Counterion-only electrical double layer: A constrained entropy approach

A counterion-only double-layer theory is developed taking a constrained entropy maximization approach based on an isothermal thermodynamic system. The double-layer interaction free energy per unit area between two charged planar surfaces is obtained in a consistent manner for the boundary conditions of constant surface charge density and charge regulation. Once applied to the nonpolar medium, it reveals that the electrical double-layer repulsion is weak and long-ranged. Asymptotically, the interaction decays as a power law, in contrast with that in the presence of an ion reservoir which decays exponentially at large surface separation. The applicability of the counterion-only model for describing colloidal stability in nonpolar media is discussed. © 2002 American Institute of Physics. @DOI: 10.1063/1.1500359#