Diffusioosmosis of electrolyte solutions in a fine capillary tube

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary tube generated by a constant concentration gradient imposed in the axial direction. The capillary wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by an analytical approximation to the solution of the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the axial direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the radial position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a prescribed concentration gradient of an electrolyte, the magnitude of fluid velocity at a position in general increases with an increase in its distance from the capillary wall, but there are exceptions. The effect of the radial distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the double layer on the diffusioosmotic flow are found to be very significant.     

Diffusioosmosis of electrolyte solutions in a capillary slit with adsorbed polyelectrolyte layers

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary slit with each of its inside walls coated with a layer of polyelectrolytes generated by an imposed tangential concentration gradient. In this solvent-permeable and ion-penetrable surface charge layer, idealized polyelectrolyte segments are assumed to be distributed at a uniform density. The electric double layer and the surface charge layer may have arbitrary thicknesses relative to the gap width between the slit walls. The Poisson-Boltzmann equation and a modified Navier-Stokes/Brinkman equation are solved numerically to obtain the electrostatic potential, dynamic pressure, tangentially induced electric field, and fluid velocity as functions of the lateral position in the slit in a self-consistent way, with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions. The existence of the surface charge layers can lead to a diffusioosmotic flow quite different from that in a capillary with bare walls. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the slit on the diffusioosmotic flow are found to be very significant in practical situations.     

Diffusioosmosis and electroosmosis in a capillary slit with surface charge layers

This study analytically examines the steady diffusioosmotic and electroosmotic flows of an electrolyte solution in a fine capillary slit with each of its inside walls covered by a layer of adsorbed polyelectrolytes. In this solvent-permeable and ion-penetrable surface charge layer, idealized polyelectrolyte segments are assumed to distribute at a uniform density. The electric double layer and the surface charge layer may have arbitrary thicknesses relative to the gap width between the slit walls. The electrostatic potential distribution on a cross section of the slit is obtained by solving the linearized Poisson–Boltzmann equation, which applies to the case of low potentials or low fixed-charge densities. Explicit formulas for the fluid velocity profile due to the imposed electrolyte concentration gradient or electric field through the slit are derived as the solution of a modified Navier–Stokes/Brinkman equation. The results demonstrate that the structure of the surface charge layer can lead to an augmented or a diminished electrokinetic flow (even a reversal in direction of the flow) relative to that in a capillary with bare walls, depending on the characteristics of the capillary, of the surface charge layer, and of the electrolyte solution. For the diffusioosmotic flow with an induced electric field, competition between electroosmosis and chemiosmosis can result in more than one reversal in direction of the flow over a range of the Donnan potential of the adsorbed polyelectrolyte in the capillary.     

Diffusioosmosis of electrolyte solutions along a charged plane wall

The steady diffusioosmotic flow of an electrolyte solution along a dielectric plane wall caused by an imposed tangential concentration gradient is analytically examined. The plane wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by the Poisson-Boltzmann equation. The macroscopic electric field along the tangential direction induced by the imposed electrolyte concentration gradient is obtained as a function of the lateral position. A closed-form formula for the fluid velocity profile is derived as the solution of a modified Navier-Stokes equation. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential of the wall and the properties of the electrolyte solution. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field in the double layer on the diffusioosmotic flow is found to be very significant and cannot be ignored.     

Diffusioosmosis and electroosmosis of electrolyte solutions in fibrous porous media

The steady diffusioosmotic and electroosmotic flows of an electrolyte solution in the fibrous porous medium constructed by a homogeneous array of parallel charged circular cylinders are analyzed under conditions of small Peclet and Reynolds numbers. The imposed electrolyte concentration gradient or electric field is constant and can be oriented arbitrarily with respect to the axes of the cylinders. The thickness of the electric double layers surrounding the cylinders is assumed to be small relative to the radius of the cylinders and to the gap width between two neighboring cylinders, but the polarization effect of the diffuse ions in the double layers is incorporated. Through the use of a unit cell model, the appropriate equations of conservation of the electrochemical potential energies of ionic species and the fluid momentum are solved for each cell, in which a cylinder is envisaged to be surrounded by a coaxial shell of the fluid. Analytical expressions for the diffusioosmotic and electroosmotic velocities of the bulk electrolyte solution as functions of the porosity of the ordered array of cylinders are obtained in closed form for various cases. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. In the limit of maximum porosity, these results can be interpreted as the diffusiophoretic and electrophoretic velocities of an isolated circular cylinder caused by the imposed electrolyte concentration gradient or electric field.     

The effects of unequal ionic sizes for an electrolyte in a charged slit

The modified Gouy-Chapman (MGC) theory has been used to study the electrical double layer near two charged plates immersed in a model electrolyte. The effects of assigning to the cations and anions different distances of closest approach to the charged surfaces are examined. The dependence of overcharging and charge reversal on the system parameters such as concentration, ion size and valence, is investigated both inside and outside the charged slit.     

Polymolecular adsorption and capillary condensation in narrow slit pores

Capillary condensation and polymolecular adsorption in narrow slits has been calculated, where the fields of surface forces overlap one another. The calculations were carried out on the basis of macroscopic theory of dispersion forces and the isotherms of lone adsorption layers at the free surface. It has been shown that under the effect of mutual attraction through a gap, polymolecular adsorption films lose their stability long before their thickness has approached the half-width of a flat slit. This results in hysteresis of the capillary condensation in an ensemble of plane-parallel slits.

In the case of systems having strong adsorbate-adsorbate interaction, there has been detected the existence of the lower limit of sizes of slit pores, wherein the capillary meniscus can coexist with adsorption films. With a slit width smaller than the critical one, the meniscus is likely to form a finite contact angle with “dry” surfaces of a slit. Thus an explanation has been given of the lower limit of the capillary condensation in an ensemble of flat-surface, slit pores. In the case of strong adsorbate-adsorbent interaction, the coexistence of meniscus with adsorption films within the scope of the approach used is possible in slits of any width.

The value of corrections for the surface forces effect to be entered in the calculations of slit pores dimensions has been analyzed on the basis of the capillary condensation data obtained.

In wedge-shaped slits there also exists, besides lower limit the upper limit of capillary hysteresis.     

Thermochemistry of electrolyte solutions

The results of calorimetric investigations of electrolyte solutions in the mixtures of water, methanol, N,N-dimethylformamide, and acetonitrile with numerous organic cosolvents are discussed with regard to the intermolecular interactions that occur in the solution. Particular attention is given to answer the questions how and to what extent the properties of the systems examined are modified by the cosolvent added and how much the properties of the cosolvent are revealed in the mixtures with the solvents mentioned above. To this goal, the analysis of the electrolyte dissolution enthalpies, single ionic transfer enthalpies, and enthalpic pair interaction coefficients as well as the preferential solvation (PS) model are applied. The analysis performed shows that in the case of the dissolution enthalpies of simple inorganic electrolytes in water–organic solvent mixtures, the shape of the dependence of the standard dissolution enthalpy on the mixed solvent composition reflects to a large extent the hydrophobic properties of the organic cosolvent. In the mixtures of methanol with organic cosolvents, the ions are preferentially solvated either by methanol molecules or by molecules of the cosolvent, depending on the properties of the mixed solvent components. The behavior of inorganic salts in the mixtures containing N,N-dimethylformamide is mostly influenced by the DMF which is a relatively strongly ion solvating solvent, whereas in acetonitrile mixtures, the thermochemical behavior of electrolyte solutions is influenced to a large extent by the properties of the cosolvent particularly due to the PS of cation by the cosolvent molecules.     

Hall voltage in electrolyte solutions

Abstract

Hall coefficient for CuSO₄ liquid electrolyte has been measured and found to be positive. Detection of Hall signal was limited to de methods although ac techniques were also investigated. The Hall coefficient increases with decreasing concentration of solute and for distilled water approaches 5 × 10⁵ cm³/coul. Calculations of H⁺ ion mobility using the two carrier expression for Hall coefficient show the charge carrier in a liquid electrolyte to be the H⁺ ion. Mobility of the proton in water is of the order of 1 cm² voltsec, which is near the value in ice     

Electrostatic potential and electroosmotic flow in a cylindrical capillary filled with symmetric electrolyte: analytic solutions in thin double layer approximation

The electrostatic potential in a capillary filled with electrolyte is derived by solving the nonlinear Poisson-Boltzmann equation using the method of matched asymptotic expansions. This approach allows obtaining an analytical result for arbitrary high wall potential if the double layer thickness is smaller than the capillary radius. The derived expression for the electrostatic potential is compared to numerical solutions of the Poisson-Boltzmann equation and it is shown that the agreement is excellent for capillaries with radii greater or equal to four times the electrical double layer thickness. The knowledge of the electrostatic potential distribution inside the capillary enables the derivation of the electroosmotic velocity flow profile in an analytical form. The obtained results are applicable to capillaries with radii ranging from nanometers to micrometers depending on the ionic strength of the solution.     

Overcharging of nanoparticles in electrolyte solutions

Monte Carlo simulations are performed to investigate the effects of salt concentration, valence and size of small ions, surface charge density, and Bjerrum length on the overcharging of isolated spherical nanoparticles within the framework of a primitive model. It is found that charge inversion is most probable in solutions containing multivalent counterions at high salt concentrations. The maximum strength of overcharging occurs near the nanoparticle surface where counterions and coions have identical local concentrations. The simulation results also suggest that both counterion size and electrostatic correlations play major roles for the occurrence of overcharging.     

On a new approximation in the theory of electrolyte solutions

We compare the results of a new approximation for the interionic radial distribution function developed previously by Olivares and McQuarrie to those from the nonlinear Poisson—Boltzmann equation for the highly-charged system of the spherical protein bearing a charge as 20 in an aqueous electrolyte solution. In particular, we use both approximations to predict the experimental results for protein titration, which are the experimental data to which the results of the Poisson—Boltzmann equation had been directed.     

Osmotic behavior of a Nafion membrane in methanol-water electrolyte solutions

In this paper, an experimental study was carried out in order to investigate the osmotic transport of methanol-water electrolyte solutions through a Nafion membrane. The experimental data indicated that the Nafion membrane showed the typical anomalous osmotic behavior of charged membranes. The influence of some relevant parameters, such as electrolyte concentration difference, weight fraction of methanol on solution, and nature of cation was considered. The results showed that the osmotic volume flow was decreased with the presence of methanol on solvent, but did not alter the anomalous osmotic behavior of the membrane.     

Pressure driven flow of polymer solutions in nanoscale slit pores

Polymer solutions subject to pressure driven flow and in nanoscale slit pores are systematically investigated using the dissipative particle dynamics approach. The authors investigated the effect of molecular weight, polymer concentration, and flow rate on the profiles across the channel of the fluid and polymer velocities, polymer density, and the three components of the polymers radius of gyration. They found that the mean streaming fluid velocity decreases as the polymer molecular weight and/or polymer concentration is increased, and that the deviation of the velocity profile from the parabolic profile is accentuated with increase in polymer molecular weight or concentration. They also found that the distribution of polymers conformation is highly anisotropic and nonuniform across the channel. The polymer density profile is also found to be nonuniform, exhibiting a local minimum in the center plane followed by two symmetric peaks. They found a migration of the polymer chains either from or toward the walls. For relatively long chains, as compared to the thickness of the slit, a migration toward the walls is observed. However, for relatively short chains, a migration away from the walls is observed.     

A view of electrolyte solutions

The uncertainties in the route to infinite dilution for 2–2 electrolytes are discussed in relation to the practical difficulties of determining the standard emf's of simple reversible cells containing ZnSO₄ in H₂O and D₂O solutions. These difficulties are due to uncertainties in the theory of highly charged ions in aqueous solution. Recent developments in theories of electrolytes, especially those for which numerical results are available, are critically evaluated for their accuracy and adaptability to changes in the solute potential. Simple refinements to the model (i.e., the solute potential) are described, and the changes are interpreted, in terms of the molecular interactions between sets or pairs of ions in the pure solvent. Recent work on the effect of solvent granularity and other molecular properties of the solvent (e.g., dipole moment) on the solute potential is reviewed.This paper was presented at the symposium, The Physical Chemistry of Aqueous Systems, held at the University of Pittsburgh, Pittsburgh, Pennsylvania, June 12–14, 1972, in honor of the 70th birthday of Professor H. S. Frank.     

Thermochemistry of nonaqueous electrolyte solutions

Heats of solution and specific heats have been measured for NaI and KI in methanol at 25 and 50 for the full range of concentrations; the integral heat of solution of NaI or KI in methanol has a positive temperature coefficient, whereas the heats of solution of these salts and all strong electrolytes in water have negative temperature coefficients. The thermal capacity of an aqueous electrolyte is less than the sum of the thermal capacities of the components, whereas the result for methanol is the reverse. In addition, the integral heat of solution has a concentration coefficient much larger than that found for water, mainly because water has a dielectric constant about 2.5 times that of methanol. This leads to stronger interactions between ions in methanol, which contains ion pairs.     

Acidity of frozen electrolyte solutions

Ice is selectively intolerant to impurities. A preponderance of implanted anions or cations generates electrical imbalances in ice grown from electrolyte solutions. Since the excess charges are ultimately neutralized via interfacial (H(+)/HO(-)) transport, the acidity of the unfrozen portion can change significantly and permanently. This insufficiently recognized phenomenon should critically affect rates and equilibria in frozen media. Here we report the effective (19)F NMR chemical shift of 3-fluorobenzoic acid as in situ probe of the acidity of extensively frozen electrolyte solutions. The sign and magnitude of the acidity changes associated with freezing are largely determined by specific ion combinations, but depend also on solute concentration and/or the extent of supercooling. NaCl solutions become more basic, those of (NH(4))(2)SO(4) or Na(2)SO(4) become more acidic, while solutions of the 2-(N-morpholino)ethanesulfonic acid zwitterion barely change their acidity upon freezing. We discuss how acidity scales based on solid-state NMR measurements could be used to assess the degree of ionization of weak acids and bases in frozen media.