Fluxes counterions

It is easy to find the counterion flux ratio r near the equilibrium ... 

Fig. 4.4.2b. Calculated variation oj counterion flux ratio with the applied voltage.

In a typical experiment, proton flux might be driven by placing liposomes that contain pH 8 buffer in a solution buffered at pH 6, so that the initial proton flux is driven by 10 6-M protons outside and 10 6 hydroxide ions inside. Buffers are required to make the decay rate of pH gradients sufficiently slow so that initial rates can be conveniently estimated. It is also necessary to release proton diffusion potentials by addition of valinomycin or a permeant anion otherwise the proton flux will be limited by counterion flux (9). 

The above statements are valid for monomolecular layers only. In the case of polymer films with layer thickness into the p-range, as are usually produced by electropolymerization, account must also be taken of the fact that the charge transport is dependent on both the electron exchange reactions between neighbouring oxidized and reduced sites and the flux of counterions in keeping with the principle of electroneutrality Although the molecular mechanisms of these processes... 

Earlier, Gavach et al. studied the superselectivity of Nafion 125 sulfonate membranes in contact with aqueous NaCl solutions using the methods of zero-current membrane potential, electrolyte desorption kinetics into pure water, co-ion and counterion selfdiffusion fluxes, co-ion fluxes under a constant current, and membrane electrical conductance. Superselectivity refers to a condition where anion transport is very small relative to cation transport. The exclusion of the anions in these systems is much greater than that as predicted by simple Donnan equilibrium theory that involves the equality of chemical potentials of cations and anions across the membrane—electrolyte interface as well as the principle of electroneutrality. The results showed the importance of membrane swelling there is a loss of superselectivity, in that there is a decrease in the counterion/co-ion mobility, with greater swelling. 

V is the voltage applied to the system. Unit activity coefficients and zero standard counterion potentials in both phases are assumed for the sake of simplicity. As was pointed out in 4.3, the solution of (4.4.15)-(4.4.22) with voltage V given corresponds to potentiostatic experimental conditions and yields the concentration, electric potential fields, and the ionic fluxes as functions of V. We could alternatively fix the total current density... 

If a membrane separates two solutions with mixtures of counterions — in which each counter-ion is present only on one side of the membrane — and the same co-ion, we meet with a so-called multi-ionic system. These are also treated by F. Helfferich (53, 55) (ref. 55, page 327). An explicit solution of the flux equations in this case is obtained if the flow of co-ions is neglected and if all the counter-ions possess the same valency. Gradients of activity coefficients in the membrane and convection are also neglected. Diffusion coefficients and concentration of active groups are considered to be constant. It is assumed that there is equilibrium between the salt solution and the membrane surface on either side of the membrane. 

For the ratio of the fluxes of two counterions, which are present on the same side of the membrane is found ... 

I.2. Interdiffusion. F. Helfferich and H. D. Ocher (54) studied the interdiffusion of counterions through an ion-exchange membrane. Bases for their calculations were the Nemst-Planck flux equations combined with the M.S.T. model. Ion-fluxes and concentration profiles in the membrane were calculated. 

Fig. 2.1. Zero-current ion fluxes in the ion-selective membrane. Left (A) Concentrated inner solution induces coextraction of electrolyte into the membrane increasing the primary ion-ionophore concentration within the membrane. Consequently, primary ions leach into the sample increasing the activity of primary ions at the membrane/sample phase boundary. (B) Diluted inner solution and ion exchange at the inner solution side decreases the concentration of the complex within the membrane. Primary ions are siphoned-off from the sample, and their activity at the membrane/sample phase boundary is significantly decreased. (C) Ideal case of perfectly symmetric sample and inner solution resulting in no membrane fluxes. Note that fluxes of other species (counterions or interfering ions) are not shown for clarity. Right potential responses for each case. Ideal LOD is defined by the Nikolskii-Eisenman equation (Y Kj°jaj) and is obtained only in the ideal case (C). Fluxes in either direction significantly affect the LOD.

If the co-ion concentration in the ion exchanger is quite low, then the concentrations and fluxes of the exchanging counterions A and B are tightly coupled with each other (Helfferich, 1966). The total counterion concentration must remain constant and be equal to the concentration of fixed ionic groups such that... 

Nevertheless, hj f°r general cases where the fluid contains more than one electrolytes can either be computed numerically or be derived using an asymptotic expression for equilibrium electrical potential for the case with highly charged particle. O Brien [7] found that counterions with the highest valency play a major role in the ionic flux normal to the particle surface. Therefore, to first-order approximation, only the contributions from these counterions to the normal ionic flux need to be considered. 

This equation expresses that the co-ion flux Into (or from) the double layer Is negligible this Is in line with the fact that there is no significant lateral transport of these ions. For the counterions the result can be written as... 

Earlier [26,27,43,46] a phenomenological approach, based on the premise that the thermodynamics of irreversible processes [29] joined with Nemst-Planck equations for ion fluxes, would be useful was applied to the solution of intraparticle diffusion controlled ion exchange (IE) of fast chemical reactions between B and A counterions and the fixed R groups of the ion exchanger. In the model, diffusion within the resin particle, was considered the slow and sole controlling step. 

For the calculation of the fluxes the following parameters are needed porosity, sedimentation rate, diffusion coefficients, distribution constants, and the concentration gradients for each species dCildz)z=o- In assessing diffusion coefficients, coupling-effects due to electroneutrality between coions and counterions may have to be considered. Serious errors may be introduced by using wrong values of dQldz, because it is very difficult to collect undisturbed sediment. 

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