Analysis of solute diffusion in poly(vinyl alcohol) hydrogel membrane

Measurement of diffusion and partitioning of solutes having molecular weights ranging 180–66000 in PVA gel membranes with various crosslinking degree were carried out. With increasing solute size or decreasing number of average molecular weight between crosslinks of the membranes, both the solute permeability and partition coefficient decreased. In spite of similar solute sizes, the more hydrophilic solute ribonuclease showed higher permeability and partition coefficient than the less hydrophilic α-lactalbumin, probably due to interaction with the hydrophilic PVA. The solute diffusion through swollen gel membrane was analyzed by the equation based on free volume theory. In this analysis equation, the partition coefficient, which is defined as the ratio of solute concentration in gel membrane standardized by water volume in the membrane to that in bulk solution, was introduced as the probability of a diffusing species finding a mesh with a volume of at least the solute size. The efficiency of the proposed analysis equation was confirmed by the experimental results of the effects of solute size and water volume fraction in the membrane.     

The use of moment theory to interpret diffusion and sieving measurements in terms of the pore size distribution in heteroporous membranes

Moment theory has been applied to model porous membranes to show that one can place reasonable bounds on the cumulative pore size distribution, the hindered diffusivity or the reflection coefficient of large solutes in a heteroporous membrane by measuring the diffusive permeability to a small solute, the hydraulic permeability and one or two additional transport characteristics. These additional measurements involve either the flux of a small solute at Pe1, the hindered diffusivity of a large solute or the reflection coefficient of a large solute at Peå1. Membrane heteroporosity is incroporated in the predicted bounds without requiring one to make any a priori assumptions about the nature of the pore size distribution. In this paper, the results from calculations performed with different model membranes containing log-normal pore size distributions are reported. A comparison of the results obtained with three different membranes shows that one can distinguish between membranes with the same average pore size but different pore size distributions by measuring either the hindered diffusion coefficient or the reflection coefficient of two different sized solutes. A comparison of the bounds on D and the bounds on σ predicted from different types of transport measurements shows that, under certain conditions, one can place tighter bounds on one transport characteristic by measuring a different one.     

Solute diffusion in swollen membranes VII. Diffusion in semicrystalline networks

A model is developed to express the solute diffusion coefficient through semicrystalline polymeric networks. The crystallites create impermeable diffusional barriers around the amorphous regions. Solute diffusion is determined by applying a transport model to the amorphous phase and incorporating the crosslinked polymer structure characteristics. This model is tested with theophylline and vitamin B₁₂ permeation experiments through semicrystalline poly(vinyl alcohol) membranes prepared by annealing of amorphous PVA membranes. The degree of crystallinity varies between 23.1 % and 40.5 % on a dry basis. The solute diffusion coefficients correlate well with various parameters of the model.     

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.     

Pore structure of gel chitosan membranes. II. Modelling of the pore size distribution from solute diffusion measurements. Gaussian distribution—Mathematical limitations

It was assumed that the pore size distribution in water-swollen gel membranes can be described by the Gaussian distribution function with a mean pore radius r_m and standard deviation σ. The function was applied to the Renkin capillary model based on solute diffusion measurements through membranes. The numerical analysis showed that the problem does not have a unique solution but a family of solutions approximated by the function r_m = Aσ² + r_Renkin, with the pore radius, r_Renkin, obtained on the assumption of uniform radii, being the largest of all r_m obtained with the distribution. The uncertainty of the solution remained also after modification of the experimental data with a molecular probe of permeability coefficient equal to zero, and after cutting the tails of the Gaussian pore size distribution.     

Facilitated transport mechanism in fixed site carrier membranes

Facilitated transport of gases, such as O₂, has been observed for fixed site carrier membranes. Carrier-impregnated ion-exchange membranes have also been used to produce facilitated transport of CO₂, H₂S and olefins when the carriers are not completely mobile. The actual mechanism for this facilitated transport has not been determined previously. The facilitated transport is provided by the exchange of solute between the free solute region and the bound complexing agent combined with gradients in the free solute and complexed carrier. The ratio of mobility for exchange between the regions is the dimensionless equilibrium constant of the reversible reaction. An expression is also derived for the relationship between the effective diffusion coefficient of the complex in facilitated transport, D_AB, and the diffusion coefficients for exchange between free and complexed solute, D_DH and D_HD. Since D_AB can be determined from experimental results, D_DH and D_HD can be calculated. The results also show the morphology dependence of D_AB. The diffusion coefficient of the free solute D_A also changes with the loading of the complexing agent in the film. This morphology dependence can explain why the gas permeability can decrease when the concentration of the complexing agent increases in the membrane.     

Characterization of the pore area distribution in porous membranes using transport measurements

An approach originally proposed by Mason and coworkers has been applied to model porous membranes to show that transport measurements with small and large solutes can be used to distinguish between porous membranes with the same average pore size but different pore size distributions. In addtion, it is shown that such measurements can be used to account for membrane heteroporosity when predicting the sieving characteristics of a membrane. This is done by applying moment theory to results from flux measurements for a small solute at Pe ≈ 1 or to results from measurements of the reflection coefficient for a large solute at infinite Pe. No a priori assumptions about the nature of the distribution of pore areas are necessary.In this paper, the results from calculations performed with three different model membranes with log-normal pore size distribution are reported. These results show that one can begin to distinguish between membranes by measuring the hydraulic and diffusive permeability and performing at least one additional flux measurement — with either a small, non-hindered solute at Pe ≈ 1 or a large solute at infinite Pe. Results also show that a fairly narrow window can be placed on the sieving curve for a heteroporous membrane without performing any sieving measurements. This is an interesting and encouraging result because it means that many of the problems that arise from measuring and interpreting pore size distributions using more traditional techniques can be avoided by using small solute flux measurements to predict the separation characteristics of many porous membranes.     

Membrane characterization and solute diffusion in porous composite nanocellulose membranes for hemodialysis

The membrane and solute diffusion properties of Cladophora cellulose and polypyrrole (PPy) functionalized Cladophora cellulose were analyzed to investigate the feasibility of using electroactive membranes in hemodialysis. The membranes were characterized with scanning electron microscopy, ζ-potentiometry, He-pycnometry, N₂ gas adsorption, and Hg porosimetry. The diffusion properties across the studied membranes for three model uremic toxins, i.e. creatinine, vitamin B12 and bovine serum albumin, were also analyzed. The characterization work revealed that the studied membranes present an open structure of weakly negatively charged nanofibers with an average pore size of 21 and 53 nm for pristine cellulose and PPy-Cladophora cellulose, respectively. The results showed that the diffusion of uremic toxins across the PPy-Cladophora cellulose membrane was faster than through pure cellulose membrane, which was related to the higher porosity and larger average pore size of the former. Since it was found that the average pore size of the membranes was larger than the hydrodynamic radius of the studied model solutes, it was concluded that these types of membranes are favorable to expand the Mw spectrum of uremic toxins to also include conditions associated with accumulation of large pathologic proteins during hemodialysis. The large average pore size of the composite membrane could also be exploited to ensure high-fluxes of solutes through the membrane while simultaneously extracting ions by an externally applied electric current.     

Rotational-diffusion anomalies in dye solutions from transient-dichroism experiments

Subnanosecond transient-dichroism experiments have been performed to investigate the rotational diffusion of dyes in solution. Dyes and solvents were chosen in a way to obtain information on the influence of size, shape and hydrogen-bonding abilities either of the solute or the solvent molecules. One finds slow orientational relaxation of di-anionic xanthene dyes in alcohols, while oblate cationic dyes rotate faster in spite of their comparable size. The rotational diffusion times for alcohol solutions exceed the theoretical values predicted by the Debye-Einstein model except for prolate molecules. For a solute molecule with internal mobility the rotational diffusion exhibits a partial slip behaviour. It is shown that the deviations from the Debye-Einstein model are restricted to alcohols since for other solvents either with or without strong hydrogen-bonding abilities the experimental values agree with the hydrodynamic model including the stick-boundary condition. Experiments on erythrosine B reveal the influence of size and shape of the attached solvent molecules.     

A spray technique for the determination of membrane diffusion and distribution coefficients by the time-lag method: evaluated for electrolyte transport through charged and uncharged membranes

Using solution sprays, a sharp concentration step may be effected at the surface of a membrane in less than 0.1 sec. This technique allows the time-lag method to be used to determine rapidly both solute permeability and diffusion coefficient in a single experiment. From the mathematical analysis of diffusion into a cell with finite collecting volume, limiting conditions are derived which define experimental conditions under which the conventional linear, steady state analysis of time lag will be valid. These limiting conditions were used to determine the dimensions of the experimental diffusion cell. Diffusion, permeability and distribution coefficients were measured for a variety of electrolytes in both charged and uncharged membranes and shown to be in good agreement with conventional methods. A Donnan analysis is given by which the charged nature of an unknown membrane may be assessed precisely and rapidly.     

Modeling and simulation of the dynamic behavior of monoliths. Effects of pore structure from pore network model analysis and comparison with columns packed with porous spherical particles

A mathematical model is presented that could be used to describe the dynamic behavior, scale-up, and design of monoliths involving the adsorption of a solute of interest. The value of the pore diffusivity of the solute in the pores of the skeletons of the monolith is determined in an a priori manner by employing the pore network modeling theory of Meyers and Liapis [J. Chromatogr. A, 827 (1998) 197 and 852 (1999) 3]. The results clearly show that the pore diffusion coefficient, Dmp, of the solute depends on both the pore size distribution and the pore connectivity, nT, of the pores in the skeletons. It is shown that, for a given type of monolith, the film mass transfer coefficient, Kf, of the solute in the monolith could be determined from experiments based on Eq. (3) which was derived by Liapis [Math. Modelling Sci. Comput., 1 (1993) 397] from the fundamental physics. The mathematical model presented in this work is numerically solved in order to study the dynamic behavior of the adsorption of bovine serum albumin (BSA) in a monolith having skeletons of radius r(o) = 0.75x10(-6) m and through-pores having diameters of 1.5x10(-6)-1.8x10(-6) m [H. Minakuchi et al., J. Chromatogr. A, 762 (1997) 135]. The breakthrough curves of the BSA obtained from the monolith were steeper than those from columns packed with porous spherical particles whose radii ranged from 2.50x10(-6) m to 15.00x10(-6) m. Furthermore, and most importantly, the dynamic adsorptive capacity of the monolith was always greater than that of the packed beds for all values of the superficial fluid velocity, Vtp. The results of this work indicate that since in monoliths the size of through-pores could be controlled independently from the size of the skeletons, then if one could construct monolith structures having (a) relatively large through-pores with high through-pore connectivity that can provide high flow-rates at low pressure drops and (b) small-sized skeletons with mesopores having an appropriate pore size distribution (mesopores having diameters that are relatively large when compared with the diameter of the diffusing solute) and high pore connectivity, nT, the following positive results, which are necessary for obtaining efficient separations, could be realized: (i) the value of the pore diffusion coefficient, Dmp, of the solute would be large, (ii) the diffusion path length in the skeletons would be short, (iii) the diffusion velocity, vD, would be high, and (iv) the diffusional response time, t(drt), would be small. Monoliths with such pore structures could provide more efficient separations with respect to (a) dynamic adsorptive capacity and (b) required pressure drop for a given flow-rate, than columns packed with porous particles.     

Transport of Carbamazepine,Ciprofloxacin and Sulfamethoxazole in Activated Carbon: Solubility and Relationships between Structure and Diffusional Parameters

The transport of carbamazepine, ciprofloxacin and sulfamethoxazole in the different pores of activated carbon in an aqueous solution is a dynamic process that is entirely dependent on the intrinsic parameters of these molecules and of the adsorbent. The macroscopic processes that take place are analyzed by interfacial diffusion and reaction models. Modeling of the experimental kinetic curves obtained following batch treatment of each solute at 2 µg/L in tap water showed (i) that the transport and sorption rates were controlled by external diffusion and intraparticle diffusion and (ii) that the effective diffusion coefficient for each solute, with the surface and pore diffusion coefficients, were linked by a linear relationship. A statistical analysis of the experimental data established correlations between the diffusional parameters and some geometrical parameters of these three molecules. Given the major discontinuities observed in the adsorption kinetics, the modeling of the experimental data required the use of traditional kinetic models, as well as a new kinetic model composed of the pseudo first or second order model and a sigmoidal expression. The predictions of this model were excellent. The solubility of each molecule below 60 °C was formulated by an empirical expression.     

Nonstationary diffusion of polystyrenes through a cellophane membrane

Diffusion of five polystyrene fractions at various concentrations in toluene through cellophane membranes has been observed. The results have been used to calculate friction coefficients between solvent and solute, and between solute and membrane. The calculation requires measurement of the diffusion coefficient and the reflection coefficient of the solute, of the permeability for the solvent, of the pore volume of the membrane, and of the partition coefficient of the solute between membrane and solvent. By comparing the friction coefficient between solvent and solute in the membrane with this coefficient in free solution, the tortuosity factor and the pore diameter of the membrane can be estimated. The dependence of the friction coefficients on molecular weight M₂ of the solute is determined. For large values of M₂, the friction between solute and solvent is the determining factor. The friction coefficient between solute and solvent increases more strongly with M₂ in the membrane than in free solution owing to an entrance effect for the permeating solute at the interface.     

Factors influencing reverse osmosis rejection of inorganic solutes from aqueous solution

Reverse osmosis (RO) rejection is strongly influenced by the distribution of solute between the membrane and solvent phases. For this reason, we examined the partition coefficients of inorganic compounds between water and cellulose acetate (CA) membranes. Cation and anion partition coefficients were determined by independent analyses. Effects of fixed (negative) membrane charges on CA are clearly apparent at low solute concentrations. The mean cation/anion partition coefficients decrease with the product of the cation and anion valence, and increase with increasing ionic size. Un-ionized inorganic compounds, HgC1₂ and HAuC1₄, are strongly sorbed by CA membranes. All of these observations are consistent with electrostatic theory.Experimental membrane/water partition coefficients are influenced by temperature, pH, and ion-pairing. CA membranes exhibit swelling and shrinkage when exposed to certain aqueous solutions. Swelling and shrinkage influence solute partition and diffusion coefficients, the water content of the membranes, and their RO rejection.The present results provide a comprehensive experimental basis for understanding the mechanism of RO rejection by CA membranes. Moreover, these results can be used to predict RO behavior under a wide variety of experimental conditions. The potential use of reverse osmosis in a variety of wastewater applications is considered in some detail.     

Novel calcium-alginate capsules with aqueous core and thermo-responsive membrane

Novel calcium-alginate (Ca-alginate) capsules with aqueous core and thermo-responsive membrane are successfully prepared by introducing a co-extrusion minifluidic approach, and the thermo-responsive gating characteristics of Ca-alginate capsule membranes embedded with poly(N-isopropylacrylamide) (PNIPAM) microspheres are investigated systematically. The experimental results show that the prepared Ca-alginate capsules are highly monodisperse, and the average diameter and membrane thickness of Ca-alginate capsules are about 2.96 mm and 0.11 mm respectively. The Ca-alginate capsule membranes exhibit desired thermo-responsive gating property. With increasing the content of PNIPAM microspheres embedded in the Ca-alginate capsule membranes, the thermo-responsive gating coefficient of the capsule membranes increases simply. When solute molecules diffuse through the capsule membrane, the thermo-responsive gating coefficient is significantly affected by the molecular weight of solute molecules.     

Diblock copolymer membranes investigated by single-particle tracking

We report a study on particle diffusion in membranes formed from polystyrene-block-poly(2-(dimethylamino)ethyl methacrylate) (PS-b-PDMAEMA) diblock copolymers. The membranes were investigated by scanning electron microscopy and by single-particle tracking employing carboxy-functionalized polystyrene beads loaded with a fluorophore as spectroscopic probes. From the diffusion trajectories we extracted the domain size distribution of the membranes and the local diffusion coefficient of the beads as a function of the size of the beads. The single-particle tracking data revealed that the effective domain sizes of the membranes are reduced with respect to the domain sizes obtained from scanning electron microscopy, reflecting the confined diffusion of the probe particles due to interactions with the domain walls. This is corroborated by a clear correlation between the diffusion coefficient of an individual polystyrene bead and the size of the actual domain to which it is confined.     

Size dependence of protein diffusion very close to membrane surfaces: measurement by total internal reflection with fluorescence correlation spectroscopy

The diffusion coefficients of nine fluorescently labeled antibodies, antibody fragments, and antibody complexes have been measured in solution very close to supported planar membranes by using total internal reflection with fluorescence correlation spectroscopy (TIR-FCS). The hydrodynamic radii (3-24 nm) of the nine antibody types were determined by comparing literature values with bulk diffusion coefficients measured by spot FCS. The diffusion coefficients very near membranes decreased significantly with molecular size, and the size dependence was greater than that predicted to occur in bulk solution. The observation that membrane surfaces slow the local diffusion coefficient of proteins in a size-dependent manner suggests that the primary effect is hydrodynamic as predicted for simple spheres diffusing close to planar walls. The TIR-FCS data are consistent with predictions derived from hydrodynamic theory. This work illustrates one factor that could contribute to previously observed nonideal ligand-receptor kinetics at model and natural cell membranes.     

Relation between pore sizes of protein crystals and anisotropic solute diffusivities

The diffusion of a solute, fluorescein, into lysozyme protein crystals with different pore structures was investigated. To determine the diffusion coefficients, three-dimensional solute concentration fields acquired by confocal laser scanning microscopy (CLSM) during diffusion into the crystals were compared with the output of a time-dependent 3-D diffusion model. The diffusion process was found to be anisotropic, and the degree of anisotropy increased in the order: triclinic, tetragonal and orthorhombic crystal morphology. A linear correlation between the pore diffusion coefficients and the pore sizes was established. The maximum size of the solute, deduced from the established correlation of diffusion coefficients and pore size, was 0.73 +/- 0.06 nm, which was in the range of the average diameter of fluorescein (0.69 +/- 0.02 nm). This proves that size exclusion is the key mechanism for solute diffusion in protein crystals. Hence, the origin of solute diffusion anisotropy can be found in the packing of the protein molecules in the crystals, which determines the crystal pore organization.     

Oscillations with a long periodical time observed in solute transport by diffusion combined with convection through a single hollow-fiber membrane

Solute transport by diffusion combined with convection through a single hollow-fiber membrane fixed on an axis of a circular tube was studied precisely. Purified water and an aqueous solution of a solute were fed at constant flow rates into the circular tube and the lumen of the membrane, respectively, and oscillations with a long periodical time were observed in the concentration of solution discharged from the lumen. Results obtained with varying experimental conditions (different solutes, membranes and flow rates at the lumen inlet and outlet) suggest that the oscillations are related to solute transport caused by convection flow through the membranes.