Counterion Permselectivity

The permselectivity of an ion-exchange membrane for different counterions is determined by the concentration and the mobility of the different ions in the membrane as indicated earlier. The concentration of the different counterions in 

A typical counterion-exchange sequence of a cation-exchange membrane containing S03 group as fixed charge is  

A similar counterion-exchange sequence is obtained for anions in an anion-exchange membrane containing quaternary ammonium groups as fixed charges  

The permselectivity is the product of ion-exchange selectivity and mobility selectivity. The mobility of different ions is determined mainly by steric effects, that is, the size of the ions and the cross-linking density of the membrane [4], 

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An ion-exchange membrane consists of an ionomer, which contains fixed ions that are covalently bound to the polymer backbone. It is electrically neutral because of included counterions . If water-or probably another sufficiently polar solvent - is absorbed and if the fixed and counterions can be separately solvated to an adequate degree, the counterions become mobile and the ion-exchange membrane can work as an ion conductor. Owing to the electric field of the fixed ions coions with the same charge as the fixed ions are rejected and are typically absent inside the membrane. Thus the membrane is selective for the transfer of counterions ( permselectivity = permeation selectivity, e.g. [70]). 

In support of permselectivity, later radiotracer diffusion studies of calcium chloride through selective PVC matrix calcium ion-selective membranes based on organophosphate sensor showed calcium counterion permselectivity with negligible permeation by chloride co-ions ( l) The PVC matrix membrane permeation studies also showed selective permeation of calcium ions when compared with other cations (31 ). 

In addition to high permselectivity, the membrane must have low-elec trical resistance. That means it is conductive to counterions and does not unduly restrict their passage. Physical and chemical stabihty are also required. Membranes must be mechanically strong and robust, they must not swell or shrink appreciably as ionic strength changes, and they must not wrinkle or delorm under thermal stress. In the course of normal use, membranes may be expec ted to encounter the gamut of pH, so they should be stable from 0 < pH < 14 and in the presence of oxidants. 

The transport number is a measure of the permselectivity of a membrane. If, for example, a membrane is devoid of colons, then all current through the membrane is carried by the counterion, and the transport number = 1. The transport numbers for the membrane and the solution are different in practical ED applications. 

Conversely, the fundamentals for the UDL he on the coextraction of counterions into the membrane therefore, the membrane is no longer permselective (Donnan failure) [9]. Ideally, when the ionophores are saturated by ions, the ion-ionophore complex functions as an ion-exchanger and the membrane shows an anion Nernstian response. The UDL can be estimated from the membrane composition, formation constant and coextraction coefficients obtained from the so-called sandwich membrane method [73]. 

In this section we shall consider the simplest model problem for the locally electro-neutral stationary concentration polarization at an ideally permselective uniform interface. The main features of CP will be traced through this example, including the breakdown of the local electro-neutrality approximation. Furthermore, we shall apply the scheme of 4.2 to investigate the effect of CP upon the counterion selectivity of an ion-exchange membrane in a way that is typical of many membrane studies. Finally, at the end of this section we shall consider briefly CP at an electrically inhomogeneous interface (the case relevant for many synthetic membranes). It will be shown that the concentration and the electric potential fields, developing in the course of CP at such an interface, are incompatible with mechanical equilibrium in the liquid electrolyte, that is, a convection (electroconvection) is bound to arise. 

The chief phenomenon to be considered here is non-uniform distribution of electric charge in charged membranes. The effect of this on ionic sorption and transport properties is of considerable practical interest, because membrane permselectivity for the counterion against the coion (or for uncharged species vs electrolytes), and hence membrane performance in important technical applications (such as electrodialysis) is directly involved. 

Fig. 15. Cluster network model for highly cation-permselective Nafion membranes126). Counterions are largely concentrated in the high-charge shaded regions which provide somewhat tortuous, but continuous (low activation energy), diffusion pathways. Coions are largely confined to the central cluster regions and must, therefore, overcome a high electrical barrier, in order to diffuse from one cluster to the next...

It is possible now to explain a number of important membrane properties in a qualitative way. The permselectivity i.e. the increased transference number of cations in a cation-exchange membrane respectively of anions in an anion-exchange membrane compared with the free solutions is due to the fact that the number of counterions is much higher than the number of co-ions. 

In summary, there is evidence that the skin presents a weak cation permselectivity [25,76,77,80,93,125], which can be reversed by acidifying the pH of the solutions bathing the skin [10,23,76,77]. At pH>p/, the skin is negatively charged and electroosmotic flow proceeds in the anode-to-cathode direction. At pH < pi, the skin becomes positively charged and electroosmotic flow reverses to the cathode-to-anode direction. Under the application of an electric field, counterions (cations at physiological pH) are preferentially admitted into the skin. As a consequence, the sodium and chloride transport numbers are 0.6 and 0.4, respectively, during transdermal iontophoresis (in contrast to their values in a neutral membrane tNa = 0.45 rCi = 0.55) [126]. 

An ideal permselective cation-exchange membrane would transmit positively charged ions only, that is, for a transport number of a counterion in a cation-exchange membrane is T m = 1 and the permselectivity of the membrane is xFcm = 1. The permselectivity approaches zero when the transport number within the membrane is identical to that in the electrolyte solution, that is, for T = Tc is xFcm = 0. For the anion-exchange membrane the corresponding relation holds. 

A polyion in the form of a thin membrane is used as ion-exchange membrane in another application of the ion-exchange phenomenon. When exposed to an electrolyte, an ion-exchange membrane will allow counterions to pass through it, but will act as a barrier to the complementary ion, and is therefore said to be permselective. Thus a polyanionic membrane will allow passage of cations and a polycationic membrane that of anions, so that under the influence of an electric current, continuous fluxes of cations and anions, respectively, can be set up across these membranes. This principle is exploited in electrodialysis and in chlor-alkali cells as described later. 

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