Equilibrium between phases with electrical charges

4 Equilibrium between phases with electrical charges 

In systems using, say, ion exchange resins (see Section 3.3.7.7), the resin particles have fixed electrical charges. Similarly, ion exchange membranes (Section 3.4.2.5) have fixed electrical charges. If there is no externally applied electrical field, it is useful to enquire what criteria govern chemical equilibrium in two-phase systems containing such a phase. 

It is common practice to define an electrochemical potential in theyth region by 

Regardless of the Donnan potential, however, electroneutrality is maintained in the ion exchange resin or the solution. Helfferich (1962) states that 

Migration of just a few ions is sufficient to build up so strong an electric field counteracting any further migration that deviations from electroneutrality remain far from the limit of accuracy of any method except for the measurement of the electric field itself. 

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When two conducting phases come into contact with each other, a redistribution of charge occurs as a result of any electron energy level difference between the phases. If the two phases are metals, electrons flow from one metal to the other until the electron levels equilibrate. When an electrode, i.e., electronic conductor, is immersed in an electrolyte, i.e., ionic conductor, an electrical double layer forms at the electrode-solution interface resulting from the unequal tendency for distribution of electrical charges in the two phases. Because overall electrical neutrality must be maintained, this separation of charge between the electrode and solution gives rise to a potential difference between the two phases, equal to that needed to ensure equilibrium. 

Polyelectrolyte gels, often referred as ionic polymer gels are quite attractive intelligent materials. They consist of a solid phase, i.e., a polymer network with fixed charges, and a liquid phase with mobile ions. Typically these gels are immersed in a solution bath. An application of different kinds of stimuli - e.g., chemical (change of salt concentration or pH), thermal, magnetical, or electrical -leads to a new equilibrium between the different forces, such as osmotic pressure... 

Both the equilibria considered in Section 1.4 occur in a single phase— either in the gas phase or in solution. However we saw earlier that the essential feature of an electrochemical equilibrium, such as the one displayed in Fig. 1.1, is that it involves two separate phases, the electrode and the solution. Moreover the equilibrium involves the transfer of a charged particle, the electron, between these two phases. This complicates the approach we have adopted since we have now to concern ourselves not only with differences in the chemical energy of the reactants and products (as in eqn 1.4) but also with electrical energy differences. The latter arise since typically a difference in potential exists between the solution and the metal electrode so that the relative electrical energy of the electron in the two phases helps control the final point of equilibrium. 

Consider a system of two solvents in contact in which a single electrolyte BA is dissolved, consisting of univalent ions. A distribution equilibrium is established between the two solutions. Because, in general, the solvation energies of the anion and cation in the two phases are different so that the ion with a certain charge has a greater tendency to pass into the second phase than the ion of opposite charge, an electrical double layer appears at... 

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