Comparison of 1-pK and 2-pK Versions of Surface Complexation Theory by the Goodness of Fit in Describing Surface Charge Data of (Hydr)oxides

Abstract

1-pK and 2-pK formulations exist in surface complexation theory with respect to the description of basic charging behavior of (hydr)oxide electrolyte interfaces. The 2-pK approach has been commonly used with at least four different electrostatic models, whereas the 1-pK model has been primarily used with only one of those electrostatic models. In this paper the 1-pK approach is combined with three more electrostatic models. The eight resulting possible combinations have been tested on several sets of data. Applying the 2-pK basic Stern model (BSM) and the triple-layer model (TLM) was not satisfactory: due to the high number of adjustable parameters involved in these model variations the optimization procedure of the applied computer codes did not converge. This was taken as an a priori justification to exclude even more complicated (four-layer) models. For the remaining six models which could be successfully applied in the present paper, the goodness of fit parameter given by a computer code was used to compare the quality of the description of the chosen experimental data by the respective models. A purely diffuse layer model (DLM) generally gave the poorest fit to experimental data when combined with the 1-pK approach and was only sligthly better when combined with the 2-pK formalism. Either the 1-pK BSM or the 2-pK constant capacitance model (CCM) gave the best fit to the data in all the examples. However, it was found in two cases that some arbitrary constraint was necessary to define a unique (and thus meaningful) parameter set for the 2-pK CCM. The 1-pK TLM version allowed in more than half of the examples to determine a unique parameter set, which is impossible with the 2-pK TLM. It is concluded that the 1-pK BSM should be considered as the first choice model with respect to the goodness of fit and the uniqueness of the estimated parameters. The 2-pK CCM is still a good choice for a constant ionic strength case when the experimental data allow a determination of unique parameters and if only goodness of fit is used as a criterion.