Onsager–Dupuis theory, old and new

The first theory that coupled electrostatics to structural polarization has been the Onsager-Dupuis theory for ice. The basic concepts that these authors developed were rapidly transferred to water as the usual solvent in liquid electrolytes. Subsequently, the Onsager-Dupuis approach has been forgotten and reinvented several times. In this short contribution, I discuss a simplified version of the structural polarization theory that I have formulated with Rudi Podgornik. I show that a phenomenological fourth-order equation for the electrostatic potential follows strictly from the Onsager-Dupuis theory. Furthermore, I derive generalizations of the Grahame equation for a set of different boundary conditions for a charged and polarizable electrode bounding a structured solvent, paving the way for the application of the general theory to experimentally realizable systems.