<![CDATA[Liquid-liquid extraction is one of the methods for separating rare earth elements (REE) in the presence of an extractant. The separation of REE ions, complex with an extractant, involves interfacial migrations that are influenced by the diffusion of the respective ions. Therefore, we performed molecular dynamics simulations on REE ions (La3+, Sm3+, Eu3+, Gd3+, and Tb3+) in a water-n-hexane system to determine if each ion exhibited a distinct diffusion coefficient. By employing molecular dynamics simulations, we calculated diffusion coefficients for these ions based on the Einstein relation. The diffusion coefficients for La3+, Sm3+, Eu3+, Gd3+, and Tb3+ were found to be 4.21×10–6, and 3.96×10–6, 4.57×10–6, 4.17×10–6, and 5.19×10–6 cm2/s, respectively. However, statistical analysis via the Kruskal-Wallis test revealed no significant variance in the diffusion coefficients (p-value greater than 0.05), indicating that diffusion is not a rate-limiting factor in REE separation. The findings suggest that effective mixing during extraction can eliminate the role of diffusion as a differentiating factor in REE separation. Overall, this study offers critical insights into optimizing REE extraction processes]]>
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