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.     

Effects of concentration on the partitioning of macromolecule mixtures in agarose gels

To test the effects of solute concentration on the equilibrium partitioning of single macromolecules and macromolecule mixtures between bulk solutions and gels, the partition coefficient in agarose was measured for BSA and for four narrow fractions of Ficoll with Stokes radii of 30-59 A. Solutions of each test macromolecule were equilibrated with a known volume of gel, final liquid concentrations measured, and partition coefficients (gel concentration divided by bulk concentration) calculated by applying a material balance. The partition coefficient of each macromolecule was measured in 4 and 6% gels under dilute conditions and with BSA present at initial concentrations up to 13.5 g/dl. As expected, the partition coefficients decreased with increasing agarose concentration and with increasing macromolecular size. Moreover, increasing the BSA concentration increased the partition coefficient of BSA itself and that of all four Ficolls. This effect was most pronounced for the largest test solutes. Measurements at two ionic strengths confirmed that electrostatic interactions were negligible under the conditions used. The experimental results were compared with predictions from a previously developed excluded volume theory for the partitioning of mixtures of rigid, spheroidal macromolecules in fibrous media. Agarose was represented as a randomly oriented array of cylindrical fibers, BSA as a prolate spheroid, and Ficoll as a sphere. The quantitative agreement between the model predictions and the data was generally quite good, indicating that steric interactions among solute molecules and between solute molecules and gel fibers could explain the partitioning results. The theory is simple enough computationally to be applied to a variety of processes that are influenced by the equilibrium partitioning of macromolecules.     

The Effect of Solute Concentration on Equilibrium Partitioning in Polymeric Gels

The effect of solute concentration on the equilibrium partitioning of sphere-like, colloidal solutes in stiff polymer hydrogels is examined theoretically and experimentally. The theoretical development is a statistical mechanics approach, and allows quantitative calculations to be performed to determine the concentration-dependent partition coefficient correct to first order in solute concentration at specific surface charge densities. The theory predicts that repulsive steric and/or electrostatic solute-fiber interactions exclude solute from the gel phase, but that repulsive solute-solute interactions cause partitioning into the gel to increase with increasing solute concentration. These trends are enhanced for larger solutes, increased fiber volume fractions, or stronger electrostatic repulsion. Partition coefficients have also been measured for two proteins, bovine serum albumin (BSA) and alpha-lactalbumin (ALA), in a system consisting of a salt solution and cubes of agarose hydrogel. To investigate the effect of electrostatic interactions, the experiments were performed at 0.15 M KCl and 0.01 M KCl. The theory underpredicts the strong electrostatic repulsion between BSA macromolecules at the lower ionic strength. The experimental results for ALA show the influence of an attractive interaction between the protein macromolecules, in addition to hard-sphere repulsive and electrostatic interactions. Copyright 2001 Academic Press.     

Theoretical effects of macromolecule concentration and charge on membrane rejection coefficients

A hydrodynamic model for the convection of rigid, spherical solutes through cylindrical pores, which includes both steric and electrostatic interactions between pairs of solute particles and between solutes and the pore wall, has been developed to examine the effects of solute concentration and charge on solute rejection by membrane pores during ultrafiltration. Calculations have been performed for a wide range of charge conditions and the results are presented in terms of the membrane rejection coefficient at infinite dilution and a correction factor which accounts for the first-order effects of concentration. For pores and solutes of like charge, the rejection coefficient is predicted to decrease with increasing feed concentration or ionic strength.     

Noncircular pores in model membranes: A calculation of the effect of pore geometry on the partition of a solute

The partition of a solute between a bulk phase and the rhomboidal pores of tracketched membranes is studied theoretically. The partition coefficient is concentration dependent and is reported (to first order in the bulk phase concentration) for varying solute sizes. A generalization to the case of pores of general polygonal cross section shows that narrow pore corners greatly enhance the partition coefficient due to the accumulation of solute in them. The use of an equivalent circular pore underestimates the equilibrium partition coefficient because it neglects the presence of corners.     

Determination of liquid-liquid partition coefficients by separation methods

By essence, all kinds of chromatographic methods use the partitioning of solutes between a stationary and a mobile phase to separate them. Not surprisingly, separation methods are useful to determine accurately the liquid-liquid distribution constants, commonly called partition coefficient. After briefly recalling the thermodynamics of the partitioning of solutes between two liquid phases, the review lists the different methods of measurement in which chromatography is involved. The shake-flask method is described. The ease of the HPLC method is pointed out with its drawback: the correlation is very sensitive to congeneric effect. Microemulsion electrokinetic capillary electrophoresis has become a fast and reliable method commonly used in industry. Counter-current chromatography (CCC) is a liquid chromatography method that uses a liquid stationary phase. Since the CCC solute retention volumes are only depending on their partition coefficients, it is the method of choice for partition coefficient determination with any liquid system. It is shown that Ko/w, the octanol-water partition coefficients, are obtained by CCC within the -1 < log Ko/w < 4 range, without any correlation or standardization using octanol as the stationary phase. Examples of applications of the knowledge of liquid-liquid partition coefficient in the vast world of solvent extraction and hydrophobicity estimation are presented.     

On the behavior of the electrostatic colloidal interaction in the membrane filtration of latex suspensions

In order to investigate effects of the colloidal interaction in the membrane filtrations, the dead-end ultrafiltration of latex colloids was conducted with fully retentive membranes. Experimental results concerning the permeate flux during the filtration indicate that the void fraction of cake layer increased with the decrease of the ionic strength, due to the expanded Debye double layer thickness around the particles. The concentration dependence of the gradient diffusion coefficient of colloidal particles has been examined as a function of solution ionic strength. The NVT Monte Carlo simulation was applied on the bulk suspension so as to determine the thermodynamic coefficient, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. The long-range electrostatic interactions between the particles are determined by using a singularity method, which provides accurate solutions to the linearized electrostatic field. The predictions on the variation of concentration polarization layer have been presented, from which we found that both the permeate flux and the particle diffusion are related to determine the concentration distribution above the cake layer.     

Effects of Multisolute Steric Interactions on Membrane Partition Coefficients

A key parameter in membrane and chromatographic separations is the partition coefficient, the equilibrium ratio of the solute concentration in a porous or fibrous material to that in bulk solution. The theoretical effects of solute size on partition coefficients in straight pores or randomly oriented fiber matrices have been investigated previously for very dilute solutions, where solute-solute interactions are negligible, and also for more concentrated solutions consisting of spherical solutes of uniform size. For concentrated solutions it has been found that steric and other repulsive interactions among solutes increase the partition coefficient above the dilute limit. To extend the results for porous or fibrous media to include concentrated mixtures of solutes with different sizes or shapes, we used an excluded volume approach. In this formulation, which describes steric interactions only, partition coefficients were computed by summing all volumes excluded to a solute molecule by virtue of its finite size, the finite size of other solutes, and the presence of fixed obstacles (pore walls or fibers). For a mixture of two spherical solutes, the addition of any second solute at finite concentration increased the partition coefficient of the first solute. That increase was sensitive to the size of the second solute; for a given volume fraction of the second solute, the smaller its radius, the larger the effect. When the total volume fraction of solutes was fixed, an increase in the amount of a second, smaller solute increased the partition coefficient of the first solute, whereas an increase in the amount of a second, larger solute had the opposite effect. Results were obtained also for oblate or prolate spheroidal solutes and for fibrous media containing fibers of different radii. For constant total fiber volume fraction, an increase in the amount of a second, smaller fiber decreased the partition coefficient of a spherical solute, whereas an increase in the amount of a second, larger fiber had the opposite effect. Overall, the theory suggests that the introduction of heterogeneities, whether as mixtures of solute sizes or mixtures of fiber sizes, may cause partition coefficients to differ markedly from those of uniform systems. Copyright 2000 Academic Press.     

Colloid-colloid and colloid-wall interactions in driven suspensions

We investigate the nonequilibrium fluid structure mediated forces between two colloids driven through a suspension of mutually noninteracting Brownian particles as well as between a colloid and a wall in stationary situations. We solve the Smoluchowski equation in bispherical coordinates as well as with a method of reflections, both in linear approximation for small velocities and numerically for intermediate velocities, and we compare the results to a superposition approximation considered previously. In particular, we find an enhancement of the friction (compared to the friction on an isolated particle) for two colloids driven side by side as well as for a colloid traveling along a wall. The friction on tailgating colloids is reduced. Colloids traveling side-by-side experience a solute induced repulsion while tailgating colloids are attracted to each other.     

A novel algorithm for creating coarse-grained, density dependent implicit solvent models

Implicit solvent simulations are those in which solvent molecules are not explicitly simulated, and the solute-solute interaction potential is modified to compensate for the implicit solvent effect. Implicit solvation is well known in Brownian dynamics of dilute solutions but offers promise to speed up many other types of molecular simulations as well, including studies of proteins and colloids where the local density can vary considerably. This work examines implicit solvent potentials within a more general coarse-graining framework. While a pairwise potential between solute sites is relatively simple and ubiquitous, an additional parametrization based on the local solute concentration has the possibility to increase the accuracy of the simulations with only a marginal increase in computational cost. We describe here a method in which the radial distribution function and excess chemical potential of solute insertion for a system of Lennard-Jones particles are first measured in a fully explicit, all-particle simulation, and then reproduced across a range of solute particle densities in an implicit solvent simulation.     

The mechanism of hemolysis by surfactants: effect of solution composition

The effect of ionic strength, solute size, and osmolarity of the suspending solution on surfactant-induced erythrocyte hemolysis was studied. Two possible mechanisms of hemolysis were considered: osmotic lysis (affected by solute particle size) and solubilization (not affected by solute particle size). It was found that the ionic strength of the solution has a major effect on the hemolysis process, depending on the surfactant nature and concentration. An increase in the ionic strength lowers the rate of hemolysis induced by DTAB, and enhances SDS-induced hemolysis. Changes in ionic strength have little effect on hemolysis induced by Triton X-100. To explain these effects, it was assumed that the changes in ionic strength differently affect the adsorption of cationic and anionic surfactants to the membrane. The change in the amount of adsorbed surfactant either influences the rate of osmotic hemolysis by changing the membrane permeability or induces a transition from the osmotic mechanism to solubilization. These phenomena were observed for isotonic as well as hypertonic solutions.     

Effect of electric field on the partitioning behavior of solutes in entropic interaction chromatography

In this study, a novel column design with a round cross‐section was proposed to be suitable for a transverse electric field (EF). Additionally, two beads for entropic interaction chromatography (EIC) were prepared by grafting glycidyl methacrylate onto Toyopearl HW‐65F (T65F) beads. Solute partitioning was then investigated to elucidate the role of graft polymerization with and without an EF. In a T65F column, solute partitioning was attributed to the distinct pore structure in the beads and was governed by pore flow. Under EF, partition coefficients (K_p) for solutes decreased with increasing EF strength. In the two EIC columns, a decrease of K_p was also observed without an EF while the fractionation windows were extended. It was more pronounced in the EIC column with a high grafting density (T65F‐H). This was explained by the decrease in the effective pore size of solutes caused by the steric hindrance of polymer chains. Under an EF, the solutes showed different partitioning behaviours in the T65F‐H column. With increasing EF strength, K_p for vitamin B₁₂ and myoglobin was decreased. In contrast, K_p for large solutes increased as a result of concentration polarization on the bead surface. Both behaviors were related to the modulation of graft polymerization to residual charge on the matrix and the pore size of the solutes.     

Partitioning of hexavalent chromium in temperature-sensitive,polyelectrolyte hydrogels

Partitioning data for hexavalent chromium (Cr(VI)) are presented for systems where thermally sensitive poly-N-isopropylacrylamide (NIPA)-based hydrogels are in contact with aqueous solutions of potassium dichromate (K₂Cr₂O₇). The poly-NIPA hydrogels contain 0–3% quatemized amine comonomer. Experimental results are given for the effect of gel charge, ionic strength and temperature on the partitioning of Cr(VI) into these NIPA-copolymer gels. At low ionic strength, the partition coefficient increases with the content of quatemized amine. The effect of rising temperature is to increase the partition coefficient. Swelling equilibria in aqueous K₂Cr₂O₇ solutions decrease with ionic strength and, at ionic strengths <0.1 M, are lower compared to swelling in aqueous sodium chloride solutions. Experimental partitioning data as a function of ionic strength and gel charge are compared with predictions based on two theoretical models for mixed electrolyte solutions. Predictions based on the cell model for polyelectrolyte solutions agree best with experimental results. Calculated results are in semi-quantitative agreement with experimental data for the effects of solution ionic strength and gel charge on Cr(VI) partitioning and in qualitative agreement for the effect of temperature.     

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.     

Study of the mass transfer phenomena involved in an electrophoretic membrane contactor

Electrophoretic separators, in which a porous membrane is used as a contactor, offer the possibility to scale up electrophoresis as well as to extend the field of application of electrodialysis to fractionate polyamino acids, peptides or small proteins for instance. This paper deals with the study of the mass transfer mechanisms involved in such electroseparation processes. On one hand, a theoretical approach is carried out. The different contributions to the mass transfer are considered in order to establish a relationship providing the solute concentration as function of the main parameters of the system, i.e. the operating conditions and the membrane, buffer and solute characteristics. In this expression, a partition coefficient is used to represent the interactions taking place at the membrane–solution interface. Then, an experimental study is performed with different representative solutes using a prototype apparatus in order to determine the dependence of the solvent and solute transfer with respect to the operating and physicochemical parameters of the system. The experimental results show the existence of a limiting electro-osmotic flux, the origin of which is explained. Then the partition coefficient is determined for any set of conditions by fitting the variations of the solute concentration calculated by the model with experimental ones. The dependence of the partition coefficient with respect to the solute and buffer characteristics, together with that of the transmission coefficient obtained during filtration experiments, shows that the main limitation with respect to the mass transfer is due to electrostatic interactions taking place at the membrane–solution interface.     

SECM study of solute partitioning and electron transfer at the ionic liquid/water interface

Molecular partitioning and electron-transfer kinetics have been studied at the ionic liquid/water (IL/water) interface by scanning electrochemical microscopy (SECM). The ionic liquid C8mimC1C1N is immiscible with water and forms a nonpolarizable interface when in contact with it. Partitioning of ferrocene (Fc) across the IL/water interface was studied by SECM and found to be kinetically fast with a partition coefficient CIL/CW of 2400:1. The partition coefficient value was measured by SECM under quasi-steady-state conditions without waiting for complete solute equilibration. To investigate the kinetics of the electron transfer (ET) between aqueous ferricyanide and Fc dissolved in IL, a new approach to the analysis of the SECM current-distance curves was developed to separate the contributions of Fc partitioning and the ET reaction to the tip current. Several combinations of different aqueous and nonaqueous redox species were investigated; however, only the Fc/Fe(CN)63- system behaved according to the Butler-Volmer formalism over the entire accessible potential range.     

Dense colloid transport in a bifurcating fracture

In this work, the transport of dense colloids through a water-saturated, bifurcating fracture is investigated using a constant spatial step particle tracking technique. The size of the constituents of a colloid plume is an important factor affecting the partitioning of dense colloids at the bifurcation. While neutrally buoyant colloids partition between daughter fractures in proportion to flow rates, dense colloids will preferentially exit fractures that are gravitationally downgradient, notwithstanding that the majority of the interstitial fluid may flow through the upper fracture. Comparison of the partitioning ratio between daughter fractures with the ratios of characteristic settling, diffusion, and advection time reveal that these parameters control how colloids behave at fracture bifurcations.     

Electrostatic Interaction and Partitioning of Ion-Penetrable Spheres

Electrostatic interaction between two ion-penetrable spheres near a horizontal plate or in a slit pore is investigated theoretically. The orientation of the line connecting the two particle centers can be arbitrary relative to the plate(s). The electrostatic interaction energy and force on each particle are obtained analytically by the method of images. Emphasis is placed on the effect of the presence of the second particle, compared to the case of a single particle or the case without any plate(s). It is found that the horizontal electrical force on each particle is always repulsive. This repulsive force is enhanced by the plate(s) of constant surface charge density, while it is reduced by the plate(s) of constant surface potential. The electrostatic interaction together with the steric effect is used to determine the partition coefficient for the case of a slit pore, correct to O(C(infinity)), where C(infinity) is the volume fraction of particles in the bulk solution. The positive correction coefficient is larger for conducting plates than for insulating plates. Copyright 2001 Academic Press.     

Ionic exclusion phase transition in neutral and weakly charged cylindrical nanopores

A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir [S. Buyukdagli, M. Manghi, and J. Palmeri, Phys. Rev. Lett. 105, 158103 (2010)]. It is shown that an ion located in a neutral pore undergoes two opposing mechanisms: (i) a deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions from the pore, and (ii) an attractive contribution to the ion self-energy due to the increased screening with ion penetration of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall. For pore radii around 1 nm and bulk concentrations lower than 0.2 mol/l, this mechanism leads to a first-order phase transition, similar to capillary "evaporation," from an ionic-penetration state to an ionic-exclusion state. The discontinuous phase transition exists within the biological concentration range (～0.15 mol/l) for small enough membrane dielectric constants (ε(m) < 5). In the case of a weakly charged pore, counterion penetration exhibits a nonmonotonic behavior and is characterized by two regimes: at low reservoir concentrations or small pore radii, coions are excluded and counterions enter the pore to enforce electroneutrality; dielectric repulsion (image forces) remain strong and the counterion partition coefficient decreases with increasing reservoir concentration up to a characteristic value. For larger reservoir concentrations, image forces are screened and the partition coefficient of counterions increases with the reservoir concentration, as in the neutral pore case. Large surface charge densities (>2 × 10(-3) e/nm(2)) suppress the discontinuous transition by reducing the energy barrier for ion penetration and shifting the critical point toward very small pore sizes and reservoir concentrations. Our variational method is also compared to a previous self-consistent approach and yields important quantitative corrections. The role of the curvature of dielectric interfaces is highlighted by comparing ionic penetration into slit and cylindrical pores. Finally, a charge regulation model is introduced in order to explain the key effect of pH on ionic exclusion and explain the origin of observed time-dependent nanopore electric conductivity fluctuations and their correlation with those of the pore surface charge.