Non-local screening effects in the long-range interionic interaction in a polar solvent

Abstract

The electrostatic interaction between ionic charges embedded in liquid media depends crucially on the local medium structure at interionic distances comparable with the extension of this structure. At short distances the dielectric screening thus reflects the collective polarization response to the electric field of the ions. This effect is incorporated in the theory of non-local electrostatics, previously applied to metals and semiconductors with a band structure, and recently also developed as a phenomenological theory for liquids.

In the present work we analyse the electric field around a point charge and a charge distribution of finite size is a non-locally screening medium. We analyse subsequently the classical problem of the deviation of pK₂–pK₁ for diamines and dicarboxylic acids from the statistical limiting value of ln4, which is one of the few directly accessible measures of the electrostatic interactions of the protonic and carboxylate charges. By representing the organic molecular cavity as a cylindrical region with a (non-dispersive) low dielectric constant and the dielectric function of the external aqueous medium by an exponential function containing the long- and short-range dielectric constants and the extension of the local medium structure (a model also adopted for semiconductor crystals), we can illustrate the effects of all these parameters. By comparison with the experimental values of pK₂–pK₁ and using reasonable estimates of the molecular dimensions we finally determine the most probable values for the extension of the local medium structure and the short-range dielectric constant.