A new integrated method for characterizing surface energy heterogeneity from a single adsorption isotherm

To characterize surface energy heterogeneity of fine particles, this paper presents an integrated strategy from a single adsorption isotherm. By coupling the well-known integral equation method and derivative isotherm summation (DIS) procedure based on a patchwise model, the newly proposed strategy could calculate adsorption energy distributions (AEDs) for different surface patches. Correspondingly, the surface heterogeneity of materials can be described by weighted summation of patch AEDs, that is, the total AED. The validity of this new method is confirmed by both tests of rutile nanoparticles and multiwalled carbon nanotubes (MWNTs). The total AED obtained by the new method agrees well with the result from solving the integral equation directly, and it shows that AED peaks can be assigned to specific energy patches of real surface exactly. Furthermore, a detailed comparison showed that some artificial oscillation in the results can be identified with the new strategy, and the patches with low area and high surface energy could be characterized as well. In conclusion, this strategy constructs a correspondence between derived AEDs and different patches of real surface, so it will be more effective to understand surface heterogeneity by using the adsorption probe method.