Fig. 2: Difference between ion-water friction in 2D nanochannels and bulk water: higher ratio τ_channel/τ_bulk leads to larger ∆I_FACF.

a ∆I_FACF (\({I}_{{{\rm{FACF}}}}^{{{\rm{channel}}}}-{I}_{{{\rm{FACF}}}}^{{{\rm{bulk}}}}\)) of Li⁺, Na⁺ and K⁺ at mid-position (blue area) or edge-position (red area). b FACFs of Na⁺ (simulated with Merz FF) in different solvation environments, bulk solution (green), mid- (red) or edge- (blue) position. These FACFs all oscillate violently in the head part, then smoothly decay to 0 in the tail part. See Supplementary Figs. 15–18 for FACFs of other ions. c Compared with bulk solution, I_head changes slightly (∆I_head = \({I}_{{{\rm{head}}}}^{{{\rm{channel}}}}-{I}_{{{\rm{head}}}}^{{{\rm{bulk}}}}\) ≈ 0), thus I_tail dominates the change of I_FACF (∆I_tail = \({I}_{{{\rm{tail}}}}^{{{\rm{channel}}}}-{I}_{{{\rm{tail}}}}^{{{\rm{bulk}}}}\) ≈ ∆I_FACF). d ∆λ (or ∆I_FACF) correlates with τ_channel/τ_bulk. ∆λ is the difference between ion-water friction coefficient (λ) in nanochannel and that in bulk solution, which equals to ∆I_FACF multiplied by a constant, \(\frac{1}{\gamma {{{\rm{k}}}}_{{{\rm{B}}}}T}\) (see Eq. (4) in “Methods”). The black curve is exponential fitting result. The dash curve represents the quantitative correlation between ∆I_FACF (unit: 10¹⁵ N²·mol^-2 · s) and τ_channel/τ_bulk: \(\Delta {I}_{{{\rm{FACF}}}}=-5.71\bullet \exp (-0.87\bullet \frac{{\tau }_{{{\rm{channel}}}}}{{\tau }_{{{\rm{bulk}}}}})+1.24\) and the shadowed area represents the prediction error. e Exchange of water molecules between the 1^st HS of Na⁺ (simulated with Merz FF) and the surrounding water layers. 100 snapshots of a 1 ns simulation trajectory are superimposed. In each sub-figure, the left one is the side view, while the right is top view. For clarity, only the upper water layer is shown in the top view. When τ is small, water molecules exchange rapidly, while they exchange slowly when τ is large. Source data are provided as a Source Data file.