Determination of the adsorption energy distribution function with the LOGA method.

A method to determine the adsorption energy distribution function from adsorption data is presented. The overall isotherm on a heterogeneous surface is the summation of local adsorption contributions. The distribution function of the adsorption energy of affinity can be calculated, provided the overall isotherm and the local isotherm function are known. The LOGA method uses a special function to approximate the local isotherm, so that an analytical expression results for the energy distribution function. Results of the LOGA method are presented for “synthetic” overall isotherms based on various energy distribution functions and the Langmuir equation as local isotherm. Special attention is paid to the effect of experimental errors in the overall isotherm data. In this case pretreatment of the data is required. A smoothing spline (SP) procedure is recommended in which the extent of smoothing of the data corresponds with the experimental error in the data. A comparison of results obtained with the SP-LOGA method and the more sophisticated CAESAR method shows that the SP-LOGA result is satisfactory but is somewhat less precise than that obtained with CAESAR. In the presence of lateral interaction the expression for the LOGA distribution function depends on the type of heterogeneity. Expressions are given for both random and patchwise surfaces.