Counterion-release versus dielectric entropy: insights from the Gouy-Chapman model for a uniformly charged plate

We investigate temperature-dependent electrostatics at a charged plate in electrolyte solution using the Gouy-Chapman model including the dependence of the dielectric constant ϵ(T) on temperature. We consider the adsorption of a test charge on a charged plate as well as the interaction between two oppositely charged plates. The experimental temperature dependence of the dielectric constant ϵ(T) of pure water is well represented by ϵ(T) ∼ T−α with α = 1.43. Thus, the entropic part of the electrostatic interaction includes for α ≠ 0 in addition to the ion configurational entropy a contribution from the dielectric response of water. For high-surface charge or low-salt concentration, the electrostatics is dominated by entropy but the dielectric entropy is negligible compared to the counterion-release entropy. This changes at low surface charge or high salt, where the free energy exhibits internal energy as well as entropic contributions and the entropy is due to dielectric and counterion-release effects, the precise decomposition of the free energy in this limit depends on the value of α.