The following paper offers a modern REE 1.0 computer application designed to model the behavior of REE ions in adsorptive materials and membranes. The current version of the application is based on several models, such as the Lagergren pseudo-first order, pseudo-second-order and Elovich kinetic models, and the intraparticle diffusion model, the diffusion-chemisorption model, and the Boyd model. The application has been verified on a sample of four different types of adsorptive materials and membranes. The proposed application allowed the analysis of kinetics, but also the mechanisms of the adsorption process, especially those responsible for the rate-determining steps. It was found that Lagergren pseudo-second-order kinetic model was the best-fit model to describe the adsorption behavior of REE ions onto the novel materials and membranes. Other models determined the process of chemisorption was in force for the analyzed cases, and the mechanisms controlling the adsorption processes are diffusion-chemisorption and adsorption is mostly controlled by film diffusion. Additionally, characteristic parameters, such as qe designated from two different models, showed very similar values, which indicates the correctness of the analysis.
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