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Membranes 2021, 11, 940 result of the significant shielding of a considerable amount of Li+ ions which are prevented from reaching the electro-adsorption layer of the charged groups. This weakens the inter- action with the Li+ ions, and promotes their diffusion through the polyelectrolyte. These results suggest that increasing the concentration of the Mg2+ ions enhances the diffusion of Li+ ions, making the membrane material suitable for the recovery of Li+ ions in br9ionfe12 containing high concentrations of Mg2+ ions. Membranes 2021, 11, 940 presented in Figure 9. The polyelectrolyte exhibited a significant attraction for dival1e0ntof 12 ons, and the energy of the aqueous polyelectrolyte system were determined following a Figure 8. Radial distribution functions of O-atoms in the sulfonic and phosphoric fixed-charge The permeability of the ions was further investigated by constructing an ensemble groups to Li+ ions in an ensemble comprised of Mg2+/Li+ ions. consisting of the polyelectrolyte chain, 500 molecules of H2O, 20 ions each of Li+, Na+, Mg2+, and Ca2+, and a balanced charge of Cl− ions. At the end of the NVT dynamic simulation, The permeability of the ions was further investigated by constructing an ensemble the final frame was taken and the spatial position of constraints of the polyelectrolyte chain consisting of the polyelectrolyte chain, 500 molecules of H2O, 20 ions each of Li+, Na+, Mg2+, was removed. The total energy of the system, the energies of the solvated counterions, and and Ca2+, and a balanced charge of Cl- ions. At the end of the NVT dynamic simulation, the energy of the aqueous polyelectrolyte system were determined following a previously the final frame was taken and the spatial position of constraints of the polyelectrolyte reported method [32]. The interaction energies were calculated using Equation (4) and chain was removed. The total energy of the system, the energies of the solvated counteri- ions (Mg2+ and Ca2+), which increased the energy barrier between them, resulting in the previously reported method [32]. The interaction energies were calculated using Equation lowering of their diffusion characteristics. The order of interaction energies (Mg2+ > Ca2+ > (4) and presented in Figure 9. The polyelectrolyte exhibited a significant attraction for di- Na+ > Li+) indicates the selective permeation of monovalent ions through the system. valent ions (Mg2+ and Ca2+), which increased the energy barrier between them, resulting in the lowering of their diffusion characteristics. The order of interaction energies (Mg2+ > Ca2+ > Na+ > Li+) indicates the selective permeation of monovalent ions through the system. 50 40 30 20 10 0 50 100 200 0 2 4 6 8 10 12 14 16 18 20 r (Å) Figure 8. Radial distribution functions of O-atoms in the sulfonic and phosphoric fixed-charge groups to Li+ ions in an ensemble comprised of Mg2+/Li+ ions. Figure 9. Interaction energy of the counterions towards the sulfonic and phosphoric pendant groups in the polyelectrolyte membrane. Figure 9. Interaction energy of the counterions towards the sulfonic and phosphoric pendant groups in the polyelectrolyte membrane. 4. Conclusions We have investigated the diffusion of Li+, Na+, Mg2+, and Ca2+ ions in brine through the polyelectrolyte membrane materials containing sulfonic and phosphoric pendant gO-Li+ ions Mg2+ ions groups by means of molecular dynamics simulations. It was revealed that the O-atoms ofPDF Image | Diffusion of Monovalent Ions in Polyelectrolyte
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