Thermodynamic investigation and mathematical modeling of ion-imprinted membrane adsorption

Nickel ion-imprinted membrane was synthesized using PVDF microfiltration membrane as support. In the current study, thermodynamic and kinetic of Ni(II) and Co(II) ions adsorption onto the membrane was investigated. Classical adsorption isotherms including Langmuir, Freundlich, Redlich–Peterson and Langmuir–Freundlich (Sips) were employed to describe the adsorption equilibria. The Sips equilibrium model could superiorly represent the equilibrium adsorption of the ions. Calculation of principle thermodynamic parameters such as free energy, enthalpy and entropy change revealed exothermic and spontaneous adsorption on the basis of the negative ΔH° and ΔG° values, respectively. Meanwhile, adsorption of Co(II) ions on the imprinted membrane was less favorable than that of Ni(II) ions. Moreover, negative values of ΔS° demonstrated randomness reduction at the solid–liquid interface. Pseudo-first-order, pseudo-second-order and intra-particle diffusion models were utilized to describe the adsorption kinetic. Ion diffusivity through the membrane was also examined versus time and initial concentration. The kinetic results indicated superior adsorption-permeation rate of Ni(II) compared with Co(II) ions. In addition, a novel mathematical model was developed for prediction of the ions adsorption-transport behavior. Well fitted to the experimental data, the model provided a new insight into the phenomena involved in ion adsorption on imprinted membranes.