A thermodynamic model of gas/solid adsorption has been constructed from two elements. The first is the original Gibbs equation. The second consists of functions psi(Theta) or psi(P) that are calculable from measured isotherms. Based on this model the characteristic adsorption functions (CAFs) were defined and calculated. The CAFs, which concentrate into one function all measured isotherms having the same change in relative free energy of the surface, are very sensitive to the structure of the adsorbents. This statement was tested with nitrogen isotherms measured at 77 K on well-characterized chemically/physically treated activated carbons prepared from poly(ethylene terephthalate). Changes in the surface structure were followed by small angle X-ray scattering (SAXS). This experimental approach made it possible to observe the correspondence between structural changes and the CAF.