EFFECTS OF DIELECTRIC SATURATION ON PLANAR DOUBLE-LAYER INTERACTIONS FOR NO ADDED SALT

The effect of dielectric saturation of water on the interaction between electric double layers on two charged plates is theoretically investigated in the absence of low molecular weight salts. The dielectric constant of water, ε, is given as a function of the electric displacement, D, instead of the electric field, E, by ε = (ε0 + 3αD2)/(1 + αD2) or in shorter form by ε = ε0/(1 + αD2), which is derived on the basis of the assumption that the self-free energy of polarized dielectrics is expressed as (aP2 + bP4) where P is the dielectric polarization. By using this expression for ε, we solved the Poisson-Boltzmann equation analytically, and the potential, the field, and the counterion concentration were obtained as functions of the distance from the plates for various values of the charge density on the plates. The electric energy, entropy, and free energy are also calculated, and the effect of dielectric saturation is estimated for various values of the parameter α. The counterion activity cannot exceed a certain limit as the charge density increases and the limit decreases with increasing distance between the two plates. The electric field is made small by the dielectric saturation except in the vicinity of the plates where the field is made large. The electric entropy is decreased by the dielectric saturation (its absolute value is increased), while the electric energy is little influenced. The electric displacement is made smaller everywhere except at the surface of the plate. The effect of dielectric saturation becomes less significant with increasing distance between the two plates. © 1979 American Chemical Society.