Energy of an ion crossing a low dielectric membrane: The role of dispersion self-free energy

The Born charging equation predicts that the permeability of a cell membrane to ions by the solubility-diffusion mechanism depends on the ionic radius and on the dielectric constant of the membrane. However, experiments, for example, on red blood cells and on lysosome membranes, show that the permeability depends strongly on the choice of salt anion in a way that cannot be accommodated by differences in ionic size. We demonstrate that one step towards understanding this ion specificity is to take account of the previously ignored dispersion self-free energy of the ion. This is the quantum electrodynamic analogue of the (electrostatic) Born self-energy of an ion. We show that the dispersion self-free energy contribution can be and often is of the same order of magnitude as the Born contribution. To understand the observed specificity, it is essential to take into account of both ionic size and ionic polarizability. In parallel and to reinforce these observations, we also give simple estimates for how self-free energy changes that occur when an ion moves into the air-water interface region (which has a density profile for water molecules) can influence the surface tension of salt solutions. Consistency can be found between the Hofmeister sequences observed in ion permeation and in surface tension of electrolytes when these previously ignored self-free energies are included properly.