A cut-off criterion for calculating more reliable adsorption energy distributions from gas adsorption isotherms

Adsorption energy distributions from experimental gas adsorption isotherms are capable to characterize the energetic heterogeneity of a solid surface. Unfortunately, they can only be computed by the adsorption integral equation, which represents an ill-posed problem, i.e., the solution is highly sensitive to errors in the input data. Ill-posed problems are usually solved by means of regularization, but general regularization schemata do not provide useful criteria to estimate the approximation quality. In this paper, a former presented solution strategy tailor-made for the Langmuir kernel of the adsorption integral equation is extended to Fourier transform. This yields a simple and effective cut-off criterion for the Fourier cosine transform of the adsorption energy distribution. The cut-off criterion is applied to calculate adsorption energy distributions from synthetic and experimental adsorption isotherms.