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Membranes 2021, 11, 940 10 of 12 References 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 groups by means of molecular dynamics simulations. It was revealed that the O-atoms of the charged groups exhibit stronger attractions for the divalent ions, resulting in a rise in the diffusion energy barrier and, consequently, lowering their diffusion through the membrane material. The analysis of the mean square displacement of the ions revealed that Li+ and Na+ ions exhibit greater values due to the weak attraction by the charged groups. In the presence of higher concentrations of Mg2+ ions, the radial distribution function of the O-Li atoms decreases, suggesting the diffusion of Li+ ions through the polyelectrolyte system. This study demonstrates the role of both the sulfonic and the phosphoric pendant groups in promoting the diffusion of monovalent ions. Our results could serve as a guide for the design of effective cation-exchange membranes for the recovery of Li+ and Na+ ions from brine. Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/membranes11120940/s1, Figure S1: log (MSD) vs log t plots of (a) Mg2+, (b) Ca2+ and (c) Na+ ions. Author Contributions: Conceptualization, I.A. and Q.P.; methodology, I.A.; software, I.A.; validation, B.S. and N.B.; resources, I.A.; data curation, I.A.; writing—original draft preparation, I.A. and Q.P.; writing—review and editing, B.S. and N.B.; visualization, Q.P.; supervision, Q.P.; funding acquisition, Q.P. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The raw data generated during this study will be made available by the corresponding authors, without undue reservation, upon request. Acknowledgments: The authors acknowledge the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum and Minerals for providing the computing resources and for the financial support. Conflicts of Interest: The authors declare no conflict of interest. 1. Dutta, D.; Kumari, A.; Panda, R.; Jha, S.; Gupta, D.; Goel, S.; Jha, M.K. Close loop separation process for the recovery of Co, Cu, Mn, Fe and Li from spent lithium-ion batteries. Sep. Purif. Technol. 2018, 200, 327–334. [CrossRef] 2. Zhang, W.; Xu, C.; He, W.; Li, G.; Huang, J. A review on management of spent lithium ion batteries and strategy for resource recycling of all components from them. Waste Manag. Res. 2018, 36, 99–112. [CrossRef] [PubMed] 3. Sun, Y.; Zhu, M.; Yao, Y.; Wang, H.; Tong, B.; Zhao, Z. A novel approach for the selective extraction of Li+ from the leaching solution of spent lithium-ion batteries using benzo-15-crown-5 ether as extractant. Sep. Purif. Technol. 2020, 237, 116325. [CrossRef] 4. Ikram, R.; Mohamed Jan, B.; Atif Pervez, S.; Papadakis, V.M.; Ahmad, W.; Bushra, R.; Kenanakis, G.; Rana, M. Recent Advance- ments of N-Doped Graphene for Rechargeable Batteries: A Review. Crystals 2020, 10, 1080. [CrossRef] 5. Mun, S.C.; Won, J.H. Manufacturing Processes of Microporous Polyolefin Separators for Lithium-Ion Batteries and Correlations between Mechanical and Physical Properties. Crystals 2021, 11, 1013. [CrossRef] 6. Dang, H.; Li, N.; Chang, Z.; Wang, B.; Zhan, Y.; Wu, X.; Liu, W.; Ali, S.; Li, H.; Guo, J.; et al. Lithium leaching via calcium chloride roasting from simulated pyrometallurgical slag of spent lithium ion battery. Sep. Purif. Technol. 2020, 233, 116025. [CrossRef] 7. Zhang, X.; Han, A.; Yang, Y. Review on the production of high-purity lithium metal. J. Mater. Chem. 2020, 8, 22455–22466. [CrossRef] 8. Sato, Y. Electrowinning of Metallic Lithium from Molten Salts. ECS Proc. Vol. 2002, 2002, 771. [CrossRef] 9. Chen, M.; Zhang, Y.; Xing, G.; Tang, Y. Building High Power Density of Sodium-Ion Batteries: Importance of Multidimensional Diffusion Pathways in Cathode Materials. Front. Chem. 2020, 8, 152. [CrossRef] [PubMed] 10. Pandit, B.; Rondiya, S.R.; Dzade, N.Y.; Shaikh, S.F.; Kumar, N.; Goda, E.S.; Al-Kahtani, A.A.; Mane, R.S.; Mathur, S.; Salunkhe, R.R. High Stability and Long Cycle Life of Rechargeable Sodium-Ion Battery Using Manganese Oxide Cathode: A Combined Density Functional Theory (DFT) and Experimental Study. ACS Appl. Mater. Interfaces 2021, 13, 11433–11441. [CrossRef]PDF Image | Diffusion of Monovalent Ions in Polyelectrolyte
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