Electrostatic interaction models for ion binding to humic substances

Preferably, the description of ion binding to humic substances (HSs) is done with thermodynamic constants that do not depend on the environmental conditions. To solve this problem, models have to be made that describe the electrostatic and specific interactions. With a given electrostatic model the charge/pH curves of HS at different salt levels can be re-plotted as a function of the local pH near the sites (pHloc) of HSs. If the model is appropriate, the charge/pHloc curves will merge into a master curve (MC). In this study five electrostatic models were investigated to obtain pHloc for purified Aldrich humic acid (PAHA): rigid sphere (RS), ion-permeable sphere, Donnan (NICA), Donnan-EV, and Donnan-EDL. The RS model is tested in two versions; one based on the measured hydrodynamic radius (RS-ah) and the other on an optimized radius (RS-aopt). The ion-permeable sphere model uses the hydrodynamic radius and provides the potential distribution; as characteristic potential the radial average inside the sphere is used. In the Donnan (NICA) model the volume of the sphere, VD, in which the charge of PAHA is neutralized, is optimized with a constraint between VD and ionic strength, and in the Donnan-EV model VD is calculated by setting the radius of the gel as the sum of the hydrodynamic radius of PAHA and the Debye length. The Donnan-EDL model uses the hydrodynamic particle radius and is based on a combination of the Donnan model and the diffuse electrical double layer model. Only the RS-aopt, Donnan (NICA), and Donnan-EV models give adequate MCs. The positions of the MCs differ with respect to each other. This means that the discrimination between electrostatic and intrinsic interactions is model-dependent and therefore arbitrary. The Donnan (NICA) model has a practical advantage over the other two models because this model needs no measurements of the size of HS. For the purpose of the routine fitting of ion-binding data to an ion-binding isotherm equation that includes the electrostatics, this advantage is quite important.