Solubility-normalized Dubinin–Astakhov adsorption isotherm for ion-exchange systems

The well-known Dubinin–Radushkevich adsorption isotherm is extensively used for vapour adsorption on activated carbon and its use has been extended to cover the cases of the adsorption of organic compounds from aqueous solutions and the ion exchange of metals on several porous materials. In the later cases, the use of the Dubinin–Radushkevich adsorption isotherm is questionable as it is not taking into account the pore structure of the materials used. In the present paper the more general Dubinin–Astakhov adsorption isotherm is used modified by introducing a solubility-normalized adsorption potential. Then, it is applied in experimental isotherms in order to determine adsorption energy and heterogeneity parameter for the ion exchange of Pb2+ in the zeolite clinoptilolite. The results indicate that the Dubinin–Astakhov adsorption isotherm represents the experimental data well and in the same time provides the heterogeneity parameter of the material which is an important adsorbent physical parameter as well as the adsorption energy. The calculated values are found to be n = 5.2 and E ≅ 18 kJ/mol, respectively. An extended review is conducted by applying the proposed isotherm in experimental data found in the literature for clinoptilolite cation exchange systems (22 experimental isotherms, 175 equilibrium points). The average value of the heterogeneity parameter is n = 5.84 ± 2.09 (35.8% deviation) with a range of 2.1–10.4. The results indicate that the heterogeneity parameter value is strongly influenced from the structure of the adsorbent and in lesser extend from the cation exchanged. The average value of the adsorption energy is E = 16.7 ± 3.21 (19.2% deviation) with a range of 9.47–21.74 kJ/mol.