However, the model accounts only for the Stern layer (the inner portion of the electrical double layer coating the surface of mineral grains) polarization  and neglects an important polarization mechanism in the intermediate frequency range (0.1 MHz-100 MHz), often referred to as Maxwell-Wagner polarization or interfacial polarization, due to the build-up of charge on the interfaces of the heterogeneous systems (e.g., ).
This requires the development of a multiphase anisotropic dielectric model where the complex mineral composition and the orientation distribution of the clay minerals can be accounted for; the model should also take into account the Stern layer polarization associated with clay minerals.
In Stern's model, ions in contact with the solid surface behave as in the Helmholtz model, while the remaining ions, located outside this Stern layer
, form a diffuse Gouy-Chapman layer.
Therefore, the catalytic role is due to the presence of premicelle and preponement of micellization by reactant; the two reactants are assumed to have penetrated the stern layer electrostatically .
If [k.sub.m] = 0, [IO.sup.-.sub.4] is completely excluded from the stern layer of the micelle and 2) becomes
The counter ions in the Stern layer
are acted upon by electrostatic attraction, and those in the diffuse layer are acted upon by two equal but opposing forces: the electrostatic attraction force and the diffusive or thermal forces.
A more complex polarization model (O'Konski, 1960) that includes a conducting Stern layer around the particle surface has been proposed, mostly to reconcile the failure of the classical theory for latex particles.
where the Debye screening length [lambda] for the double layer thickness is taken to be the thickness of the Stern layer. The Stern layer conductivity and permittivity are usually also taken to be the same order as the medium permittivity and conductivity or are fitted to data.
The IHP and OHP form the Stern layer, which firmly adheres to the solid surface.
[Q.sub.0] represents the charge density of the surface minerals; [Q.sub.[beta]] represents the charge density of the Stern layer; finally, [Q.sub.S] represents the charge density of the diffuse layer .
In clay bearing rocks, the presence of a connate brine results in the so-called surface effects: electric double layer polarization (i.e., Stern layer polarization) and Maxwell-Wagner space-charge polarization.
It has been shown that the counter ions located in the Stern layer of clay particles are the dominant contributors to surface conduction and in brine saturated rocks with salinity above 1mol/l the mobility of K and Na ions develops 1/10 of that in the free fluid and is independent from the salinity .