Charge reversal in electrical double layers - A balance between energy and entropy

Monte Carlo simulations and accurate analytical theories predict a charge reversal in an electric double layer under some specific conditions. One typical situation is for very highly charged aggregates in the presence of divalent counterions, where ionic correlations become important. Here, we reexamine the phenomenon in terms of a balance between energy and entropy contributions. High surface charge density, low temperature, low dielectric permittivity or multivalent counterions, all these factors increase the influence of the energetic term and favour a charge reversal. Previous studies have focused on the energy term and attempts to increase that. An alternative and equally valid way is to reduce the entropy term, which can be accomplished by replacing single atomic or molecular counterions by polyelectrolyte chains. The entropy of the charged chains is of course much lower than that of the small ions and the dominance of the energy term will again lead to a charge reversal, but in this case at a much lower and more realistic value of the electrostatic coupling.