Fig. 3: High free energy in the HS helps water molecules to escape, resulting in a small τ_channel/τ_bulk.

a Spatial distribution functions (SDFs) for water molecules in the 1st hydration shells (HS) of Li⁺, Na⁺ and K⁺ at the mid- or edge-position in a 2D nanochannel. At the mid-position, Li⁺ and Na⁺ possess sphere-like HSs while the K⁺ HS splits into two rings. At the edge-position, the HSs of all three ions are distorted to rings and poles. b Potential of mean force (PMF) profiles of water molecules around Li⁺, Na⁺ and K⁺ in bulk solution, mid- or edge-position of the 2D nanochannels, simulated with Merz FF. ∆F refers to the free energy difference between the ion HS and the surrounding (e.g. the water layers in nanochannel, or bulk water in the bulk solution), with subscripts ‘R’ and ‘P’ referring to the ring and pole part of HS, respectively. c ln(τ_channel/τ_bulk) correlates linearly with ΔF_channel-ΔF_bulk: \({\mathrm{ln}}\left(\frac{{\tau }_{{{\rm{channel}}}}}{{\tau }_{{{\rm{bulk}}}}}\right)=\frac{-0.00443({\Delta F}_{{{\rm{channel}}}}-{\Delta F}_{{{\rm{bulk}}}})}{{{\rm{R}}}T}+1.265\), where R is the ideal gas constant. Note at ∆F_channel-∆F_bulk ≈ 0, τ_channel/τ_bulk is yet above 1, which can be attributed to the nanoconfinement effect of 2D nanochannels, i.e. the channel walls prevent water molecules from leaving the HS along the channel height direction, thus hindering water molecules to exchange between HS and surrounding solvent in nanochannel⁵². Source data are provided as a Source Data file.