Phase boundary potential, dissociation

In the phase-space treatment the situation is very similar. However, rather than study the morphology of the potential energy surface, we must focus on the total energy surface. The geometry of this surface, which is defined on phase space instead of coordinate space, can also be characterized by its stationary points and their stability. In this treatment, the rank-one saddles play a fundamental result. They are, in essence, the traffic barriers in phase space. For example, if two states approach such a point and one passes on one side and the other passes on the other side, then one will be reactive and the other nonreactive. Once the stationary points are identified, then the boundaries between the reactive and nonreactive states can be constructed and the dynamical structure of phase space has been determined. As in the case of potential energy surfaces, saddles with rank greater than one occur, especially in systems with high symmetry between outcomes, as in the dissociation of ozone. 

The polyion domain volume can be computed by use of the acid-dissociation equilibria of weak-acid polyelectrolyte and the multivalent metal ion binding equilibria of strong-acid polyelectrolyte, both in the presence of an excess of Na salt. The volume computed is primarily related to the solvent uptake of tighdy cross-linked polyion gel. In contrast to the polyion gel systems, the boundary between the polyion domain and bulk solution is not directly accessible in the case of water-soluble linear polyelectrolyte systems. Electroneutrality is not achieved in the linear polyion systems. A fraction of the counterions trapped by the electrostatic potential formed in the vicinity of the polymer skeleton escapes at the interface due to thermal motion. The fraction of the counterion release to the bulk solution is equatable to the practical osmotic coefficient, and has been used to account for such loss in the evaluation of the Donnan phase volume in the case of linear polyion systems. 

It should also be mentioned that the Gibbs energy of ion transfer can be affected by complexation phenomena at the liquid liquid boundary. A classical example is given by the work of Koryta [25], who studied the transfer of from water to nitrobenzene assisted by dibenzo-18-crown-6. The complexation step decreases the energy of solvation of the cation in the organic phase, decreasing the formal transfer potential as defined in Eq. (5). Various mechanisms have been proposed for assisted ion-transfer processes, namely, aqueous complexation followed by transfer, transfer followed by complexation in the organic phase, transfer by interfacial complexation, or transfer by interfacial dissociation [26,27]. 

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