Transfer functions for solid-solution partitioning of cadmium, copper, nickel, lead and zinc in soils: derivation of relationships for free metal ion activities and validation with independent data

Models to predict the solid-solution partitioning of trace metals are important tools in risk assessment, providing information on the biological availability of metals and their leaching. Empirically based models, or transfer functions, published to date differ with respect to the mathematical model used, the optimization method, the methods used to determine metal concentrations in the solid and solution phases and the soil properties accounted for. Here we review these methodological aspects before deriving our own transfer functions that relate free metal ion activities to reactive metal contents in the solid phase. One single function was able to predict free-metal ion activities estimated by a variety of soil solution extraction methods. Evaluation of the mathematical formulation showed that transfer functions derived to optimize the Freundlich adsorption constant ( K _f ), in contrast to functions derived to optimize either the solid or solution concentration, were most suitable for predicting concentrations in solution from solid phase concentrations and vice versa . The model was shown to be generally applicable on the basis of a large number of independent data, for which predicted free metal activities were within one order of magnitude of the observations. The model only over-estimated free-metal ion activities at alkaline pH (>7). The use of the reactive metal content measured by 0.43 m HNO₃ rather than the total metal content resulted in a close correlation with measured data, particularly for nickel and zinc.