Modeling the effect of surface heterogeneity in equilibrium of heavy metal ion biosorption by using the ion exchange model.

This paper is focused on the theoretical modeling of the heavy metal ions biosorption process. The origin of the commonly observed, so-called "heterogeneity effects" has been explained. Two popular models were considered for that purpose: the adsorption model and the ion exchange model. The Condensation Approximation method has been used to develop the model describing the influence of surface heterogeneity on biosorption equilibria. As this model has been derived by accepting the ion exchange processes on the biosorbent surface, the obtained expressions are able to also take into account the pH effect. The mentioned "heterogeneity effects" may be treated as the result of (i) the existence of the continuous function expressing the binding site heterogeneity, (ii) the existence of a few different kinds of binding sites, having different values of ion exchange constant; (iii) stoichiometry of the ion exchange reaction occurring on the biosorbent surface. The latter case is responsible for the so-called "apparent" heterogeneity, when the adsorption model and the ion exchange model offer equally good fits of data but the degree of the surface heterogeneity estimated in this way might be different.