An adsorption isotherm equation for multi-types adsorption with thermodynamic correctness

From the perspective of adsorption energy distribution, the Langmuir adsorption isotherm equation is modified and reformulated on the basis of Fermi–Dirac distribution function. The proposed isotherm model including the loading, the adsorbent–adsorbate interaction and the surface structural heterogeneity factors, overcomes the limitations of the existing isotherm models such as Langmuir, Tόth or Dubinin equations. The proposed equation is validated with experimentally measured multi-types of adsorption isotherms according to IUPAC. Non-monotonic adsorption isotherms stemming from Gibbs adsorption could also be described by the proposed adsorption isotherm directly and it is verified with experimental data. The surface energy and structural factors of the modified equation are demonstrated by the energy distribution functions.