Studies on adsorption energy distributions computation from adsorption isotherms by the ansatz method

Since the well-known adsorption integral equation (AIE) is an ill-posed problem, calculation of relevant energetic properties from gas and liquid adsorption isotherms on porous solids still remains a challenging field of research. There are two approaches for solving the AIE: (1) the numerical regularization method and (2) the fitting of the experimental adsorption data by functions possessing an analytical solution. Up to now the latter approach has been treated without consideration of the ill-posedness. The inclusion of ill-posedness in the approach leads to its specification which we call the ansatz method. By showing that a certain class of ansatz functions cannot be used for describing the total isotherms, we were urged to consider more general solutions being connected with the Stieltjes integrals. After applying a general inversion formula we can restrict the theoretically possible total isotherms and outline a feasible general ansatz.