The intimate relationship between the dielectric response and the decay of intermolecular correlations and surface forces in electrolytes

Abstract

A general, exact theory for the decay of interactions between any particles immersed in electrolytes, including surface forces between macroscopic bodies, is derived in a self-contained, physically transparent manner. It is valid for electrolytes at any density, including ionic gases, molten salts, ionic liquids, and electrolyte solutions with molecular solvent at any concentration. The ions, the solvent and any other particles in the system can have any sizes, any shapes and arbitrary internal charge distributions. The spatial propagation of the interactions in electrolytes has several decay modes with different decay lengths that are given by the solutions, κ_ν, ν = 1, 2,…, to a general equation for the screening parameter κ; an equation that describes the dielectric response. There can exist simultaneous decay modes with plain exponential decay and modes with damped oscillatory exponential decay, as observed experimentally and theoretically. In the limit of zero ionic density, the decay length 1/κ_ν of the mode with the longest range approaches the Debye length 1/κ_D. The coupling between fluctuations in number density and charge density, described by the density–charge correlation function H_NQ(r), makes all decay modes of pair correlations and interaction free energies identical to those of the screened electrostatic potential, and hence they have the same values for the screening parameters. The density–density and charge–charge correlation functions, H_NN(r) and H_QQ(r), also have these decay modes. For the exceptional case of charge-inversion invariant systems, H_NQ(r) is identically zero for symmetry reasons and H_NN(r) and H_QQ(r) have, instead, decay modes with different decay lengths.