Oscillatory and monotonic polarization. The polarization contribution to the hydration force

The propagation of polarization in water, in the vicinity of a planar surface containing dipoles, is considered to be a consequence of the nonuniformity of the dielectric constant near the dipoles. Discrete finite difference equations have been derived by assuming a layered icelike structure. These equations predicted a polarization that oscillates with the distance from the surface. When the polarizing surface was considered rough or fluctuating, the oscillations were smoothed out and a monotonically decaying average polarization was obtained. Assuming that there are local icelike structures around any of the water molecules, a second-order differential equation for the polarization and expressions for its decay length were derived.