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Thus the free energy of transfer of i from electrolytes to polyelectrolytes is defined by 

To demonstrate the general partitioning behavior, the equilibrium distribution of ions is derived in the following discussion under the 

The dependence of the Donnan potential on the electrolyte concentration can be calculated using Eqn. 19 and the electroneutrality condition within the membrane phase. For a (1, — l)-valent electrolyte of concentration c, it is given by Eqn. 20a 

As an example consider a typical cation exchanger, such as the poly(A-sulfopropyl pyrrole-co-pyrrole) in Fig. 3.2 in the reduced form. We assume that for the uni-univalent salt KX the local relaxation free energy of transfer into the polymer is zero (Aju. = A/u,J = 0). The interfacial situation is shown in Fig. Note the excess cations ( ) 

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 A f D becomes 

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