recently developed force field for imidazolium-based ionic liquid [C(n)MIM][NTf(2)]. Mutual diffusion coefficients D(12) have been calculated from the tracer diffusion coefficients using the Nernst-Hartley equation strictly valid only at low ionic concentration. The agreement between the diffusion coefficients reported in the literature, the experimental data obtained in this work and the MD results is excellent.

Diffusion in macromolecular crowded media: Monte Carlo simulation of obstructed diffusion vs. FRAP experiments

The diffusion of tracer particles in 3D macromolecular crowded media has been studied using two methodologies, simulation and experimental, with the aim of comparing their results. First, the diffusion of a tracer in an obstructed 3D lattice with mobile and big size obstacles has been analyzed through a Monte Carlo (MC) simulation procedure. Secondly, fluorescence recovery after photobleaching (FRAP) experiments have been carried out to study the diffusion of a model protein (alpha-chymotrypsin) in in vitro crowded solution where two type of Dextran molecules are used as crowder agents. To facilitate the comparison, the relative size between the tracer and the crowder is the same in both studies. The results indicate a qualitative agreement between the diffusional behaviors observed in the two studies. The dependence of the anomalous diffusion exponent and the limiting diffusion coefficient on the obstacle size and excluded volume shows, in both cases, a similar tendency. The introduction of a reduced mobility parameter in the simulation model accounting for the short-range tracer–obstacle interactions allows obtaining a quantitative agreement between the limiting diffusion coefficient values yielded by both procedures. The simulation–experiment quantitative agreement for the anomalous diffusion exponent requires further improvements. As far as we know, this is the first reported work where both techniques are used in parallel to study the diffusion in macromolecular crowded media.

Diffusion coefficients of the ternary system (2-hydroxypropyl-β-cyclodextrin + caffeine + water) at T = 298.15 K

Ternary mutual diffusion coefficients measured by Taylor dispersion method ( D 11, D 22, D 12, and D 21) are reported for aqueous solutions of 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) + caffeine at T = 298.15 K at carrier concentrations from (0.000 to 0.010) mol · dm −3, for each solute, respectively. These diffusion coefficients have been measured having in mind a better understanding of the structure of these systems and thermodynamic behaviour of caffeine and 2-hydroxypropyl-β-cyclodextrin in solution. For example, from these data it will be possible to estimate some parameters, such as the fraction of associated species HP-β-CD ( X 1) and caffeine ( X 2) in this complex, the monomer and dimer fractions, X 2 M and X 2 D , respectively, and the limiting diffusion coefficients of the HP-β-CD, D HPBCD ∘ , of the dimers caffeine entities, D D ∘ , and of those complexes (1:1), D complex ∘ .

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.

Limiting Diffusion Coefficients of Ethyl Benzoate, Benzylacetone, and Eugenol in Carbon Dioxide at Supercritical Conditions

The binary diffusions of ethyl benzoate, benzylacetone, and 2-methoxy-4-(2-propenyl)phenol (eugenol) at infinite dilution in supercritical carbon dioxide were measured between (15.0 and 35.0) MPa and in the temperature range of (313 to 333) K by the Taylor−Aris chromatographic method. The measured values were compared with the calculated ones using several predictive formulas. The effect of temperature, pressure, viscosity, and density is also discussed.

Limiting transport properties and hydration numbers of actinyl ions in pure water

Abstract The transport properties in pure water, i.e. the limiting ionic conductivity (λ°) and the limiting diffusion coefficient (D°), and the hydration numbers (N) of the singly and doubly charged uranyl, neptunyl, plutonyl and americyl ions MO2 n + (n = 1 or 2) have been calculated at 298.15K. A geometric model was applied in which the actinyl ions described by ellipsoids of revolution, with the axis O-M-O as axis of revolution, were transformed into spherical ions. The microscopic version of the Stokes–Einstein law has been used to derive the limiting transport properties of the ions. The main parameters involved in the calculations were the size of the bare ion, the effective cationic charge of the central actinide M, the viscosity of the water molecules in the first hydration shell of the ion and the size of this first hydration shell. The results obtained for the limiting transport properties and for the hydration numbers of the actinyl ions were found in good agreement with experimental data from the literature.

Limiting transport properties of lanthanide and actinide ions in pure water

Summary The limiting transport properties, i.e. the limiting ionic conductivity (λ°) and the limiting diffusion coefficient (D°), of lanthanide and actinide ions at 298.15K have been calculated by means of the microscopic version of the Stokes–Einstein law involving (i) the effective charge and the ionic radius of the ions and (ii) the ion micro-viscosity, i.e. the viscosity of the hydrated water molecules in the vicinity of the ion. The latter quantity was derived from the variation of the dynamic properties of the water molecules in the first hydration shell with the surface charge density of common mono-atomic cations of various charges. The obtained results were found to be consistent with the experimental data given in the literature.

Binary Mutual Diffusion Coefficients of Aqueous Cyclic Ethers at 25 °C. Tetrahydrofuran, 1,3-Dioxolane, 1,4-Dioxane, 1,3-Dioxane, Tetrahydropyran, and Trioxane

Taylor dispersion and differential refractometry are used to measure mutual diffusion coefficients (D) for the binary mixtures 1,4-dioxane + water, 1,3-dioxolane + water, and tetrahydrofuran + water at 25 °C. For each of these systems the plot of D against composition shows a pronounced minimum. Activity and viscosity data for aqueous 1,4-dioxane are used to discuss the strong composition dependence of D in terms of changes in the mobilities and thermodynamic driving forces. Diffusion coefficients are also reported for dilute aqueous solutions of 1,3-dioxane, tetrahydropyran, and trioxane. The limiting diffusion coefficients of the infinitely dilute aqueous ethers are discussed in terms of ring size, number and relative location of the oxygens, and the ether partial molar volume. A second or a third oxygen in the five- or six-membered rings reduces the ether partial molar volumes by about 10 cm3·mol-1 and increases the limiting diffusion coefficients by (0.14 to 0.21) × 10-5 cm2·s-1.

A group contribution correlation of the mutual diffusion coefficients of binary liquid mixtures

A group contribution method is developed on the basis of the UNIDIF model [Y.D. Hsu, Y.P. Chen, Fluid Phase Equilibria 152 (1998) 149–168] for the correlation of the mutual diffusion coefficients of binary liquid mixtures. In this group contribution UNIDIF (GC-UNIDIF) model, a mole fraction average of the logarithm of the infinite dilution limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIFAC equation with two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from generalized data regression, for each pair of functional groups. Optimal group interaction parameters are presented. The mutual diffusion coefficients of binary liquid mixtures are calculated for non-polar+non-polar, non-polar+polar and polar+polar fluid mixtures in this study. The calculation results using the GC-UNIDIF model for mutual diffusion coefficient are satisfactory. This model also requires lesser number of parameters than other correlative methods.

Determination of coupled acid catalysis-diffusion processes in a positive-tone chemically amplified photoresist

Acid diffusion during postexposure baking is viewed to be a limiting factor in the extension of lithography using chemically amplified resists to formation of nanoscale features. Quantification of thermally activated reaction-diffusion kinetics in these materials is therefore an important step in understanding the extendability of this class of resist systems. Previous investigations have addressed this issue, however there is poor agreement among them, and too few data exist in the literature to allow the systematics of the effect of polymer, photoacid generator, added base or other resist components on the diffusion process to be understood. We describe in this article a combined experimental and modeling protocol that is designed to elucidate the chemistry and physics of the reaction-diffusion process. Because it is physically based, not phenomenological, it provides a means of developing a set of predictive, mutually comparable data that will allow new insights to be developed into the nanoscale behavior of chemically amplified resist materials. We apply the protocol to a p-t-butyloxycarbonyloxystyrene/bis(t-butylphenyl)iodonium perfluorobutanesulfonate positive-tone photoresist system. The resulting kinetics measurements show that diffusion is environment sensistive and describable with two limiting diffusion coefficients. The Arrhenius parameters for the coefficients in p-t-butyloxycarbonyloxystyrene are D0=1.9×108 cm2/s and Ea=36.5 kcal/mol; those for diffusion in the deprotected polymer product p-hydroxystyrene are D0=9×10−3 cm2/s and Ea=22.1 kcal/mol. The coefficients are much smaller than previously reported, resulting in a very slow diffusion rate. The model indicates that the considerable image spreading observed during the postexposure bake process is attributable primarily to the efficiency of the catalytic chemistry. Our results suggest that numerical models currently used for prediction of imaging in chemically amplified resists may require refinement in order to be useful for feature sizes below 100 nm and for new classes of resist systems.

Effect of chain length in ethoxylated and sulfonate surfactants upon the limiting diffusion coefficients in water at 25.0 °C

Limiting diffusion coefficients of ethoxylated surfactants of general formula CH3(CH2)p−1(OCH2CH2)qOH (CpEq) and sulfonate surfactants of formula CH3(CH2)p−1SO3− Na+(CpSO3Na) were measured at 25°C by the Taylor dispersion technique. The series C6Eq, with 0⩽q⩽5, was studied to evaluate the effect of the length of ethoxylic chain, (–OCH2CH2–)q, on the mobility of the surfactant, the series CpE5 with 0⩽p⩽8 was studied to evaluate the effect of the length of the hydrophobic group, (–CH2–)p. The series CpSO3Na was also studied to compare the experimental results with the intradiffusion coefficients obtained by the NMR-PGSE technique and with the data computed by the Nernst–Hartley equation.

Effect of Gasoline Contamination on the Permeation of Organic Liquids through Rubber Membranes

Abstract The effect of gasoline and oil contamination on the barrier properties of natural rubber, nitrile rubber and bromobutyl rubber have been experimentally studied for the following organic environmental contaminants: dichloromethane, acetone and toluene. Oil contamination has little effect on the subsequent transport of these organic penetrants. However, gasoline contamination alters the subsequent transport behavior of these organic penetrants, depending on the nature of the rubber and the contamination conditions. Nitrile rubber experiences minor effects, while natural rubber is severely affected. Penetrant breakthrough times as well as limiting diffusion coefficients increase with increasing temperature and/or contamination time.

Correlation of the mutual diffusion coefficients of binary liquid mixtures

A correlative UNIDIF model for the mutual diffusion coefficients of binary liquid mixtures is developed using statistical thermodynamics and the absolute reaction rate theory. In this model, a mole fraction average of the logarithm of the pure-component limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIQUAC equation which comprises two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from data regression, for each binary mixture. Mutual diffusion coefficients of nonpolar+nonpolar, nonpolar+polar and polar+polar fluid mixtures are correlated in this study. Optimal binary interaction parameters are presented. Correlation results using the UNIDIF model for mutual diffusion coefficient are satisfactory and are superior to those from other methods.

Experimental Studies and Modelling of Sorption and Diffusion of Water and Alcohols in Cellulose Acetate

The sorption characteristics of water, methanol and ethanol vapours in cellulose acetate (CA) films were measured by microgravimetry. The sorption isotherms for water vapours in the CA film at different temperatures in the range 20-40°C do not obey the Flory equation over the whole water activity range. At high water activities, the sorption extent increases much faster with the water activity than it should according to the Flory approach. The isotherms over the whole water activity range can be fitted well by the ENSIC model, a new mechanistic model developed to account for the possibility of solvent cluster formation in the polymer material. Similar behaviour was observed for ethanol, which shows a lower tendency to form clusters, but higher affinity to CA. The sigmoidal shape found for the methanol sorption isotherm suggests a strong sorption on CA sites at low methanol activities. The Guggenheim-Anderson-De Boer equation fitted well this isotherm. The diffusion coefficient, which was calculated from Fickian sorption kinetics at different solvent activities by curve fitting, was constant for water but increased with ethanol content in the membrane according to an exponential relationship characterized by a limit diffusion coefficient and a plasticization coefficient. The limit diffusion coefficient for water was two orders of magnitude larger than that for ethanol, but the activation energy for ethanol was twice as large. Methanol diffusion was only Fickian at a low solvent activity; the diffusion coefficient was one order of magnitude lower than that for water.

Crossover from molecular to ionic diffusion in dilute aqueous solutions of hydrolysed ethylamine, diethylamine and triethylamine

D. G. Leaist and R. Lu, J. Chem. Soc., Faraday Trans., 1997, 93, 1341 DOI: 10.1039/A607224K

Prediction of the temperature dependence of the limiting diffusion coefficients of five helium–fluoromethane systems from diffusion coefficients at 300 K and limiting thermal diffusion factors at the same temperature and zero pressure

Thermal diffusion factors αT are reported at 300 K for five binary systems consisting of helium and a fluoromethane. The data are extrapolated to zero pressure and used to predict the temperature dependence of the binary diffusion coefficients of these systems.

Sorption and Diffusion of Solvent Vapours in Poly(vinylalcohol) Membranes of Different Crystallinity Degrees

Solvent sorption and diffusion are the key processes that control membrane performances in membrane processes. The sorption characteristic of water and ethanol vapours in poly(vinylalcohol) (PVA) membranes of different crystallinity degrees was measured by microgravimetry and the diffusion characteristic was calculated from the sorption kinetics at different water activities by curve fitting. The sorption isotherms for water vapour in membranes of 28, 37, 44 and 56% crystallinity degrees at 40°C obey the Flory equation based on the polymer lattice model. When the sorption extent was corrected by assuming that only the polymer amorphous phase is accessible to the penetrant, a unique Flory χ interaction parameter, 0.3, was obtained for all samples except for the 28% crystallinity sample. For the latter sample, the lower χ value (0.18) obtained can be explained by a change in the sorption behaviour of the original crystalline domains which may undergo partial destruction. The diffusion coefficient increases with the average water content in the membrane according to an exponential relationship characterized by a limit diffusion coefficient and a plasticization coefficient. The higher the crystallinity of the membrane, the lower the values of the limit diffusion coefficient and the plasticization coefficient. The ethanol sorption was also well described by the Flory-Huggins equation. The limit diffusion coefficient for water was two orders of magnitude larger than that for ethanol.

Sorption and Diffusion of Solvent Vapours in Polyvinylalcohol Membranes of Different Crystallinity Degrees

Solvent sorption and diffusion are the key processes that control membrane performances in membrane processes. The sorption characteristic of water and ethanol vapours in poly(vinylalcohol) (PVA) membranes of different crystallinity degrees was measured by microgravimetry and the diffusion characteristic was calculated from the sorption kinetics at different water activities by curve fitting. The sorption isotherms for water vapour in membranes of 28, 37, 44 and 56% crystallinity degrees at 40°C obey the Flory equation based on the polymer lattice model. When the sorption extent was corrected by assuming that only the polymer amorphous phase is accessible to the penetrant, a unique Flory χ interaction parameter, 0.3, was obtained for all samples except for the 28% crystallinity sample. For the latter sample, the lower χ value (0.18) obtained can be explained by a change in the sorption behaviour of the original crystalline domains which may undergo partial destruction. The diffusion coefficient increases with the average water content in the membrane according to an exponential relationship characterized by a limit diffusion coefficient and a plasticization coefficient. The higher the crystallinity of the membrane, the lower the values of the limit diffusion coefficient and the plasticization coefficient. The ethanol sorption was also well described by the Flory–Huggins equation. The limit diffusion coefficient for water was two orders of magnitude larger than that for ethanol.