Diffusion counterion

If now the diffuse counterion binding is viewed in terms of one residue of the polyion, we may apply Eq. (2.21) in the suggestive form... 

FIGURE 10.2. A model for the mediated reduction of species Y by the 0/R redox couple immobilized in a polymeric film at the electrode surface. The governing process may be either substrate diffusion to the film substrate partition into and diffusion within the layer charge transport within the PME film (governed by relative rates of electron hopping, redox site diffusion, counterion transport, or polymer motions) and electrode or mediation kinetics. 

To obtain Eqs. 11, 12, 13, and 14, it was assumed that the concentration of each ionic species within the electric double layer is related to the electric potential energy by a Boltzmann distribution. A comparison of Eq. 11 with the numerical results obtained by Prieve and Roman [2] shows that the thin-layer polarization model is quite good over a wide range of zeta potentials when Ka > 20. If 1(1 is small and Ka is large, the interaction between the diffuse counterions and the particle surface is weak and the polarization of the double layer is also weak. In the limit of... 

Surface active electrolytes produce charged micelles whose effective charge can be measured by electrophoretic mobility [117,156]. The net charge is lower than the degree of aggregation, however, since some of the counterions remain associated with the micelle, presumably as part of a Stem layer (see Section V-3) [157]. Combination of self-diffusion with electrophoretic mobility measurements indicates that a typical micelle of a univalent surfactant contains about 1(X) monomer units and carries a net charge of 50-70. Additional colloidal characterization techniques are applicable to micelles such as ultrafiltration [158]. 

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

Back-diffusion is the transport of co-ions, and an equivalent number of counterions, under the influence of the concentration gradients developed between enriched and depleted compartments during ED. Such back-diffusion counteracts the electrical transport of ions and hence causes a decrease in process efficiency. Back-diffusion depends on the concentration difference across the membrane and the selectivity of the membrane the greater the concentration difference and the lower the selectivity, the greater the back-diffusion. Designers of ED apparatus, therefore, try to minimize concentration differences across membranes and utilize highly selective membranes. Back-diffusion between sodium chloride solutions of zero and one normal is generally [Pg.173]

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

In ion-exchange resins, diffusion is further complicated by electrical coupling effec ts. In a system with M counterions, diffusion rates are described by the Nernst-Planck equations (Helfferich, gen. refs.). Assuming complete Donnan exclusion, these equations canbe written... 

For mixtures of unlike ions (the usual case), the apparent diffusivity will be intermediate between these values because of the elec tric coupling effect. For a system with two counterions A and B, with charge z-a and z-b, Eqs. (16-73) and (16-74) reduce to ... 

In binary ion-exchange, intraparticle mass transfer is described by Eq. (16-75) and is dependent on the ionic self diffusivities of the exchanging counterions. A numerical solution of the corresponding conseiwation equation for spherical particles with an infinite fluid volume is given by Helfferich and Plesset [J. Chem. Phy.s., 66, 28, 418... 

Winstein suggested that two intermediates preceding the dissociated caibocation were required to reconcile data on kinetics, salt effects, and stereochemistry of solvolysis reactions. The process of ionization initially generates a caibocation and counterion in proximity to each other. This species is called an intimate ion pair (or contact ion pair). This species can proceed to a solvent-separated ion pair, in which one or more solvent molecules have inserted between the caibocation and the leaving group but in which the ions have not diffused apart. The free caibocation is formed by diffusion away from the anion, which is called dissociation. 

In the polar pores, the diffusion coefficient of all ions is strongly reduced relative to the bulk values. No counterion dependence is observed for the SDC of CP. A more detailed analysis shows that the ion SDC depends on the ion s relative position in the pore [174]. In the case of the K ion, this dependence is particularly strong. K ions forming contact pairs with the surface charges are almost completely immobilized on the time scale of the simulations. The few remaining ions in the center of the pore are almost unaffected by the (screened) surface charges. The fact that most of the K ions form contact pairs substantially reduces the average value of the normalized K SDC to 0.2. The behavior of CP is similar to that of K. The SDC of sodium ions, which... 

The mechanism by which analytes are transported in a non-discriminate manner (i.e. via bulk flow) in an electrophoresis capillary is termed electroosmosis. Eigure 9.1 depicts the inside of a fused silica capillary and illustrates the source that supports electroosmotic flow. Adjacent to the negatively charged capillary wall are specifically adsorbed counterions, which make up the fairly immobile Stern layer. The excess ions just outside the Stern layer form the diffuse layer, which is mobile under the influence of an electric field. The substantial frictional forces between molecules in solution allow for the movement of the diffuse layer to pull the bulk... 

The application of the above methods of calculation has shown that the quasi-diffusion of organic counterions is profundly affected by both the amount of the crosslinking agent in a crosslinked polyelectrolyte and the method of formation of the crosslinked structure [109-112]. Fig. 28 shows the dependence of diffusion coefficients for streptomycin ions on the amount of the crosslinking... 

Mechanisms of micellar reactions have been studied by a kinetic study of the state of the proton at the surface of dodecyl sulfate micelles [191]. Surface diffusion constants of Ni(II) on a sodium dodecyl sulfate micelle were studied by electron spin resonance (ESR). The lateral diffusion constant of Ni(II) was found to be three orders of magnitude less than that in ordinary aqueous solutions [192]. Migration and self-diffusion coefficients of divalent counterions in micellar solutions containing monovalent counterions were studied for solutions of Be2+ in lithium dodecyl sulfate and for solutions of Ca2+ in sodium dodecyl sulfate [193]. The structural disposition of the porphyrin complex and the conformation of the surfactant molecules inside the micellar cavity was studied by NMR on aqueous sodium dodecyl sulfate micelles [194]. 

FIG. 17 Diffusion coefficients of the counterions and coions of a 1 1 RPM model electrolyte in a cylindrical nanopore of i = lOd. The circles and triangles represent the results of coions and counterions, respectively. 

Rymden, R. Stilbs, P. (1985a). Counterion self-diffusion in aqueous solutions of poly(acrylic acid) and poly(methacrylic acid). Journal of Physical Chemistry, 89, 2425-8. 

The operation of a double-layer capacitor is tied to a displacement of electrolyte ions. In a fully charged capacitor, anions accumulate as counterions in the solution layer next to the positively charged electrode while the eoncentration of the cations decreases. At the negative electrode, the opposite situation is seen. During discharge, the ionic concentrations level out to the bulk solution values by migration and diffusion. 

By definition, in a solution all ions belong to the same phase, even though counterions may cluster more or less diffusely around the macroions. When significant amounts of a simple 1 1 electrolyte (such as KCl) are added to a polyelectrolyte solution, dissociation of the polyelectrolyte macromolecule is repressed in an extreme case the polyelectrolyte may be salted out. An undissociated polyacid may be precipitated by generous addition of a simple acid such as HCl. 

The physical meaning of the g" (ion) potential depends on the accepted model of ionic double layer. The proposed models correspond to the Gouy Chapman diffuse layer, with or without allowance for the Stern modification and/or the penetration of small counterions above the plane of the ionic heads of the adsorbed large ions [17,18]. The presence of adsorbed Langmuir monolayers may induce very high changes of the surface potential of water. For example. A/" shifts attaining ca. —0.9 (hexadecylamine hydrochloride), and ca. -bl.OV (perfluorodecanoic acid) have been observed [68]. 

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