Adsorption-energy distribution of heterogeneous surfaces predicted by projections onto convex sets

The method of projections onto convex sets (POCS) is used to calculate the adsorption-energy distribution-function from the adsorption integral (using a modified Langmuir local isotherm) for energetically heterogeneous surfaces. The POCS-method, originally developed in the 1960s, has been successfully applied for many years to estimation problems, mainly in the fields of image processing, signal recovery, and optics. It allows one to incorporate into an iteration scheme available information about the experimental data and the measurement error as well as a priori constraints (such as nonnegativity) based on physical reasoning. It is important to note that the POCS-method doesn't lead to a unique "optimum" solution. Rather, a feasible solution is found within a "solution space" that is consistent with all imposed constraints. The "size" of this solution space depends on how large the measurement errors are; it also depends on the accuracy of the error statistics, and the number and significance of a priori constraints used. In several examples, the POCS-method is used to recover energy distributions from simulated adsorption data containing normally distributed errors. The excellent recoveries obtained demonstrate the value of the POCS-method as a robust and reliable tool for adsorption-integral inversions