The Dielectric Constant of Ionic Solutions: A Field-Theory Approach
  We study the variation of the dielectric response of a dielectric liquid (e.g. water) when a salt is added to the solution. Employing field-theoretical methods we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. We predict analytically the dielectric decrement which depends on the ionic strength in a complex way. Furthermore, a qualitative description of the hydration shell is found and is characterized by a single length scale. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles. 
Amir Levy, David Andelman and Henri Orland
cond-mat.soft cond-mat.stat-mech physics.bio-ph physics.chem-ph