Fixed ion concentration

Here Yi and y2 are the activity coefficients of ions in solution, y, and y2 are the coefficients of resin activity, cx and c2 are ion concentrations in solution, ntj and m2 are fixed ion concentrations (exchange or weight concentrations) and Ks is the concentration constant of ion exchange, the selectivity constant. 

Equation 5.14 indicates that the co ion concentration in the membrane and with that the permselectivity of the membrane is decreasing with salt concentration in the solution and will vanish when the salt concentration in the solution is identical to the fixed ion concentration of the membrane. 

The strong acidity and high hydrophilicity of the perfluoro-sulfonic acid group result in a membrane of high water content and low electric resistance. Since the fixed-ion concentration in the sulfonic acid membrane is also low, current efficiency is less than 80% with caustic concentrations of 17% or more (26). The chemical stability of perfluorosulfonic acid group is excellent. Because of its low pKa value, the membrane can be exposed to solutions of pH 1. 

As a result, the perfluorocarboxylated membrane with a high ion exchange capacity attains a high fixed ion concentration, which is defined as milliequivalent of carboxylic acid group per a gram of absorbed water in the membrane. 

From these water contents, fixed ion concentration is calculated and plotted in Figure 13 against caustic concentration. 

Such a high fixed ion concentration is quite effective to prevent migration of anions into the membrane, which leads to high permselectivity in ionic transport. 

Figure 19 shows the dependence of the transport number of the sodium ion upon the caustic concentration. High value of more than 0.9 is achieved at caustic concentrations beyond 25 wt%. This characteristic behavior is explained by the high fixed ion concentration within the membrane. 

Based on electro-neutrality, we deduce the following equation for the ion exchange membrane, where X is the fixed ion concentration of the membrane, and Q) is the sign of the fixed charge (—1 for negatively charged membranes, + 1 for positively charged membranes),... 

Because the ion exchange membrane shows ideal permselectivity at sufficiently low solution concentration, compared with the fixed ion concentration of the membrane, the difiusional flux is expressed as follows, for a cation exchange membrane... 

These equations mean that the flux of electrolyte through the membrane decreases with decreasing C fCK. Namely, when the fixed ion concentration of the membrane is high compared with the concentration of the outer solution, the flux of electrolyte through the membrane decreases (the membrane acts as a barrier for ions). This effect is remarkable when the valence of counter-ions is low and that of co-ions is high. For example, sodium sulfate is difficult to diffuse through a cation exchange membrane compared with sodium chloride. 

Dj is proportional to the fixed ion concentration of the membrane and inversely proportional to the specific flow resistance and specific conductivity. Also, Df is independent of membrane thickness. Figure 2.6 shows the change in electro-osmotic water transport with the fixed ion concentration of an anion exchange membrane measured with 0.5 N sodium chloride solution.25 Dj decreases with increasing fixed ion concentration. The specific conductance of the membrane increases and the water content of the membrane decreases (po increases) with increasing fixed ion concentration of the membrane. The electro-osmotic behavior through the membrane is not simply explained from this experimental data. 

Figure 2.6 Change in electro-osmotic water coefficient with fixed ion concentration of an anion exchange membrane. Measured in 0.50 N sodium chloride solution using an anion exchange membrane (v = fit, v volume flux ft electro-osmotic water coefficient I current density t period).

When liquid permeates through the ion exchange membrane by hydraulic pressure, there is the following relationship between the flux of ion i through the membrane, transport number of i ions, fixed ion concentration, CR, etc. from Eqs. (2.87), (2.92) and (2.98). 

Figure 2.7. Relationship between salt rejection and fixed ion concentration in strongly basic anion exchange membranes. Salt rejection — [(Ct — C2)/CJ X 100 (C concentration offeed solution C2 concentration of permeate).

Permselectivity of counter-ions through the ion exchange membrane depends on the fixed ion concentration of the membrane (Chapter 2.3). Many attempts have been made to increase the fixed ion concentration of the membrane to increase the ion exchange capacity and to decrease the water content of the membrane, namely, to increase the fixed ion concentration without increasing the electrical resistance of the membrane. Figure 4.8 shows an example of the relationship between current efficiency to produce sodium hydroxide and the fixed ion concentration of the membrane for the electrolysis of sodium chloride solution.17 It is apparent that the current efficiency increases with increasing fixed ion concentration of the membrane. 

Figure 4.8 Current efficiency versus fixed ion concentration of a cation exchange membrane in the electrolysis of a sodium chloride solution. Cation exchange membrane sulfonated styrene—divinylbenzene type. Anolyte saturated NaCl catholyte 3.0 N NaOH current density 10Adm 2 at 70 °C.

The transport number of counter-ions is determined by the difference between the concentration of electrolyte solution in contact with a membrane and the fixed ion concentration of a membrane areas of low fixed ion concentration occur and reduce membrane performance. To obtain a high transport number for counterions in membranes exposed to a higher concentration of solution, the fixed ion concentration of the membrane should be increased to lessen the effect of areas of low fixed ion concentration. Glueckauf et al. determined the heterogeneity of the fixed ion concentration in the membrane by measuring the adsorbed ions in the membrane by equilibrating the membrane with salt solutions of various concentrations.111... 

The swelling pressure is proportional to the concentration of the fixed ions and inversely proportional to the concentration of the electrolyte. In ion-exchange membranes with high fixed ion concentrations and dilute solutions it can reach very high values well in excess of 100 bars [13]. 

An increase in membrane uniformity leads to a higher Hmiting current. The membrane surface condition has a noticeable influence on the Hmiting current value. The polarization characteristic may deteriorate as a result of fixed ion concentration reduction due to ion-exchange membrane degradation at the time of manufacturing or at the time of operation, or adsorption of low-mobility organic substances present in the solution or leached from the membranes. 

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