Reconsideration of Theoretical Basis of Freundlich Adsorption Isotherm Equation : II. Approximative Derivation

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I constructed a modified surface complexation model that leads to the Freundlich isotherm approximately. The derivation of the Freundlich isotherm equation is based on the assumption that cations and anions are adsorbed onto the same surface simultaneously. This situation results in the formation of attractive forces between adsorbed cations and anions on the surface. Then the electrostatic energy of the surface should decrease with the increase of adsorption provided that the amount of the ion under consideration is smaller than that of the oppositely charged ion. By using the quadratic approximation theorem, we can approximate this electrostatic energy of quadratic polynomial : E^<Freun>_<elec>(n)=An^2-Bn+C, by the following function : E^<Freun>_<elec>(n)^<app>=D(nln(n/E)-n)+F, where n is the number of ions adsorbed, A, B, C, D, and E are constants with a positive value. Using this equation as the approximated electrostatic energy, we can deduce the Freundlich isotherm easily. This model provides a theoretical basis to the fact that heavy metal adsorption on the edge surface of layer silicate minerals often follows the Freundlich adsorption isotherm equation.
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