Affinity distributions and acid-base properties of homogeneous and heterogeneous sorbents: Exact results versus experimental data inversion

Ionization properties of simple polyprotic acids and bases (oligoprotic carboxylic acids, polyelectrolytes, latex particles, proteins) can be described quantitatively with Ising models. These mechanistic models incorporate relevant molecular details and allow determination of exact affinity distributions (pK spectral. At present, such a molecularly based approach is too involved for complex heterogeneous substances, but the affinity distributions of these materials can be calculated by direct numerical inversion of the experimental data. Even though this problem is ill-posed, special numerical techniques can be used to stabilize the procedure and td select distributions that are smooth or that consist of a small number of isolated discrete peaks, which can be interpreted as a small number of ionizable sites. The results of these inversion techniques are discussed for a number of examples of environmental relevance such as oxides and humic substances, and for the simple model systems. Based on such observations for simple systems, we conclude that it is essentially impossible to extract true affinity distributions of complex environmental sorbents.