Donnan-Type Equilibria in Polyelectrolyte Gels

Donnan-Type Equilibria in Polyelectrolyte Gels.—In a somewhat more rigorous fashion we consider the reduction of the chemical potential of the solvent in the swollen gel to be separable into three terms which severally represent the changes due to the mixing of polymer and solvent, to the mixing with the mobile ionic constituents, and to the elastic deformation of the network. Symbolically 

In essence, we assume that the gel solution is sufficiently dilute to justify the assumption that the first two contributions enter additively. The first and third are given by Eq. (38). Proceeding at once to the case of swelling equilibrium, we observe that fulfillment of the condition jLti = Ml is required, where mi is the chemical potential in the external solution. Inserting this condition in Eq. (B-1) and writing (Ami )z for Mi - 

Turning now to the case of equilibrium with an infinite external solution containing c/ moles of electrolyte Mp Av per liter, we note that Eq. (B-3) is then equivalent to Eq. (45). As a further condition of equilibrium, it is required that the activity of this electrolyte be the same inside and outside the gel. The activity of the electrolyte being equal to the product of the activities of the individual ions into which it dissociates, this condition may be stated as follows 

Making the customary approximation that activities are equal to concentrations, we obtain by inserting Eqs. (43)  

Since we are interested in the excess mobile electrolyte concentration, we introduce the variable tj defined by 

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