The Determination of Affinity Distributions: A Numerical Algorithm and its Application for Estimating the Energetic Heterogeneity of Complexing Silicas and Humic Substances

The characterization of energetic heterogeneity has been discussed in the investigation of ion-binding and chemisorption processes. Both the calculation and the interpretation of the distribution of affinity constants are ambiguous. Methodological difficulties arise connected to the fact that electrostatic effects are difficult to separate from energetic heterogeneity because of the chemical biography of a given material. Only a close similarity between the distribution functions calculated for different ionic strengths allows the electrostatic interactions to be neglected. The numerical estimation of the distribution functions is complicated by the ill-posed nature of the problem. Some computational methods are briefly compared and methods for providing robust and unbiased estimations outlined. In contrast to differential distribution functions, the computation of integral ones may be transformed into the conventionally correct problem. On this basis, a fast and robust method for calculating integral dis...