Analysis of binding heterogeneity

Binding heterogeneity, due to different functional groups on a reactive surface, plays an important role in the binding of small molecules or ions to many adsorbents, both in industrial processes and in natural environments. The binding heterogeneity is described by a distribution of affinity constants since the different functional groups have different affinities for the adsorbing species.

Three appraoches are discussed to obtain distribution functions on the basis of adsorption isotherms: the Local Isotherm Approximation (LIA), the Affinity Spectrum (AS) and the Differential Equilibrium Function (DEF). The methods are compared both on the basis of their derivation and on their ability to reproduce (known) distribution functions. All methods discussed need derivatives of the binding function, which are hard to obtain from experimental data. In order to apply the methods to experimental data a smoothing spline routine was adapted for the present problem. The methodology is applied to proton and copper binding to fulvic acids.

Analogous to the heterogeneity analysis for binding under equilibrium conditions, a procedure was derived to determine first order rate constant distributions. The newly developed method is called LOcal Decay function Approximation (LODA). Also here an adapted smoothing spline routine is used to apply the method to experimental data. The method is illustrated by copper dissociation data from estuarine humic material.

Finally it is shown how on the basis of the obtained distribution function a suitable model can be chosen for the description and prediction of binding or dissociation data.