On derivatives of surface charge curves of minerals

Surface titrations of minerals in aqueous electrolyte solutions are used as building blocks for surface complexation modelling. However, these potentiometric data may contain less model relevant information than previously and presently assumed. In the literature, derivative analyses have been applied to experimental surface charge versus pH curves and four or more pK values were extracted for goethite or aluminium oxide. Derivative analysis of specific surface charge versus pH curves calculated for various published model variants for goethite shows that not more than the net-zero proton surface charge condition can be extracted from computer generated data. Generated data can be produced in density and precision superior to experimental data, but yield only relatively little output from such derivative analysis compared to what has previously been extracted from derivatives of experimental data. For the generated goethite data and for all model variants only the point of zero could be extracted. For the various goethite model variants tested a nearly symmetrical peak appeared at the point of zero charge in the derivative curve. A different pattern could be obtained for generic models, for which two sites with unequal sites densities and different pK values were assumed. Variation of these parameters could result in derivatives of the charging curves with two maxima or one maximum and a broad tailing. In the literature, curves with features nearly identical to these generated curves have been interpreted by up to four pK values (i.e., four different sites within a 1-pK model). It is concluded that the interpretation of the generated data is in all cases hampered by the overwhelming electrostatic contributions to the free energy of proton ad/desorption. In no case except for the one-site 1-pK model was it possible to extract the input pK value(s) from the derivatives. Plausible explanations for the discrepancy between generated data and published experimental data are discussed.