Suitability of L- and U-Curve Methods for Calculating Reasonable Adsorption Energy Distributions from Nitrogen Adsorption Isotherms

Abstract

Adsorption energy distributions (AEDs) can be calculated from measured adsorption isotherms by numerical methods upon regularization of the adsorption integral equation. The regularization solves the ‘ill-posed problem’ of the adsorption integral equation. In this paper, the so-called U- and L-curve methods and the modified U-curve method for estimating the optimal regularization parameter are tested with synthetic nitrogen adsorption isotherms. The isotherms are calculated from AEDs with one (minimum) to five (maximum) peaks using a simple gas adsorption model. To verify the U- and L-curve methods, the originally generated AED functions with different number of peaks are compared with those obtained back from the synthetic isotherms using the INTEG regularization method. The results show that the L-curve method is superior to the U-curve methods for finding the optimal regularization parameter.