Fixed charge concentration

To estimate the limiting value t (i) and to introduce the molal fixed charge concentration X, expressed in equivalents of univalent fixed anions per kg of water sorbed by the membrane, we have treated the ion concentrations in the membrane as being governed by a Donnan distribution. 

Here pt (i = 1,2) are again the counterion concentrations, whereas n is the co-ion concentration. Finally, N is again the fixed charge concentration, and... 

No fixed charge concentration or density of functional groups Na Avogadro number... 

The membrane is a compromise of properties the requirement for low internal resistance suggests that the membrane be porous and thin good separation dictates that the membrane be of low permeability and high fixed charge concentration and adequate physical strength requires that it be sufficiently thick. At any rate, membranes can generally be tailor-made, so that their properties can be adjusted to yield optimal cell performance and cell life. ... 

The results summarized in Fig. 3.7 demonstrate the strong dependence of the membrane state of fixed-charge polymers on the electrolyte concentration. At electrolyte concentrations above the fixed-charge concentration, the polymer becomes solutionlike. It contains both co- and counterions at substantial concentrations. The effect of AD becomes... 

At electrolyte concentrations significantly smaller than the fixed-charge concentration, the film composition is practically unaffected by variations in the electrolyte concentration. We can therefore assume that... 

As the electrolyte concentration reaches values comparable to the fixed-charge concentration, the results change considerably. 

Summarizing it is demonstrated that variation in the Donnan potential as a function of the electrolyte concentration is experimentally accessible as long as the electrolyte concentration remains below the ion exchanger s fixed-charge concentration. The Volta-potential measurements give in addition information on a surface dipole layer that forms on the membrane surface when it is removed from the electrolyte. 

Table 9.2 Average cation transport number, , correlation coefficient (r) for Equation (9.19) or Equation (9.20), effective fixed charge concentration, Xf, and average cation permselectivity, , for composite HR95, polysulfone support PS-Uf, DEAE-dextran fouled PS-Uf and dense regenerated cellulose RgC membrane.

Since the Donnan effect is significant only when the fixed charge concentration in the polymer network c g is significantly greater than the mobile ion concentration in the gel c s, under these circumstances equation 12 may be simplified to the following ... 

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