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The present paper considers the possibility of using a new type of nanocarbon materials for sorption - polycumulene modified with “Taunit-M” carbon nanotubes or graphene nanoplatelets. To evaluate the efficiency of these novel nanomodified materials as sorbents, the following studies were carried out: 1) determination of the optimum pH value to perform static batch sorption experiments, 2) identification of the onset of equilibrium for the adsorption of heavy metal ions (on the example of Cu(II) ions), and 3) elucidation of kinetic adsorption mechanisms. As a result of implementation of kinetic models such as external and internal diffusion, as well as pseudo-first- and pseudo-second-order and Elovich (to determine the contribution of chemisorption), rate constants for the Cu(II) adsorption were estimated. It was noted that the absorption process occurs in a mixed-diffusion mode with the influence of the limiting factor - “sorbate-sorbate” chemical interaction. The equilibrium time was found to be 45 min ...