Nonexchangeable Charged Sites in the Polymer Phase

For the description of the partitioning equilibrium between a liquid electrolyte and an ionic polymer, the fundamental considerations discussed for the nonionic polymers are still valid. This is so in particular for the partitioning equilibrium equation for the ionic species i, Eqn. 5, which can be written in terms of free energies 

The net density of nonexchangeable ions enters into electroneutrality considerations. For an ionic polymer in contact with an electrolyte containing the salt KmX , the electroneutrality condition inside the polymer phase takes the form 

To obtain explicit expressions for the partitioning equilibrium states of 

Note that from a thermodynamic standpoint the free-energy terms A/it and i 7 In (yT Vyf) in Eqn. 5c are indistinguishable, i.e., only their sum is a relevant quantity. In all situations the equilibrium condition can in principle be characterized under the assumption that either A/i = 0 or alternatively RT In (yf° lyf) = 0, which is the same as = yf). This fact can be used to represent the ion-partitioning equilibria in somewhat simpler formulae, which are at the same time quite appropriate for particular systems. 

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