Diffusions in Aqueous Solutions with Multivalent Cations and Especially in Cationic First Hydration Shell

Compared with univalent cationic diffusion, little is known about the diffusion behavior of multivalent cations let alone the diffusion of water in their first hydration shell. Here, we show that all published translational diffusion coefficients of multivalent cations and water measured at room temperature exhibit the same concentration dependence when plotted as a function of the mass fraction of free water or of hydrated solute. This behavior is held until only hydration and confined water remain in solutions, wherein their concentration dependences become cationic charge number-dependent. We also found that the iceberg model can well describe the diffusions of multivalent cations with decreasing water content until only hydration water is present. However, ¹H-pulsed-field-gradient nuclear magnetic resonance measurements confirmed that ¹H in the first hydration shell diffuses faster than Al³⁺ at room temperature and they have the same diffusion coefficient only with decreasing the temperature down to about 243 K. Therefore, iceberg model only equivalently describes the effect of strong ion-water interaction on multivalent cationic diffusion. These results will also help us reconceive our current understanding of the pathway for hydration water affecting the diffusion behavior of solutes with relatively weak solute-water interactions.