Stern Extended or Quad Layer Model

Further, this model is based on adsorption modeling (Section 11.1) thus, the binding of ions at each plane is treated as Langmuir competitive adsorption, with consideration for electrostatic interactions in the adsorption equilibrium constants as in Equations 11.16 and 11.17. Thus, the charge at the 0 plane is given by the balance between adsorbed protons and adsorbed hydroxide ions 

Between the planes, fixed surface capacitances are assumed thus, the following charge-potential relationships are included  

The model parameters are r5,Fj, the intrinsic constants Kj, and the capacitances, which are obtained from fitting to experimental data. The model was further extended (Barrow 1983,1986 Barrow and Ellis 1986a) to include adsorption kinetics, diffusive penetration of adsorbates into the solid, and surface heterogeneity, with Gaussian affinity spectra. 

FIGURE 12.13 Zinc adsorption on an Australian soil as a function of pH for different supporting electrolytes ( ) water (a) 1.0 M NaNOj ( ) 1.0 M NaCl. Lines fit to the quad layer model. (Reprinted with permission from Barrow, N. J. and Ellis, A. S., J.Soil Sci., 37, 2, 303-310, 1986b. Copyright 1986, John Wiley and Sons.) 

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