The effect of ionic strength on the diffusion of 125I in Gaomiaozi bentonite

The diffusion of ¹²⁵I^? in compacted Gaomiaozi (GMZ) bentonite was investigated by capillary in-diffusion method. Apparent and effective diffusion coefficients and accessible porosity of iodide in GMZ bentonite were obtained, and the effect of ionic strength on diffusion parameters was studied. The apparent diffusion coefficients of iodide in compacted GMZ bentonite are in the range of 1.0–6.0 × 10^?10 m² s^?1 under the conditions of dry bulk density 1,500 kg m^?3 and temperature 298 K, and increase with increasing ionic strength. This effect was explained through the analysis of microscopic structure of compacted bentonite. The iodide can only diffuse in unbound interparticle pore solution of compacted bentonite. The apparent diffusion coefficient is a function of accessible porosity which is decided by the thickness of diffusion double layer, and the thickness is in turn controlled by ionic strength.     

Study on protein adsorption kinetics to a dye-ligand adsorbent by the pore diffusion model

Adsorption kinetics of bovine serum albumin (BSA) and bovine hemoglobin (bHb) to Cibacron Blue 3GA (CB) modified Sepharose CL-6B has been studied. The effects of liquid-phase ionic strength and CB coupling density on the uptake rates of these two proteins in Tris-HCl buffer (pH 7.5) were evaluated by effective pore diffusivity derived from a pore diffusion model. The results showed that despite their similar molecular masses and sizes, the effects of aqueous-phase ionic strength and CB density on the effective pore diffusivities of BSA and bHb were distinctly different. The effective pore diffusivity of BSA to CB-Sepharose increased significantly with decreasing CB density and increasing liquid-phase ionic strength. This was considered due to the decrease in electrostatic repulsion between the BSA and CB molecules of like charge. That is, the increase in ionic strength and the decrease in CB coupling density reduced the electrostatic hindrance effect on BSA diffusion to CB-Sepharose, facilitating the hindered pore diffusion. In contrast, because of the higher isoelectric point of bHb (7.0) compared to BSA (4.7), bHb suffered little electrostatic hindrance effect during its diffusion to CB-Sepharose. Therefore, the effective pore diffusivity of bHb was unchanged with the change in liquid-phase ionic strength and CB coupling density.     

Porosity dependence of electron percolation in nanoporous TiO2 layers

The electron diffusion coefficient at varying porosity has been determined in a series of nanostructured TiO(2) films of different initial thicknesses. The porosity was changed by applying different pressures prior to sintering, thereby modifying the internal morphology of the films though not their chemical and surface conditions. A systematic increase of the effective diffusion coefficient was observed as the porosity was decreased, indicating the improvement of the internal connectivity of the network of nanoparticles. The experimental results have been rationalized using percolation theory. First of all, applying a power law dependence, the diffusion coefficient as a function of porosity from different films collapsed in a single master curve. In addition, application of the models of effective medium approximation (EMA) allows us to compare the experimental results with previous data from Monte Carlo simulation. The different data show a similar dependence in agreement with the EMA predictions, indicating that the geometrical effect of electron transport due to variation of porous morphology in TiO(2) nanoparticulate networks is well described by the percolation concept.     

A volume averaging approach for asymmetric diffusion in porous media

Asymmetric diffusion has been observed in different contexts, from transport in stratified and fractured porous media to diffusion of ions and macromolecular solutes through channels in biological membranes. Experimental and numerical observations have shown that diffusion is facilitated in the direction of positive void fraction (i.e., porosity) gradients. This work uses the method of volume averaging in order to obtain effective medium equations for systems with void fraction gradients for passive and diffusive mass transport processes. The effective diffusivity is computed from the solution of an associated closure problem in representative unit cells that allow considering porosity gradients. In this way, the results in this work corroborate previous findings showing that the effective diffusivity exhibits important directional asymmetries for geometries with void fraction gradients. Numerical examples for simple geometries (a section with an obstacle and a channel with varying cross section) show that the diffusion asymmetry depends strongly on the system configuration. The magnitude of this dependence can be quantified from the results in this work.     

The effects of pH and calcium on the diffusion coefficient of humic acid

Humic acid is a major component of natural organic matter in surface water and can cause serious fouling problems in membrane filtration processes for drinking water treatment. The transport of humic acid to the membrane surface and within membrane pores is related to its diffusivity. Thus, the diffusion coefficient of humic acid is an important mass transport parameter. Clark and Lucas [J. Membr. Sci. 143 (1998) 13–25] studied the diffusion and partitioning of humic acid into a porous ultrafiltration membrane and developed a model to predict how humic acid diffusivity changes under different pH and calcium concentration conditions. In this work, the diffusion coefficient of humic acid was directly measured and compared to the predictions of the Clark and Lucas model. The experiments were conducted in a two-chamber diffusion cell separated by a track-etched membrane. The results show that the diffusivity of humic acid increases with decreasing pH and increasing calcium concentration, which can be explained by the compaction of humic acid molecules at low pH and high ionic strength. The experimental measurements strongly support the predictions of the Clark and Lucas model.     

Gas diffusion in partially crystalline polymers part I: Concentration dependence

In this work, a phenomenological model for the gas diffusion in partially crystalline polymers using differential effective medium theory is presented. By making an analogy with the power law known as Archie's law which relates the d.c. conductivity of a brine saturated porous rock to its porosity; we show that gas diffusion through semicrystalline polymers can be described in a similar way. It is assumed that the diffusion coefficient in the crystalline region is zero, while in the amorphous region it is given by a free volume model, and an effective diffusion coefficient D^eff, is obtained using the mentioned analogy. The variation of D^eff upon concentration is analyzed through its free volume dependence. The crystallinity dependence is considered through an average chain immobilization factor 〈β〉 which is explicitely derived. Finally, the results of this model are compared with experimental data given by Kreituss and Frisch, obtaining a good agreement. © 1996 John Wiley & Sons, Inc.     

Poisson-Boltzmann与Donnan模型计算压实膨润土孔隙水与外部溶液间离子平衡的差异性比较

压实膨润土孔隙水与外部溶液之间的离子平衡是影响离子在压实膨润土中扩散的影响因素之一, 表征这一平衡的离子平衡系数可用压实膨润土的宏观属性参数通过Donnan 模型计算得到. 通过对膨润土主体矿物蒙脱石的TOT层结构单元进行简化, 构建了一个压实膨润土的单类孔隙结构模型, 辅以一个尺度变量H, 用Poisson-Boltzmann (PB)理论模型计算上述离子平衡系数. 对比计算结果, 发现PB模型计算的离子平衡系数总是大于Donnan模型的结果, 而参数H是联系这两种模型之间的桥梁. 通过对参数H取极限H→0, 实现了从PB模型到Donnan 模型的数学变换, 并从机理上讨论了两种模型之间的差异及其在实际扩散问题中的应用.分析表明PB模型更符合离子在压实膨润土中扩散的实际情况, 更适于处理实际扩散问题.     

Adsorptive removal of La(III) from aqueous solutions with 8-hydroxyquinoline immobilized GMZ bentonite

Due to the low permeability, high swelling capacity and good retardation properties, bentonite has been considered as the main component of buffer/backfill material for high level radioactive wastes repository all over the world. The adsorptions of metal ion were widely investigated recently. In this presentation, we provide an easy-to-use method to immobilize 8-hydroxyquinoline onto the surface of bentonite for the use of adsorption studies of La(III) from the aqueous solution. The effects of various parameters such as contact time, pH of the solution, ionic strength and metal ion concentration on the adsorption were investigated by the batch experiments. The biggest adsorption capacity is 41.7 mg/g, higher than the value reported by our previous work which is performed by the raw bentonite. Langmuir isotherm fits the experimental data well and the adsorption follows pseudo-second-order kinetic model. In summary, 8-hydroxyquinoline immobilized GMZ bentonite is an effective adsorbent for the removal of La(III) from aqueous solutions.     

Proton spin diffusion in polyethylene as a function of magic-angle spinning rate. A phenomenological approach

Starting from the phenomenological Bloembergen-Purcell-Pound equation a relation between magic-angle spinning (MAS) rate and spin diffusion is derived. The resulting model equation was fitted to observed spin diffusion versus MAS rate data obtained at 298 K on an high-density polyethylene sample, revealing a reduction in the effective spin diffusivity by (65 + 5)% when increasing the MAS rate from 2 to 12 kHz. The same model equation enabled the rigid-lattice diffusivity to be estimated and was found to be only slightly higher, by approximately 10%, compared to the spin diffusivity observed at the lowest MAS rate applied (2 kHz). Moreover, the model equation predicts a reduction in the effective spin diffusivity by more than 90% when increasing the MAS rate to more than 30 kHz.     

Influence of electrolytes on the dynamic surface tension of ionic surfactant solutions: expanding and immobile interfaces

Here, we derive analytical asymptotic expressions for the dynamic surface tension of ionic surfactant solutions in the general case of nonstationary interfacial expansion. Because the diffusion layer is much wider than the electric double layer, the equations contain a small parameter. The resulting perturbation problem is singular and it is solved by means of the method of matched asymptotic expansions. The derived general expression for the dynamic surface tension is simplified for the special case of immobile interface and for the maximum bubble pressure method (MBPM). The case of stationary interfacial expansion is also considered. The effective diffusivity of the ionic surfactant essentially depends on the concentrations of surfactant and nonamphiphilic salt. To test the theory, the derived equations are applied to calculate the surfactant adsorption from MBPM experimental data. The results excellently agree with the adsorption determined independently from equilibrium surface-tension isotherms. The derived theoretical expressions could find application for interpreting data obtained by MBPM and other experimental methods for investigating interfacial dynamics.     

Ionic Diffusivity, Electrical Conductivity, Membrane and Thermoelectric Potentials in Colloids and Granular Porous Media: A Unified Model

Ionic diffusivity, electrical conductivity, membrane and thermoelectric potentials in isotropic and homogeneous colloidal suspensions, and granular porous media saturated by a binary symmetric 1:1 electrolyte are four interrelated phenomena. The microstructure and the surface properties of the solid grains-water interface influence directly these properties. The ionic diffusivities (and the electrical conductivity, respectively) in colloids and porous media have contributions from diffusion (and electromigration, respectively) through the bulk solution occupying the pores, together with electromigration occurring at the grains-water interface in the electrical double layer. Surface diffusion in porous materials has no contribution from concentration gradients along the grains-water interface. Instead, surface diffusion is envisioned as a purely electromigration process due to the membrane potential. The tortuosities of the transport of anions and cations are equal to the bulk tortuosity of the pore space only at high ionic strength. As the ionic strength decreases, the dominant paths for transport of the ion corresponding to the counterion of the electrical double layer shift from the pore space to the solid grains-water interface. Because anions and cations do not move independently, the membrane potential created by the charge polarization alters the velocity of the anions and influences the mutual diffusivity coefficient of the salt in the porous material. An electric potential of thermal origin is also produced in nonisothermal conditions. The ionic contributions to the electrical conductivity are based on a differential effective medium approach. These ionic contributions to the electrical conductivity are used to derive the ionic diffusivities and the membrane and thermoelectric potentials. The influence of the temperature and the presence, in the pore space, of a second immiscible and nonwetting phase is also considered in this model. Porosity is shown to affect the membrane potential. Several predictions of the model are checked with success by comparing the model to a set of experimental data previously published. Copyright 1999 Academic Press.     

Moisture diffusion into epoxy adhesive: testing and modeling

Moisture diffusion into epoxy adhesive is investigated through utilizing complete fluid immersion tests in distilled water. Apparent diffusivity for each specimen is determined by two methods, one using the diffusion data at early times (at low loading) and the other using the data at large times (close to the saturation point). The results of the two methods are quite different, indicating that diffusivity is concentration dependent. The apparent diffusivity values obtained through the method using the early data points are about twice those obtained through the method utilizing the data points at large diffusion times. Variance of diffusivity with concentration is also considered as the third method of analysis to determine the concentration dependency. A good agreement is observed between the resultant Fickian model solved numerically and the experimental data. The latter result appears to indicate a change in the excess volume of mixing during the sorption process.     

Molecular thermodynamics for micellar branching in solutions of ionic surfactants

We develop an analytical molecular-thermodynamic model for the aggregation free energy of branching portions of wormlike ionic micelles in 1:1 salt solution. The junction of three cylindrical aggregates is represented by a combination of pieces of the torus and bilayer. A geometry-dependent analytical solution is obtained for the linearized Poisson-Boltzmann equation. This analytical solution is applicable to saddle-like structures and reduces to the solutions known previously for planar, cylindrical, and spherical aggregates. For micellar junctions, our new analytical solution is in excellent agreement with numerical results over the range of parameters typical of ionic surfactant systems with branching micelles. Our model correctly predicts the sequence of stable aggregate morphologies, including a narrow bicontinuous zone, in dependence of hydrocarbon tail length, head size, and solution salinity. For predicting properties of a spatial network of wormlike micelles, our aggregation free energy is used in the Zilman-Safran theory. Our predictions are compared with experimental data for branching micelles of ionic surfactants.     

Estimation of diffusion parameters in functionalized silicas with modulated porosity. Part II: pore network modeling

In this work, the pore structure of those five (5) silicas SiO2-X (see Part I) which have suffered gradual functionalization with functional groups X of increasing length (X = psi, [triple bond]Si-H, [triple bond]Si-CH2OH, [triple bond]Si-(CH2)3OH, [triple bond]Si-(CH2)11CH3), is modeled as a three-dimensional cubic network of cylindrical pores. Those hybrids organic-inorganic SiO2-X samples are characterized by different extent of pore blocking effects. The pores of samples are represented in a 9 x 9 x 9 lattice by the nodes as well the bonds that are interconnected in a so-called dual site-bond model, DSBM, network. The pore network is developed using a Monte Carlo statistical method where the cylindrical pores (nodes and bonds) are randomly assigned into the lattice, until matching of the theoretical results to the experimental data of N2 adsorption-desorption measurements. Thus, a visual picture of the porous solid is possible. This realistic network is used next in order to study the steady-state gas transport (Knudsen gas-phase and viscous diffusion) properties for the examined materials and how flow processes depend on the morphology of the pore structure. The pore diffusivity Dp and total permeability P of each porous medium is determined based on theoretical calculations and the structural statistical parameters, such as porosity epsilonp, tortuosity factor tau and connectivity c of pores is discussed with the corresponding experimental data described in Part I of this work. The results indicate clearly that the diffusion model made it possible to predict pore effective diffusivity in these porous media in very good agreement with the corresponding experimental results for all the examined solids (Part I). The pore diffusivity increases significantly as the value of the pore connectivity increases but the transport properties of the network are influenced strongly at lowest connectivity. Also the predicted tortuosity factor is related inversely to the extent of interconnection of pores in these solids, which indicates that the influence of pore branching to the tortuosity factor of the pore network decreases, as connectivity increases.     

Anomalous diffusion in an electrolyte saturated paper matrix

Diffusion of colored dye on water saturated paper substrates has been traditionally exploited with great skill by renowned water color artists. The same physics finds more recent practical applications in paper-based diagnostic devices deploying chemicals that react with a bodily fluid yielding colorimetric signals for disease detection. During spontaneous imbibition through the tortuous pathways of a porous electrolyte saturated paper matrix, a dye molecule undergoes diffusion in a complex network of pores. The advancing front forms a strongly correlated interface that propagates diffusively but with an enhanced effective diffusivity. We measure this effective diffusivity and show that it is several orders of magnitude greater than the free solution diffusivity and has a significant dependence on the solution pH and salt concentration in the background electrolyte. We attribute this to electrically mediated interfacial interactions between the ionic species in the liquid dye and spontaneous surface charges developed at porous interfaces, and introduce a simple theory to explain this phenomenon.     

Refined potential model for atomistic simulations of ionic liquid [bmim][PF6

Refined parameters of an atomistic interaction potential model for the room temperature ionic liquid 1-n-butyl,3-methylimidazolium hexafluorophosphate are presented. Classical molecular dynamics simulations have been carried out to validate this fully flexible all-atom model. It predicts the density of the liquid at different temperatures between 300 and 500 K within 1.4% of the experimental value. Intermolecular radial distribution functions and the spatial distribution functions obtained from the new model are in close agreement with ab initio simulations. The calculated diffusion coefficients of ions and the surface tension of the liquid agree well with experiment.     

Sorption and diffusion of 90Sr2+in compacted bentonite investigated by a capillary method

Summary The effects of bentonite density and fulvic acid on the sorption and diffusion of ⁹⁰Sr²⁺in compacted bentonite were investigated by using a capillary method. The experiments were carried out at pH 7.0±0.1 in the presence of 0.01M NaClO₄. The results suggest that the sorption and diffusion of ⁹⁰Sr²⁺in compacted bentonite decreases with increasing the density of compacted bentonite. The presence of FA enhances the sorption of Sr²⁺, but reduces the diffusion of Sr²⁺in compacted bentonite. The porosity of the compacted bentonite plays an important role in the sorption and diffusion behavior of ⁹⁰Sr²⁺. Using the calculated effective diffusion coefficients the long-term relative concentration distribution of strontium was evaluated in compacted bentonite.     

Diffusion behavior in polymer–clay nanocomposites

This paper reviews our previous studies on the diffusion behavior in polymers clay nanocomposites. A geometric model for predicting the effective diffusivity through this type of systems as a function of clay sheets orientation, volume fraction, polymer clay interaction, and aspect ratio is proposed. Model predictions are compared to the effective diffusivity generated using random walk simulations as well as with predictions obtained from already existing theoretical models. Fair agreement is found between the model prediction and the results of numerical simulations. With respect to the already existing theoretical models, the present mathematical derivation seems more adequate to describe diffusion behavior in conventional nanocomposites systems (i.e. when fillers present very low values of volume to surface ratio). Experimental diffusion tests are discussed and interpreted with the aid of the proposed model. In addition to the aspect ratio and clay concentration, the polymer clay interactions as well as the sheets orientation are the factors controlling the barrier properties of polymer‐layered silicate nanocomposites. Good agreement was found in the case of samples containing exfoliated clay, whereas the model fails in the case of micro‐composites, in which the inorganic lamellae are agglomerated in clusters. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 265–274, 2006     

Diffusion of sodium dodecyl sulfate micelles in agarose gels

The gradient diffusion of ionic sodium dodecyl sulfate micelles in agarose gel was investigated at moderate concentrations above the CMC. Of particular interest were the effects of micelle, gel, and sodium chloride concentration on the micelle diffusivity. Holographic interferometry was used to measure the gradient diffusion coefficient at three sodium chloride concentrations (0, 0.03, 0.10 M), three gel concentrations (0, 1, 2 wt%), and several surfactant concentrations. Time-resolved fluorescence quenching was used to measure aggregation numbers both in solution and gel. The micelle diffusivity increased linearly with surfactant concentration at the two larger sodium chloride concentrations and all gel concentrations. In general, the strength of this effect increased with decreasing sodium chloride concentration and increased with gel concentration. This behavior is evidence of decreasing micelle-micelle electrostatic interactions with increasing sodium chloride concentrations, and increasing excluded volume effects and hydrodynamic screening with increasing gel concentration, respectively. The only exception was at 0.1M sodium chloride and 2 wt% agarose, which showed a slight reduction in the slope compared to 1 wt% agarose. It was found that the concentration effect is quite strong for charged solutes: at a NaCl concentration of 0.03 M in a 2% agarose gel, in a solution with 3% SDS micelles by volume, the micelle diffusion coefficient is doubled relative to its value in the same gel at infinite dilution. The extrapolated, infinite-dilution diffusion coefficients and the rate at which the micelle diffusivity increased with surfactant concentration were compared with predictions of previously published theories in which the micelles are treated as charged, colloidal spheres and the gel as a Brinkman medium. The experimental data and theoretical predictions were in good agreement.     

Adsorption of acid dyes from aqueous solutions onto acid-activated bentonite

The adsorption of two dyes, namely, Acid Red 57 (AR57) and Acid Blue 294 (AB294), onto acid-activated bentonite in aqueous solution was studied in a batch system with respect to contact time, pH, and temperature. Acidic pH was favorable for the adsorption of these dyes. The surface characterization of acid-activated bentonite was performed using the FTIR technique. The pseudo-first-order and pseudo-second-order kinetic models and the intraparticle diffusion model were used to describe the kinetic data and the rate constants were evaluated. The dynamic data fitted the pseudo-second-order kinetic model well and also followed the intraparticle diffusion model up to 90 min, but diffusion is not the only rate controlling step. The Langmuir and Freundlich adsorption models were applied to describe the equilibrium isotherms and the isotherm constants were determined. The Freundlich model agrees very well with experimental data. The activation energies of adsorption were also evaluated for the adsorption of AR57 and AB294 onto activated bentonite.