Fractal model for adsorption on activated carbon surfaces: Langmuir and Freundlich adsorption

Adsorption of organic compounds in aqueous media onto an activated carbon surface usually follows the empirically derived Freundlich equation W=KC1/n, where W is the mass of the adsorbed solute, C is the equilibrium solute concentration, and K and n are fitting constants. To analyze this equation, we propose a simple geometrical model for adsorption of organic compounds. Activated carbon surfaces are irregular, and the irregularity is similar at any magnification. Because of the self-similarity in raggedness at various resolutions, adsorption of a bulky organic molecule sequesters several neighboring sites from binding. Based on this model, a generalized equation was derived that encompasses the Langmuir and Freundlich equations. The Freundlich equation is shown to be a special case of the expanded Langmuir equation. The parameter n in the Freundlich equation is related to the number of binding sites wasted by the adsorbate binding; hence, it is related to the size of the adsorbate molecule. The experimental result that n is larger than unity supports the above model. The main force for the carbon surface adsorption is the tendency of the adsorbate molecule to be excluded from the aqueous phase. The larger the hydrophobic molecule, the greater the tendency to be excluded from the aqueous phase becomes. For this reason, n is related to the adsorbate affinity. The parameter K is related to the size of the adsorbing space, i.e. the binding capacity, and also to the adsorbate affinity. Furthermore, the relationship between n and K was derived and discussed.