Local and average diffusion of nanosolutes in agarose gel: the effect of the gel/solution interface structure

Fluorescence correlation spectroscopy (FCS) has been used to study the diffusion of nanometric solutes in agarose gel, at microscopic and macroscopic scales. Agarose gel was prepared and put in contact with aqueous solution. Several factors were studied: (i) the role of gel relaxation after its preparation, (ii) the specific structure of the interfacial zone and its role on the local diffusion coefficient of solutes, and (iii) the comparison between the local diffusion coefficient and the average diffusion coefficient in the gel. Fluorescent dyes and labeled biomolecules were used to cover a size range of solutes of 1.5 to 15 nm. Their transport through the interface from the solution toward the gel was modeled by the first Fick's law based on either average diffusion coefficients or the knowledge of local diffusion coefficients in the system. Experimental results have shown that, at the liquid/gel interface, a gel layer with a thickness of 120 microm is formed with characteristics significantly different from the bulk gel. In particular, in this layer, the porosity of agarose fiber network is significantly lower than in the bulk gel. The diffusion coefficient of solutes in this layer is consequently decreased for steric reasons. Modeling of solute transport shows that, in the bulk gel, macroscopic diffusion satisfactorily follows the classical Fick's diffusion laws. For the tested solutes, the local diffusion coefficients in the bulk gel, measured at microscopic scale by FCS, were equal, within experimental errors, to the average diffusion coefficients applicable at macroscopic scales (>or=mm). This confirms that anomalous diffusion applies only to solutes with sizes close to the gel pore size and at short time (相似文献   

Brush-sheathed particles diffusing at brush-coated surfaces in the thermally responsive PNIPAAm system

Phase-contrast microscopy and particle tracking algorithms are used to study the near-surface diffusion of poly(N-isopropylacrylamide) (PNIPAAm) brush functionalized micron-sized silica microspheres after sedimentation from aqueous suspension onto planar substrates coated with a similar polymer brush above and below the lower critical solution temperature (LCST) of PNIPAAm, 32 degrees C. A small negative charge on the wall and the particles (zeta potential = -6 mV) prevents adhesion above and below the LCST. The near-surface translational diffusion coefficient (D(surface)) is compared to the bulk-phase translational diffusion coefficient (D(bulk)), which was measured by dynamic light scattering. We find that D(surface)/D(bulk) is approximately equal to 0.6 at temperatures T < 32 degrees C but rises abruptly to approximately 0.8-0.9 at T > 32 degrees C. Near-surface diffusion is expected to be slower than bulk diffusion owing to hydrodynamic coupling to the wall, implying reduced hydrodynamic coupling at the higher temperatures, perhaps mediated by enhanced electrostatic repulsion above the LCST transition.     

Equilibrium, Kinetics, Diffusion and Self-Association of Proteins at Membrane Surfaces: Measurement by Total Internal Reflection Fluorescence Microscopy

Abstract— The equilibrium, kinetics, diffusion and self-association of proteins at membrane/solution interfaces may deviate substantially from these processes in bulk solution. A set of methods for examining these phenomena combines substrate-supported planar model membranes and the use of evanescent illumination with laser-based, quantitative fluorescence microscopy. Measurement of the steady-state, surface-associated fluorescence can be used to examine the thermodynamic properties of proteins at membranes. When combined with fluorescence photobleaching recovery, this technique provides information about membrane-binding kinetics; and when combined with fluorescence pattern photobleaching recovery, measurement of the translational diffusion coefficients of proteins weakly bound to membranes is possible. The use of polarized evanescent illumination can provide information about the orientation distributions of adsorbed fluorophores. Fluorescence correlation spectroscopy provides information about the self-association ( e.g. dimerization) of membrane-associated proteins.     

Membrane formation by isothermal precipitation in polyamide-formic acid-water systems II. Precipitation dynamics

An analysis is presented, which describes the isothermal ternary diffusion process encountered in the formation of the aliphatic polyamide membranes such as Nylon-66 by direct immersion-precipitation of a polymeric solution in a nonsolvent bath. A material coordinate is employed to derive the mass transfer equations for the membrane solution. The convective mass transfer in the coagulation bath is taken into account by solving the hydrodynamic boundary layer equations. Diffusion coefficients were measured and used to deduce ternary phenomenological coefficients. The computed results are found to agree with measured precipitation times and with membrane morphologies observed by scanning electron photomicrographs. © 1995 John Wiley & Sons, Inc.     

Molecular dynamics simulation of self- and mutual diffusion coefficients for confined mixtures

The self- and mutual diffusion coefficients for binary mixtures of Ar-Kr both in the bulk and in the nanopores were studied by molecular dynamics simulations. The composition dependences and the relationships between the self- and the mutual diffusion coefficients both in the bulk and in the nanopores were further discussed. It was found that the simulation results (D(c.m.)) are close to the calculated ones (D(s)) for the Ar-Kr system. Both self- and mutual diffusion coefficients in nanopores are much lower than that of the bulk, and they ever decrease as the pore width decreases. Nevertheless, the self- and mutual diffusion coefficients increase as the mole fraction of Ar increases, and as expected, increase as the temperature increases. The self-diffusion coefficients of mixtures both in the bulk and in the nanopores are predicted by the Carman model and by the molecular cluster model.     

Which surfactants reduce surface tension faster? A scaling argument for diffusion-controlled adsorption

Consider the example of surfactant adsorbing from an infinite solution to a freshly formed planar interface. There is an implicit length scale in this problem, the adsorption depth h, which is the depth depleted to supply the interface with the absorbed surfactant. From a mass balance, h can be shown to be the ratio of the equilibrium surface concentration gamma eq to the bulk concentration C infinity. The characteristic time scale for diffusion to the interface is tau D = h2/D, where D is the diffusivity of the surfactant in solution. The significance of this time scale is demonstrated by numerically integrating the equations governing diffusion-controlled adsorption to a planar interface. The surface tension equilibrates within 1-10 times tau D regardless of bulk concentration, even for surfactants with strong interactions. Dynamic surface tension data obtained by pendant bubble method are rescaled using tau D to scale time. For high enough bulk concentrations, the re-normalized surface tension evolutions nearly superpose, demonstrating that tau D is indeed the relevant time scale for this process. Surface tension evolutions for a variety of surfactants are compared. Those with the smallest values for tau D equilibrate fastest. Since diffusion coefficients vary only weakly for surfactants of similar size, the differences in the equilibration times for various surfactant solutions can be attributed to their differing adsorption depths. These depth are determined by the equilibrium adsorption isotherms, allowing tau D to be calculated a priori from equilibrium surface tension data, and surfactant solutions to be sorted in terms of which will reduce the surface tension more rapidly. Finally, trends predicted by tau D to gauge what surfactant properties are required for rapid surface tension reduction are discussed. These trends are shown to be in agreement with guiding principles that have been suggested from prior structure-property studies.     

Influence of protein–protein interactions on bulk mass transport during ultrafiltration

Bulk mass transfer limitations can have a significant effect on the flux and selectivity during membrane ultrafiltration. Most previous studies of these phenomena have employed the simple stagnant film analysis, but this model is unable to account for the effects of solute–solute interactions on mass transport. We have developed a generalized framework for multicomponent mass transfer that includes both thermodynamic and hydrodynamic (frictional) interactions. Thermodynamic (virial) coefficients were evaluated from osmotic pressure data for albumin (BSA) and immunoglobulins (IgG), while hydrodynamic interaction parameters were determined from filtrate flux data obtained in a stirred cell using fully retentive membranes. The protein concentration profiles in the bulk solution were evaluated by numerical solution of the governing continuity equations incorporating the multicomponent diffusive flux. This model was used to analyze flux and protein transmission data obtained for the filtration of BSA and IgG mixtures through partially permeable membranes. The model accurately predicted the large reduction in flux and BSA transmission upon addition of IgG. These effects were due to the coupling between BSA and IgG mass transfer caused by protein–protein interactions.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Simultaneous investigation of sedimentation and diffusion of a single colloidal particle near an interface

We describe here a new procedure for the simultaneous investigation of sedimentation and diffusion of a colloidal particle in close proximity to a solid, planar wall. The measurements were made using the optical technique of total internal reflection microscopy, coupled with optical radiation pressure, for dimensionless separation distances (gap width/radius of particle) ranging from 0.01 to 0.05. In this region, the hydrodynamic mobility and diffusion coefficient are substantially reduced below bulk values. The procedure involved measuring the mean and the variance of vertical displacements of a Brownian particle settling under gravity toward the plate. The spatially varying diffusion coefficient was calculated from the displacements at small times (where diffusive motion was dominant). The mobility relationship for motion normal to a flat plate was tested by measuring the average distance of travel versus time as the particle settled under the constant force of gravity. For the simple Newtonian fluid used here (aqueous salt solution), the magnitude of the diffusion coefficient and mobility, plus their dependence on separation distance, showed excellent agreement with predictions. This new technique could be of great value in measuring the mobility and diffusion coefficient for near-contact motion in more complex fluids for which the hydrodynamic correction factors are not known a priori, such as shear-thinning fluids.     

Sorption/diffusion behaviour of anionic surfactants in polyacrylamide hydrogels: from experiment to modelling

The sorption and diffusion processes of anionic surfactants with different chain length through polyacrylamide hydrogels with low swelling degree have been studied by electrical conductivity measurements. The multicomponent equilibrium equation has been used to model the sorption isotherms of different anionic surfactant in the hydrogels. Such isotherms show that initial rapid sorption of unimer surfactant into the membranes occurs, suggesting that non-freezing water can be involved in these interactions. In aqueous solution, at concentrations near and above the critical micelle concentration an anti-co-operative region is found. The diffusion coefficients of the anionic surfactants inside the hydrogel matrix show that the mobility of diffusing surfactant entities is dependent on cross-linker concentration and chain length. The Cukier hydrodynamic model and the free volume theory as modified by Peppas and Reinhart were applied to explain the dependence of the diffusion coefficients of surfactant on surfactant concentration inside the hydrogel. The hydrodynamic model was applied with success to the more hydrophilic surfactant, sodium 1-octanesulfonate, showing that the diffusion coefficients, D, increase when the resistance to hydrodynamic medium decreases; when the surfactant chain length increases (sodium dodecyl sulfate and sodium 1-hexadecane sulphonate) the variation of D with the free volume can only be understood considering the sieving effect produced by the surfactant inside gel.     

Mass transport to and within porous electrodes. Linear sweep voltammetry and the effects of pore size: The prediction of double peaks for a single electrode process

We simulate an electrode modified with a conducting porous film, where the electrolysis occurs both at the surface of the film and within it, in order to study the effect of pore size on the peak current in linear sweep voltammetry. For redox systems with reversible electrode kinetics we find that for both very large and very small pores the peak current is given by the Randles-?ev?ik equation. For intermediate pore size, however, we observe a greatly enhanced peak current. When considering systems with irreversible electrode kinetics a very similar pattern is observed, except for the case of very small pores. In this case the peak current is actually smaller than expected from the Randles-?ev?ik equation because the peak splits into two distinct peaks; one due to ??thin layer?? diffusion within the film and another caused by planar diffusion from bulk solution. The experimental implications of this observation are significant given the widespread use of modified electrodes for analysis.     

Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.     

Precise measurement of the self-diffusion coefficient for poly(ethylene glycol) in aqueous solution using uniform oligomers

Uniform poly(ethylene glycol) (PEG) oligomers, with a degree of polymerization n=1-40, were separated by preparative supercritical fluid chromatography from commercial monodispersed samples. Diffusion coefficients, D, for separated uniform PEG oligomers were measured in dilute solutions of deuterium oxide (D(2)O) at 30 degrees C, using pulsed-field gradient nuclear magnetic resonance. The measured D for each molecular weight was extrapolated to infinite dilution. Diffusion coefficients obtained at infinite dilution follow the scaling behavior of Zimm-type diffusion, even in the lower molecular weight range. Molecular-dynamics simulations for PEG in H(2)O also showed this scaling behavior, and reproduced close hydrodynamic interactions between PEG and water. These findings suggest that diffusion of PEG in water is dominated by hydrodynamic interaction over a wide molecular weight range, including at low molecular weights around 1000.     

Morphology and permeability of cellulose/chitin blend membranes

A series of biodegradable cellulose/chitin blend membranes were successfully prepared from blend solution of cellulose and chitin in 9.5 wt% NaOH/4.5 wt% thiourea aqueous solution coagulating with 5.0 wt% (NH₄)₂SO₄. The influence of chitin content on the morphology and structure of the membranes was studied by scanning electron microscopy, environmental scanning electron microscopy and wide-angle X-ray diffractometry, as well as Fourier transform infrared spectroscopy. Using double-cell method and solution depletion method, the permeability and partition coefficients of three model drugs (ceftazidine, cefazolin sodium, and thiourea) were determined in phosphate buffer solution to clarify the diffusion mechanism governing transport of solutes in these membranes. Diffusion coefficients were calculated from the permeability and partition coefficients in terms of Fick's law. The effects of the chitin content, pH, ionic strength, molecular size and temperature on the drug diffusion were also studied. Our results revealed that all of the membranes had a porous-like structure. The introduction of chitin exhibited great influence on the morphology and crystal structure of the blend membranes, resulting in a significant different permeability. For the first time, a dual diffusion mechanism with some hindrance of molecular diffusion via polymer obstruction was employed to explain the transport of drugs in the membranes.     

Light-scattering studies on solutions of cellulose in the ammonia / ammonium thiocyanate solvent system. II. Quasielastic light-scattering and liquid crystal study

This is the second part of a two–part study of the NH₃NH₄SCN cellulose solvent system. Quasielastic light scattering was used to determine the diffusion coefficients of cellulose in solution and the effective hydrodynamic radius of the dissolved molecules. Additionally, the system was studied using light microscopy to determine the minimum critical volume fraction or liquid crystal formation. Very little change was found in the diffusion coefficients with change in cellulose concentration indicating little interaction between the chains in solution. Values of 7.69 and 2.66 × 10⁸ cm²/s were measured for samples having a degree of polymerization of 153 and 969. The value of the coefficient relating the hydrodynamic volume to the radius of gyration was found to be in the range of 0.33 to 0.53, indicating an extended coil conformation according to the Kirkwood-Riseman theory. The minimum critical volume fractions necessary for liquid crystal formation, υ₂′ were 0.039, 0.038, and 0.048 for the three solvent compositions studied. The values calculated for υ₂′ based on the measured persistence lengths were much larger than the predicted values, indicating strong deviation from theory or possible aggregation in the system.     

Diffusion of glycosylphosphatidylinositol (GPI)-anchored bovine prion protein (PrP) in supported lipid membranes studied by single-molecule and complementary ensemble methods

In this work cellular bovine prion protein (PrP^c) was incorporated in supported lipid membranes and its lateral diffusion was studied by single-dye tracking (SDT) and a complementary ensemble method, fluorescence recovery after photobleaching (FRAP). PrP^c was purified from calf brain with its native glycosylphosphatidylinositol (GPI) anchor and reconstituted into DMPC lipid vesicles. Homogeneous spreading on solid supports over macroscopic areas was confirmed with fluorescence microscopy. FRAP results demonstrated very high mobile fractions of up to 94%, confirming that most of the GPI-anchored PrP^c are freely diffusive in the fluid supported membrane matrix. Moreover, the lateral diffusivity of PrP^c significantly depends on the pH of the buffer, suggesting that the conformation of PrP^c and thus the frictional drag exerted to the protein molecule (and thus the effective hydrodynamic radius) is influenced by the effective net charge. To complement the ensemble results obtained by FRAP, the statistical variation of lateral diffusion coefficients of individual PrP^c molecules in the supported membranes were measured with SDT. Simulation-based statistical analysis indicated that in addition to the expected statistical scatter there is a significant spread of diffusion coefficients, while the average of the diffusion coefficients of individual proteins obtained by SDT is in excellent agreement with those measured by ensemble FRAP. In further experiments, PrP^c was laterally concentrated in the membrane by the application of tangential electric fields (membrane electrophoresis). However, the equilibrium concentration profile reached after 20 min was different from an exponential gradient. This finding suggests that PrP^c purified from bovine brain possesses non-uniform net charges. As the lateral diffusion coefficient of proteins in two-dimensional lipid membranes sensitively depends upon the frictional drag, the combination of SDT, ensemble FRAP, and membrane electrophoresis can be used as a powerful tool to gain insights into protein–protein binding and oligomer formation that would play a crucial role in infectious protein transmitted diseases such as BSE.     

Pore Modification in Porous Ceramic Membranes With Sol-Gel Process and Determination of Gas Permeability and Selectivity

Summary: The aim of the study was to investigate the variation in total surface area, porosity, pore size, Knudsen and surface diffusion coefficients, gas permeability and selectivity before and after the application of sol-gel process to porous ceramic membrane in order to determine the effect of pore modification. In this study, three different sol-gel process were applied to the ceramic support separately; one was the silica sol-gel process which was applied to increase porosity, others were silica-sol dip coating and silica-sol processing methods which were applied to decrease pore size. As a result of this, total surface area, pore size and porosity of ceramic support and membranes were determined by using BET instrument. In addition to this, Knudsen and surface diffusion coefficients were also calculated. After then, ceramic support and membranes were exposed to gas permeation experiments by using the CO₂ gas with different flow rates. Gas permeability and selectivity of those membranes were measured according to the data obtained. Thus, pore surface area, porosity, pore size and Knudsen diffusion coefficient of membrane treated with silica sol-gel process increased while total surface area was decreasing. Therefore, permeability of ceramic support and membrane treated with silica sol-gel process increased, and selectivity decreased with increasing the gas flow rate. Also, surface area, porosity, pore size, permeability, selectivity, Knudsen and surface diffusion coefficients of membranes treated with silica-sol dip coating and silica-sol processing methods were determined. As a result of this, porosity, pore size, Knudsen and surface diffusion coefficients decreased, total surface area increased in both methods. However, viscous flow and Knudsen flow permeability were detected as a consequence of gas permeability test and Knudsen flow was found to be a dominant transport mechanism in addition to surface diffusive flow owing to the small pore diameter in both methods. It was observed that silica-sol processing method had lower pore diameter and higher surface diffusion coefficient than silica-sol dip coating method.     

Dynamic light scattering for characterization of latices

With photon correlation spectrometry the diffusion coefficients of colloid particles in highly diluted aqueous suspensions can be measured and average diameters and polydispersities of the samples can be determined. Electrokinetic and electroviscous effects caused by polarization of the electrostatic double layer influence the diffusion of the particles. The adsorption of macromolecules at the interfaces of the particles results in an increase of the hydrodynamic diameter and a decrease of the diffusion and sedimentation coefficients. The hydrodynamic thicknesses of the polymer layers can be evaluated. The thickness values and their dependences on adsorbed amount and molar mass can only be interpreted by the existence of long tails of the adsorbed macromolecules dangling from the interface into the solution. The resulting conformation model is supported by the new theory of Scheutjens-Fleer. Special importance have those tails for the interaction of particles and their stability and flocculation in disperse systems.     

纳滤膜对电解质溶液分离特性的理论研究(II): 混合电解质溶液

假定纳滤膜具有狭缝状孔, 使用纯水透过系数、膜孔径及膜表面电势来表征纳滤膜的分离特征, 用流体力学半径和无限稀释扩散系数表征了离子特性. 采用扩展Nernst-Planck方程、Donnan平衡模型和Poisson-Boltzmann理论描述了混合电解质溶液中离子在膜孔内的传递现象, 计算了三种商用纳滤膜(ESNA1-LF, ESNA1和LES90)对同阴离子、同阳离子和含四种离子的混合电解质体系中离子的截留率, 并与实验数据进行了比较. 计算结果表明, 电解质溶液中离子在纳滤膜孔内传递的主要机理是离子的扩散和电迁移, 纳滤膜对混合电解质溶液中离子的分离效果主要由空间位阻和静电效应决定. 该模型在低浓度时对含一价离子的混合电解质溶液通过纳滤膜的截留率计算结果比较准确, 但对高浓度或含高价离子的混合电解质溶液则偏差较大.     

Further studies on solvent extraction with immobilized interfaces in a microporous hydrophobic membrane

Investigations on solvent extraction of acetic acid into xylene or methyl isobuty] ketone by using immobilized interfaces in microporous hydrophobic membranes have now been extended to a number of different membranes with a wide variation in pore size and porosity. Measured intrinsic membrane transfer coefficients of the solute are adequately described by the simple model of unhindered diffusion in tortuous pores developed earlier. Applied pressure difference did not influence the overall solute transfer coefficient as long as it was not close to that required for the breakthrough of aqueous phase into organic phase. Aqueous and organic boundary layer mass transfer coefficients in the flow type test cell have been determined with a known membrane and utilized to predict effectively the overall solute transfer coefficient observed with other membranes.