Fig. 2: Collective reorientation of water molecules driven by cathodic bias.

a Representative snapshot of the cathodic interface. Hydrogen, sodium, and silver atoms are shown in white, magenta, and blue, respectively. Oxygen atoms in the adlayer are color-coded according to their water orientation state (refer to Fig. 2d), while the other oxygen atoms are shown in red. b Local cationic (solid lines) and anionic (dashed lines) charge profiles along the surface normal direction at varying bulk electrolyte concentration (σ = −13.9 μC cm⁻²). c σ-dependent changes in the dielectric constants, ε₁ for the water between electrode and OHL₁, and ε₂ for the water between OHL₁ and OHL₂, obtained by fitting the multilayer capacitor model to the all-atom simulation results. d Populations of water orientation states and their configurations (dilute case). As σ becomes more negative, the populations of the parallel and H-up states decrease, while the population of the H-down state increases. e Potential drops between regions: \({\phi }_{1}\) between electrode and OHL₁, \({\phi }_{2}\) between OHL₁ and OHL₂, and \({\phi }_{3}\) between OHL₂ and the diffuse layer. This partitioning is achieved by fitting the multi-layer capacitor model to the all-atom simulation results. Note that the sum of \({\phi }_{1}\), \({\phi }_{2}\), and \({\phi }_{3}\) corresponds to the total potential drop across the interface, i.e., the electrode potential with respect to the PZC, E − E_PZC.