Volume-term theories, Sogami-Ise potential, and the Langmuir model for phase separation in macroion systems: a...

There is a controversy regarding the mechanism of phase separation in highly charged macroion systems. Volume-term (VT) theories propose that the transition is due to a spinodal instability sensitive only by the microions, the Sogami-Ise theory gives an attractive tail in the pair interaction potential, which promotes the formation of clusters and voids, and the Langmuir (L) model views the transition as an instability of the pressure. It is shown herein that these three seemingly different models can be brought under the same formalism and that they reflect different contributions to the same overall process. Within the context of the VT formalism, the attractive tail in the macroion-macroion pair interaction is a direct result of the screened Coulomb form of the interaction and is identified as a microion-modified electrostatic pressure. Within the context of the VT formalism the L theory is associated with the microion-microion interaction for the added electrolyte. Finally this holistic view of the VT approach is extended to include the contribution of the solvent via the Gibbs-Duhem expression.