Capability and limitations of first-order and diffusion approaches to describe long-term sorption of chlortoluron in soil

This paper compares the capability of a first-order and a spherical diffusion model to describe and predict long-term sorption and desorption processes of chlortoluron in two soils. Chlortoluron sorption was investigated at different time scales utilizing one rate experiment (120 days) and two sorption/desorption experiments. Experimental periods for sorption and desorption were set to 1 day (five desorption steps) and 30 days (three desorption steps), respectively. Upon fitting, the two models satisfactorily described the whole set of data. The spherical diffusion model performed better than the first-order model. We then tested the predictive capability of the models by predicting 30-day sorption/desorption data using kinetic parameters fitted on 1-day sorption/desorption data only. While the spherical diffusion model was able to predict the 30-day data set, the first-order model failed completely. Fitting both models to subsets of the data corresponding to different experimental time scales revealed that the rate parameter as well as the Freundlich coefficient of the first-order model are strongly time-dependent—a property that is not shared by parameters of the spherical diffusion model. The apparent stability of the spherical diffusion model with regard to time dependency of its parameters indicates that sorptive uptake may be diffusion-controlled. This also explains the models greater predictive power across different time scales compared to the first-order model. Finally, we investigate the suitability of solute class specific log-linear relationships between the first-order rate parameter and the Freundlich coefficient presented by earlier researchers in the light of the time dependency observed for the parameters of the first-order model.