Decay behavior of screened electrostatic surface forces in ionic liquids: the vital role of non-local electrostatics

Screened electrostatic surface forces, also called double layer forces, between surfaces in ionic liquids can, depending on the circumstances, decay in an exponentially damped, oscillatory manner or in a plain exponential way (the latter as in dilute electrolyte solutions where ion–ion correlations are very weak). The occurrence of both of these behaviors in dense ionic liquids, where ion–ion correlations are very strong, is analyzed in the current work using exact statistical mechanics formulated in a manner that is physically transparent. A vital ingredient in understanding the decay behaviors is the fact that electrostatics in dense electrolytes have a non-local nature caused by the strong correlations. It is shown that the effects of non-locality can be elucidated by a remarkably simple, general expression for the decay parameter κ that replaces the classical expression for the inverse Debye length κDH of the Debye–Hückel (DH) and non-linear Poisson–Boltzmann approximations. This exact expression is valid for both the plain exponential and the oscillatory cases. It shows how strong correlations can give rise to plain exponential decay with a long decay length. Such a decay can arise from anion–cation associations of various kinds, for instance transient ion pairing or association caused by many-body correlations; ion pairing is a possibility but not a necessity for this to occur. Theoretical analysis is done for systems consisting of ions with an arbitrary shape and internal charge density and immersed planar walls with arbitrary internal charge distribution and any short-range ion–surface interaction. The screened electrostatic surface force between two walls is at large separations proportional to the product of effective surface charge densities of each wall. For the oscillatory case, each wall contributes with a phase shift to the oscillations of the interaction.