Parameter Estimation for the Constant Capacitance Surface Complexation Model: Analysis of Parameter Interdependencies

Results of extensive application of the 2-pK constant capacitance surface complexation model (CCM) to surface charge data of a range of minerals in 0.1Melectrolytes are summarized where the program FITEQL has simultaneously been used to study the interdependence of the involved optimized parameters.To illustrate representative results, surface complexation and goodness of fit parameters are given as a function of the capacitance value (C). For all (ca. 150) tested data sets, one of three patterns is observed, two of which do not allow a unique parameter set to be obtained.The results indicate that the optimized site density parameter is relatively insensitive to a wide variation ofC; optimized site density is rather low in this range of (higher)Cand tends toward maximum proton uptake in the respective data set which in turn will be close to sometimes experimentally observed saturation levels. At low and with further decreasingCa steep increase of site density may occur; in this case, ΔpK_astrongly increases after a ΔpK_aminimum. Alternatively at lowC, ΔpK_amay continue to decrease and site density decreases simultaneously after a site density maximum. The observed patterns can be explained by the constraint ofCon the electrostatic correction factor.Linear correlation coefficients (which are very useful parameters but do not receive much attention) show that in the region of lowC, the optimized parameters become fully correlated, which finally causes nonconvergence in parameter optimization. In the region where the optimized site density is not significantly affected by a decrease inCthe optimized parameters are more weakly correlated. When site concentration is co-optimized high correlation between adjustable parameters suggests that it is preferable to have an estimate for this parameter.Overall, it can be stated that substantial difficulties were observed in the effort to obtain unique (and thus meaningful) parameters for the CCM in about 60% of the data sets treated.